USF Libraries
USF Digital Collections

Form and numbers

MISSING IMAGE

Material Information

Title:
Form and numbers mathematical patterns and ordering elements in design
Physical Description:
Book
Language:
English
Creator:
Thom, Alison Marie
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Mathematics
Proportion
Grid
Architecture
Art
Dissertations, Academic -- Architecture and Community Design -- Masters -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: In America, buildings are often constructed with the intent of being utile only 30-40 years. All over the world though, there are buildings that are hundreds of years old that are still very functional. Historically, architecture was a part of mathematics, and in many periods of the past, the two were indistinguishable. Architects were often required to be also mathematicians in ancient times. The idea of this thesis is to identify the relationship between mathematics and architecture and to reintroduce them in order to create a module for successful design . Presence of mathematical boundaries help to attain visual consistency by relating a small scale to a larger scale. Spaces which meet these criteria are subconsciously realized as sharing critical qualities with natural and biological forms. Accordingly, they are perceived as more comfortable psychologically.Scaling coherence is a common element of traditional and vernacular architectures, but is often extensively deficient from contemporary architecture. Architecture has used proportional systems to create, or limit, the forms in building since its inception. In almost every building tradition, there exists a system of mathematical relations which governs the relationships between elements of design. These are often quite simple: whole number ratios or easily constructed geometric shapes. Many types of revival architecture have been employed in recent years, therefore it would be critical to identify why they have achieved a resurgence in popularity. However, historical allusions are generally superficial. No authentic scale or systems are used and the formerly unique qualities are not explored spatially. The attraction to, and association with, forms possessing harmonic proportions is a mitigating factor in design that needs to be addressed.The natural beauty stemming from proportion, mathematics, and the proper relationship of elements to the whole is what renders a building aesthetically and experientially pleasing to a human. Post-Modern architecture is all but going in the opposite direction of achieving this goal. The idea that a building should scale down to dimensions humans can relate to and reveal its stature in the experiential qualities must be extracted from traditional architecture and employed in contemporary techniques.
Thesis:
Thesis (M.Arch.)--University of South Florida, 2009.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Alison Marie Thom.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 110 pages.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 002029671
oclc - 437035023
usfldc doi - E14-SFE0002969
usfldc handle - e14.2969
System ID:
SFS0027286:00001


This item is only available as the following downloads:


Full Text

PAGE 1

Form and Numbers: Mathematical Patterns and Ordering Elements in Design by Alison Marie Thom of the requirements for the degree of Master of Architecture School of Architecture and Community Design University of South Florida Major Professor: Daniel Powers, M.Arch Rick Rados, B.Arch Stanley Russell, M.Arch Date of Approval: April 10, 2009 Keywords: mathematics, proportion, grid, architecture, art Copyright 2009, Alison Marie Thom

PAGE 2

DEDICATION This thesis is dedicated to my Dad, without whom this idea would never have been born, and this ambition never fostered. Because of you, I never knew limitations, only possibility. This project is proof of your unwavering support materialized.

PAGE 3

ACKNOWLEDGEMENTS I would like to acknowledge all of my friends and family, and anyone who offered me a kind word of encouragement in the last four years. To my professors, I cannot thank you enough for taking the time to talk with me and critique my work. Seeing your passion for architecture and dedication to teaching has enriched me not only as an architect, but as a person. I would especially like to thank Rick Rados and Stanley Russell for bearing with me this past year and making sure I never lost sight of the essence of my project. To Jin Baek and Enrique Larranaga, though our interactions may have been brief I will never forget the insight and human quality you brought to my designs and conceptual thought process. To my friends, Daniel, Katrina, Miguel, Podes, Ricky, Ryan and Torend: there are no words for how grateful I am to you all. There were many times when it was your faith alone that kept me on track and in the studio. To my family, Mom, Philip, James, Grandma Mimi, Meghan and all the Thom/Burge clan: you were my rock. I made it to this point because of your eternal love and support. And to my chair, Dan Powers, I could not have realized this without you there, everyday

PAGE 4

i i TABLE OF CONTENTS LIST OF FIGURES ii iv PROBLEM STATEMENT 3 GOALS + OBJECTIVES 4 RESEARCH: METHODS + FINDINGS SITE SELECTION + ANALYSIS RESEARCH METHODS 5 RESEARCH PAPER CASE STUDY 1 27 CASE STUDY 2 34 MATHEMATICAL CONCEPTS + DIAGRAMS SITE SELECTION 39 SITE ANALYSIS 40 PROGRAMMING + PREDESIGN ANALYSIS 60 ADJACENCY DIAGRAMS 76 SCHEMATIC DESIGN 81 DESIGN DEVELOPMENT CONCLUSION 105 ENDNOTES 108 BIBLIOGRAPHY 109 HISTORICAL RELATIONSHIPS BETWEEN MATHEMATICS + ARCHITECTURE 6 MATHEMATICAL ORDERING SYSTEMS 17 THE FIBONACCI SEQUENCE IN DESIGN PRIMARY RESEARCH PROJECT SELECTION 1 ABSTRACT PLANS 83 ELEVATIONS 91 PERSPECTIVES 93

PAGE 5

ii ii LIST OF FIGURES Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Figure 32 Figure 33 Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Lambda Diagram Phi Ratios Phi Ratios Contd Golden Circle Golden Spiral Rabatment and the Occult Center Villa Stein in Garches Diagram of Golden Section Properties Villa Stein Fibonacci sequence naturally occuring in growth Fibonacci sequence naturally occuring in growth Fibonacci sequence naturally occuring in growth Rabbit breeding over a years time Fibonacci spiral inscribed in rectangle Golden Angle Meier The Hague Grid and Module Atheneum: Sketch of the site geometries 3x3 and 18x18 Module Meier 3x3 Module and 18x18 Module Site axis in line with the freeway and mountain ridge CONTEXT: Downtown Los Angeles grid in relation GEOMETRY: Grids and 22.5 degree angle intersections EXTERIOR SPACES: Placement and proportion derived Rivergate Tower viewed from Kiley Park ampitheatre Diagram of pattern constructed of Fibonacci numbers Photo of Fibonacci pattern on the bank cube Fibonacci rectangle diagram Wolfs application of Fibonacci rectangle Fibonacci ratios present in the river Figure-ground diagram showing correlation to grid View from southeast South/Riverfront view Views from SE Views from SE Views from SE Site dimensions Satellite view of Tampa Heights 18 19 19 20 20 21 22 23 23 24 24 24 25 25 26 27 28 29 30 30 31 32 32 33 34 36 36 37 37 38 38 40 41 42 42 42 46 47 Figure 39 Figure 40 Figure 41 Figure 42 Figure 43 Figure 44 Figure 45 Figure 46 Figure 47 Figure 48 Figure 49 Figure 50 Figure 51 Figure 52 Figure 53 Figure 54 Figure 55 Figure 56 Figure 57 Figure 58 Figure 59 Figure 60 Figure 61 Figure 62 Figure 63 Figure 64 Figure 65 Figure 66 Figure 67 Figure 68 Figure 69 Figure 70 Figure 71 Figure 72 Figure 73 Figure 74 Figure 75 Figure 76 Map of Tampa Heights Macro Location Micro Location Macro analysis of the existing context buildings Micro analysis of the existing context buildings Solar Azimuth Diagram Insolation Chart Clearness Chart Average Precipitation Chart Average # of Wet Days Chart Average Temperature Chart Annual Prevailing Winds Diagram Average Windspeed Chart Map of Tampa Heights Historic District Land Use Diagram Proposed development of Riverwalk and Stetson Hartline diagram courtesy of Ben Hurlbut Site Access Library spatial relationships Library-Circulation spatial relationships Library-Stacks spatial relationships Studio spatial relationships Galleries spatial relationships Media/Presentation spatial relationships Square footage of Building Program Square footage of Building Program Square footage of Building Program Square footage of Building Program Square footage of Building Program Square footage of Building Program Net Square Footages by Usage Administration adjacency diagram Faculty and Adjunct adjacency diagram Media/Presentation Space adjacency diagram Library adjacency diagram Studio adjacency diagram School adjacency diagram Schematic Volume + Section Studies 47 48 49 50 50 51 52 52 53 53 53 54 54 55 56 57 58 59 63 64 65 66 67 68 69 70 71 72 73 74 75 76 76 77 78 79 80 81

PAGE 6

iii iii Figure 77 Figure 78 Figure 79 Figure 80 Figure 81 Figure 82 Figure 83 Figure 84 Figure 85 Figure 86 Figure 87 Figure 88 Figure 89 Figure 90 Figure 91 Figure 92 Figure 93 Figure 94 Figure 95 Figure 96 Figure 97 Figure 98 Figure 99 Figure 100 Figure 101 Figure 102 Figure 103 Figure 104 Figure 105 Figure 106 Figure 107 Figure 108 Concept Diagram: plan, section + elevation overlay Site Plan :: 1=20 Scale Level 2 Plan :: 1=20 Scale Level 3 Plan :: 1=20 Scale Level 4 Plan :: 1=20 Scale Level 5 Plan :: 1=20 Scale Level 6 Plan :: 1=20 Scale Level 7 Plan :: 1=20 Scale Roof Plan :: 1=20 View of the facade when looking east View of the facade when looking south View of the facacde when looking west View of the facade when looking north Gallery Geometries: Elevation Gallery Geometries: Plan Gallery Geometries: Perspective Studio Geometries: Elevation Studio Geometries: Plan Studio Geometries: Perspective Perspective rendering: SW corner, gallery geometries SW gallery framed views Student Gallery geomtries Aerial View from SE Main approach entry at SE corne View of approach from riverwalk Perspective view of Model Gallery, Cafe, Bookstore and Classrooms Studios and circulation core SW Gallery and water feature Fabrication warehouses Classroom volume section 82 83 84 85 86 87 88 89 90 91 91 92 92 93 93 93 94 94 94 95 96 97 98 99 100 101 102 102 103 103 104 104 LIST OF FIGURES

PAGE 7

iv iv FORM + NUMBERS: MATHEMATICAL PATTERNS + ORDERING ELEMENTS IN DESIGN Alison Marie Thom ABSTRACT In America, buildings are often constructed with the intent of being utile only 30-40 years. All over the world though, there are buildings that are hundreds of years old that are still very functional. Historically, architecture was a part of mathematics, and in many periods of the past, the two were indistinguishable. Architects were often required to be also mathematicians in ancient times. The idea of this thesis is to identify the relationship between mathematics and architecture and to reintroduce them in order to create a module for successful design Presence of mathematical boundaries help to attain visual consistency by relating a small scale to a larger scale. Spaces which meet these criteria are subconsciously realized as sharing critical qualities with natural and biological forms. Accordingly, they are perceived as more comfortable psychologically. Scaling coherence is a common element of traditional and vernacular architectures, but is often Architecture has used proportional systems to create, or limit, the forms in building since its inception. ...shapes and proportions in geometry transcend limitations off time and space...geometry describes spatial making space. The essential and most fundamental ordering principles of geometric form eliminate redundancy and -Anne Tyng

PAGE 8

v v In almost every building tradition, there exists a system of mathematical relations which governs the relationships between elements of design. These are often quite simple: whole number ratios or easily constructed geometric shapes. Many types of revival architecture have been employed in recent years, therefore it would be critical to identify why they have achieved a resurgence in popularity. However, scale or systems are used and the formerly unique qualities are not explored spatially. The attraction to, and association with, forms possessing harmonic proportions is a mitigating factor in design that needs to be addressed. The natural beauty stemming from proportion, mathematics, and the proper relationship of elements to the whole is what renders a building aesthetically and experientially pleasing to a human. Post-Modern architecture is all but going in the opposite direction of achieving this goal. The idea that a building should scale down to dimensions humans can relate to and reveal its stature in the experiential qualities must be extracted from traditional architecture and employed in contemporary techniques.

PAGE 9

1 PROJECT SELECTION Art and design is realm of study where mathematics is often overlooked, but has a strong presence. Mathematics and art have a long historical relationship. Painting, drawing and photography are a few examples where mathematical properties are present in the form of perspective, the rule of thirds, and grids. The ancient Egyptians and Greeks knew about the golden ratio, regarded as an aesthetically pleasing ratio, and incorporated it into the design of their monumental buildings including the Great Pyramid, the Parthenon, the Colosseum. The golden ratio is used in the design and layout of paintings such as The Roses of Heliogabalus. Recent studies show that the golden ratio also plays a role in the human perception of beauty in body shapes and faces. The Platonic solids and other polyhedra are a recurring theme in Western art. In Leonardo Da Vincis early writings he echoes the treatises of Italian Mathematician Leone Battista Alberti and artist Piero della Francesca 1 : are transmitted to the eye by pyramidal lines. Those angles in their pyramids according to the different Da Vinci developed mathematical formulas to compute the relationship between the distance from the eye to the object and its size on the intersecting plane; that is the canvas on which the picture will be painted: If you place the intersection one meter from the

PAGE 10

2 intersection; and if it is eight meters from the eye and so on. As the distance doubles so the diminution 2 For these reasons, a building layout with these properties for Art + Design students would be complimentary as they could understand the subtle but critical presence of math in both Art and Architecture. As there is an existing layer of richness from mathematics incorporated into art, adding this concept to the design of the learning environment would enhance the creative process of the students.

PAGE 11

3 PROBLEM STATEMENT The challenge is to design a Graduate School of Art + Design for the University of South Florida. The grids and modules that will be used, are based off of mathematical intersection of spaces and points on the grid will be emphasized. Corners and points of transition have visual presence and hierarchy. Additionally, connection with an Arts District and the local university would be essential for exposure and joint endeavors. Graphicstudio is a university-based atelier engaged in a unique experiment in art and education, committed to research and the application of traditional and new techniques for the production of limited edition prints and sculpture multiples. Graphicstudio with the Contemporary Art Museum and the Public Art Program form the Institute for Research in Art in the College of Visual and Performing Arts at the University of South Florida. (USF 2008). This provides many opportunities for networking and linking with the arts and cultural scene of the greater Tampa Bay area. Finally, being the School of Art + Design, the building should facilitate teaching the students about the composition and placement of form, or even the absence of form. This will inform the students about the of using mathematical ordering properties for spatial organization.

PAGE 12

4 GOALS + OBJECTIVES Taking the element of the bend of the Hillsborough River and the shift of Tampas city grid, embracing the character of a point of intersection or transition; engaging the dynamicity of this nexus point. Use building to inform, with the use of mathematical ordering properties and systems of proportion to organize and plan the project, in a way that the students can respective realms of study. Arts District. Form a connection with the Arts District, through vistas or structural gestures. Use the building to frame the view corridors of the river so as not to isolate the residential neighborhood to the north. Integrate into the urban and suburban fabrics by relating to the grid the site is on and the proximal shifted grid of downtown Create an urban presence, while not alienating the current residential context. Encourage pedestrian engagement on the riverwalk by providing public amenities to be shared with the students and by revealing the works of students throughout the site.

PAGE 13

5 RESEARCH METHODS Research for this document will be conducted using various architectural research methods and a diverse base of sources and media. Architectural research methods employed are Interpretive-Historical, Qualitative, Correlational, and both Precedent and Case Studies. 3 Interpretive Historical research will occur in the form of Causal Explanations of History, studying facts and formulas of mathematics, and Structuralism, identifying the meaning not in the entity itself but in the relationship between entities, mathematics and architecture. Qualitative research encompasses the site and programming analysis, the collection and then interpretation of the data from a contemporary setting. Correlational research is used to explore the mathematical patterns occurring in nature, the measurement of existing structures and the subsequent ratios and proportions building type and to identify advantages and disadvantages of already proposed design solutions. The Case Studies will be the investigation of existing buildings and exploring if they possess these mathematical properties, and if so how they are enriched by them. The research will be conducted in the library, on the internet, at the site, at the Nexus 2008 Relationships in Mathematics and Architecture Conference, and through personal contact with scholars and professionals. The media will be books, periodicals, electronic journals, websites, on-site observations and photos, diagrams, email correspondence, phone interviews, and lectures. This wide-ranging collection of methods and materials will insure an unbiased and thorough research base for the project.

PAGE 14

6 The link between mathematics and architecture is often understated but always powerful. There are the obvious uses of mathematics in construction and dimensioning, however, the subtle presence of mathematics Though many see mathematics and art at opposite ends of the spectrum, in ancient times architecture was considered a mathematical topic and the disciplines have, up to the present time, retained close connections. Conceivably, once one realizes that mathematics is essentially the study of patterns, its connection with architecture becomes clearer. Mathematics is not only about formulas and logic, but about patterns, symmetry, structure, shape, and beauty. Such sequences and patterns are found everywhere in nature. Many buildings of traditional architecture employed these, and they are still being inhabited and used today. Thus, historically the connection between mathematics and the arts has been understood by humans, if only subconsciously. The challenge, then, is to identify systems of proportions and mathematical relationships that render spaces aesthetically pleasing and balanced to a person; then to create a contemporary building type incorporating of building. Architecture has used proportional systems to create, or limit, the forms in building since its inception. In almost every building tradition, there exists a system of mathematical relations which governs the relationships between elements of design. (Licklider 1965, 30) These are often quite simple: whole number ratios or easily constructed RESEARCH PAPER: HISTORIC RELATIONSHIPS BETWEEN MATHEMATICS + ARCHITECTURE

PAGE 15

7 geometric shapes. Many types of revival architecture have been employed in recent years, i.e. Gothic, Mediterranean, therefore it would be critical to identify why they achieved resurgence in popularity. The apparent incoherence of modern architecture leads one to believe that in nature there must be some correlating principle, establishing limits for the designer. Jay Hambidge, an American artist who conceived the idea that the study of arithmetic with the aid of geometrical designs was the foundation of the proportion and symmetry in Greek architecture, sculpture and ceramics, also formulated the theory of dynamic symmetry as demonstrated in his works Dynamic Symmetry: The Greek Vase (1920) and the Elements of Dynamic Symmetry (1926). In his studies of the aforementioned, Hambidge determined two types of proportion or symmetry, one of which possessed qualities of activity, the other of passivity. The static is found in 1920, 7) A study of the basis of design in art shows that this active symmetry was known to primarily two peoples, the Egyptians and the Greeks; the latter only having developed its full possibilities for purposes of art. (Sagdic 2000, 125) Through study of natural form and shapes in Greek and Egyptian art, this principle for the proportioning of areas has been reclaimed in architectural language. 2. Measurement The basis for proportion is size, so to develop a greater understanding of dimensional relationships we must recognize the systems which we use to represent this data. However objective it may seem, measurement is a system wrought with human experience and culture. Structures of measurements are highly symbolic. Historically, canonization of the bodies of leaders and gods were often the foundation historical society to another, the articulated parts of the

PAGE 16

8 2002, 63) When the notion of the perfect body was not the basis of a nations linear measures, easily tradable and taxable items in the region, often cereal grain, were used as standards. Invariably, however, these related back to the proportions of a perfect body. In Western society, a natural quality cannot be comprehended until it can be judged against the measurable. It is certain that Western culture would have scale of measures in which the (a days march for an army) variously equals 16 or 30 or 40 li and is also equal to eight krsas (keu-lu-she) : For cases such as this, measures are generally rationalized in relation to a single coherent form and nothing is more readily accessible in daily experience than the human body and its constituent parts. (Tavernor 2002, 68) Since Greek antiquity, it has been generally accepted in Western societies that a quality in nature cannot be appreciated until it has been measured, or can be compared with something that is measurable. The Greeks also realized that qualities could be described through a medium other than words, that is, through numbers. Their numbers were more than quantities, for they represented qualities too. numbers, such as 6 and 10. He considered these integers to be perfect numbers, because they can be regarded as the sum of their parts: 6 is the sum of 1+2+3; and 10 the sum of 1+2+3+4. Consequently, Plato took these

PAGE 17

9 numbers and used them to describe the natural harmony that existed in the world and universe. (Tavernor 2002, 68) Using the Pythagoreo-Platonic System a Greek sculptor, Polykleitos, created a sculpture of a man that was the visual manifestation of these perfect dimensions, in that its parts had a harmonious relationship to the whole. (Padovan 2002, 47) Here lies the inception of the the canon for perfect proportions. The system of weights and measures used in the ancient Greek world was motivated in its creation by an amalgamation of philosophy, mathematics and art. Marcus Pollio Vitruvius, the Roman architect working and writing stated what was most certainly agreed upon widely, that the human proportions of the Greek canon. (Vitruvius 1914, III.I) As the numbers of these proportions were derived from Pythagoras and Platos numerical summation of the universe, Vitruvius was aware that the measuring units he and the perfect number relations between them are a combination derived from the measures of the universe and of the idealized body of man. As a result, body, architecture and the natural world were in perfect harmony, and the body of man was regarded as a symbolic manifestation encompassing the harmonious universe. In recent centuries, measurement systems have lost any connection to the human experience, everyday life, art or symbolism. lThere is no evident reference to human form or these universal harmonies. The seemingly rational system of calibrated measurements to a disconnected object, such as the meter rod, is almost as irrational as meter has evolved into the standard of measure without relation to the corporeal form or the human condition. the conception of numbers, measurement and mathematics

PAGE 18

10 of ancient cultures. 3. Mathematics in Architecture architecture is that of Pythagoras. For the Pythagoreans, belief that all things are numbers clearly had great an impractical idea, but, in fact, it was based on some fundamental truths. Pythagoras saw the connection between music and numbers and clearly understood how the note produced by a string related to its length. He established the ratios of the sequence of notes in a scale still used in Western music. By conducting experiments with a stretched string, determined by small integers. The discovery that beautiful harmonious sounds depended on ratios of small integers led architects to designing buildings using ratios of small integers. This resulted in a module, a basic unit of length for the building, where the dimensions were now small integer multiples of the basic length. Numbers for Pythagoras also had geometrical properties. Geometry was the study of shapes and shapes were determined by numbers. More importantly, the Pythagoreans developed a notion of aesthetics based on proportion. In addition, geometrical regularity expressed beauty and harmony and was applied to architecture with the use of symmetry. However, to a mathematician today, symmetry suggests an underlying action of a group on a basic word comes from the ancient Greek architectural term symmetria which indicated the repetition of shapes and ratios from the smallest parts of a building to the whole are numbers meant to the Pythagoreans and how this was

PAGE 19

11 Static symmetry, as mentioned previously, exists as patterns and shapes found in nature. Dynamic symmetry is more subtle and more vital than static symmetry and is predominantly the form to be employed by the artist, architect and craftsman. The principles of this method for proportioning spaces are obviously more appropriate when taking into consideration movement and experiential qualities. the Egyptians pyramid and temple buildings, originated around three or four thousand B.C. There method of surveying and marking off an orthogonal plot of land involved two men and a rope which was marked off into twelve units to which allowed for the creation of a right triangle of side lengths 3, 4 and 5: the Pythagorean triad. (Hambidge 1920, 152) However, not until centuries later, did the Greeks discover this from studying the Egyptian constructs. This method was used for the plan, then rotated up for the elevations, and used for generally all design and ornament. It allowed artists and architects control over proportions, spatial dimensions, and pictorial composition that was unprecedented. Unfortunately, the Euclidean development of this practical geometry, which was one of pure mathematics, lost all artistic and human application. 3. Limits of Nature The patterns and proportional systems found in nature lay a framework of order that allows for exponential variety of shapes and designs. In The Power of Limits, Doczi uses the term dinergy when speaking of the patterns evident in nature. Dinergyreferstotheworkingofoppositesunited Dinergy refers to the working of opposites united in a harmonious proportion. Dinergyismadeupoftwo Dinergy is made up of two Greek words: dia (across, through, opposite) and energy . (Doczi 1981, 27) An example is the working of the minor and major parts of the golden proportion. Inmathematics In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the

PAGE 20

12 smaller. The golden ratio is approximately 1.6180339887. This word was invented to refer to the creating process the method for generating patterns and modules found in nature. 4 .HumanProportion Human Proportion When discussing proportion, especially human proportion, in architecture the name that most often comes to mind is Vitruvius. The aesthetics of proportion are most clearly addressed in Book III, where he gives the Vitruvius says that the proportions of a temple ought to be to describe in some detail. Often it is assumed that the its natural proportions. Advocates of different systems of proportion have argued that Vitruvius was quite right about this, but that nature happens to have designed the human when the body is viewed as a vivid diagram, familiar to all, but on the actual proportions of it. These proportions help to understand the relationship as they express the size of the parts in terms of a whole. 5. Aesthetics of Proportion Proportion is found in bringing together the various constituent parts with the whole, when symmetry is also present. The aesthetic aspect of proportion is one intuitive approach, where the proportions of an object are and error. In architecture this process may extend over forms or the selection of the most admired proportions from nature. Both cases involve the eyes desire for, what Sir Christopher Wren refers to as, customary beauty, the traditional or life-like, and its simultaneous desire for

PAGE 21

13 natural beauty, the harmony of proportion achieved in such a manner that nothing could be added or taken away Proportion at various scales is most easily achieved by use of a module. Though the module itself may have no the comparative sizes of an object and its parts, without giving us the proportions of an order in terms of a module, Though aesthetics is most often perceived as a subjective quality, there are, in fact, methods for evaluating the level of aesthetical pleasure an object invokes. The secret of this universal aesthetic pleasure in beautiful forms lies in mathematics, reveals Harvard math professor, Dr. George D. Birkhoff. He has worked out a mathematical formula from which he can obtain the aesthetic value of a shape or form, and this mathematical expression of the beauty of an object conforms to the emotional judgment of those who look upon it. Therefore this qualitative element other data and empirical research. 6. Examples in Architecture One of the most important ideals of classical architecture is that the part relates to the whole, at all relationship is between component parts and the module of one-half the diameter at the lower third of the column shaft. The proportions used to generate the orders are derived from relationships found commonly in the human body and elsewhere in nature, such as the spiral of a Nautilus shell and in the distribution and proportions by which leaves diminish in size on a fern bush stem. These relationships are latent, but are easily visible upon closer study. (Doczi 47) One of the elemental characteristics of classical design is the tri-partition of the language at all scales. There

PAGE 22

14 is a bottom, middle, top; beginning, middle, end. Each order of columns, the basis for classical post and lintel design, consists of a pedestal, a column, and an entablature. In turn, pedestals consist of a plinth at the bottom, a dado in the middle, and a cornice at the top. A column has a base, a shaft, and a capital. The entablature has an architrave, a frieze, and a cornice. These can, in most cases, be reduced even further into three parts. The relationships delineated by the Orders are merely guidelines for the designer, offering base information from which individual design can begin. The beginning of the twentieth century saw the heightened use of Euclidean or Cartesian rectilinear geometry in Modern Architecture. In the De Stijl movement constituting the universal. The architectural form therefore is constituted from the juxtaposition of these two directional tendencies, employing elements such as roof planes, wall planes and balconies, either sliding past or intersecting each other. The Rietveld Schrder House by Gerrit Rietveld is an example of this approach. Many of the latest attempts at incorporating natural proportions have been misconstrued or unsuccessful and led to the abandonment of these principles. The presence of these geometries and proportions from ancient to contemporary buildings is theory is essential. 7. Existing Problems In recent decades, historical revival styles have gained enormous popularity in residential and civic building design. Mediterranean, Greek and Gothic are just a few of those found in abundance from the cities to the suburbs. a columnar faade and an arcade. No historic construction or design methodology is used and the qualities are not explored spatially. The facades are usually out of scale, so

PAGE 23

15 It is not that these proportions are unknown, its that there full potential is not employed. Fibonacci sequences and patterns are used in elevation and to create ornament, but again not on a broader level that can be experienced by the inhabitant. Le Corbusier attempted to incorporate harmonious measurements and human proportion into architecture; however it was criticized as not having a direct correlation to anthropometric observations and not Architecture has always tried to achieve ends that not only relate to function, but also to aesthetics, philosophy, and meaning. And in many a case, the means to this end has been the beauty and structure of mathematics. 8. Research Methods and Goals At this juncture, the goal for this project is to design a public building that is based on mathematical patterns, algorithms and proportions found in nature. The symmetries and patterns will be used to generate all facets of the building: plan, section, elevation. This means that any height; corridor widths and ceiling heights; lighting position and aperture size; and stairs or walkways will all be based on for the certain scale. Additionally, the circulation both within and around the structure will be subject to these guidelines to achieve an inherently pleasing experiential condition for a person, regardless of program. The challenge will be to create a comprehensively designed space, verging on a or total work of art, that can also easily accommodate a variety of uses. The intent is to create a space and a module for construction that is site accommodate future uses. Possible future programs will be suggested and how the buildings initial design facilitates the easy transition as well. The architectural research methods most suitable for the development of this thesis project will be correlational

PAGE 24

16 research and case studies. Exploring traditional architecture still in use and identifying the presence of these patterns and ratios will establish the framework for aesthetically pleasing form. These elements will be used to generate design. Conducting surveys of both those with and without architectural background of their responses to certain Additionally, attending a conference on mathematics in architecture will provide information on both historical and modern applications to be employed. The intent is to focus on the aesthetics and functionality of the space which will be most successfully achieved with a balance of precedent and primary research.

PAGE 25

17 Ratio and proportion may seem like common terms which we use everyday, however, their mathematical they are commonly interchanged mistakenly and misused. Ratio (logos) is the relationship of one number to another, for instance 4:8 (4 is to 8). However, proportion (analogia) is a repeating ratio that typically involves four terms, so 4:8 :: 5:10 (4 is to 8 is as 5 is to 10). The Pythaogreans called this a four-termed discontinuous proportion. The invariant ratio is 1:2, repeated in both 4:8 and 5:10. Plato holds continuous geometric proportion to be the most profound cosmic bond. In his Timaeus the world soul binds together, into one harmonic resonance, the intelligible world of forms (including pure mathematics) above, and the visible world of material objects below, MATHEMATICS: RATIO + PROPORTION RATIO : between two numbers a and b Ratio between a and b a : b or a/b Inverse ratio b : a or b/a MEAN : b, between a and c Arithmetic Mean b of a and c Harmonic Mean b of a and c Geometric Mean b of a and c PROPORTION : between two ratios Discontinuous (4 termed) Continuous a:b :: c:d a:b :: b:c => a : b : c e.g., 4:8 :: 5:10 note: b is the invariant ratio 1:2 geom. mean of a and c through the 1, 2, 4, 8 and 1, 3, 9, 27 series. This results in the extended continuous geometric proportions, 1:2 :: 2:4 :: 4:8, and 1:3 :: 3:9 :: 9:27 (see Fig.X Lambda Diagram). 2 ca b ca ac b 2 acb /1 2 /1 2 2 ca b ca ac b 2 acb /1 2 /1 2 2 ca b ca ac b 2 acb /1 2 /1 2

PAGE 26

18 Platos World Soul: Extended Continuous Geometric Proportion 1:2 :: 2:4 :: 4:8 1:3 :: 3:9 :: 9:27 invariant ratio 1:2 invariant ratio 1:3 or 1/2 or 1/3 So why does Plato ask us to make an uneven cut? An even cut would result in a whole:segment ratio of 2:1, and the ratio of the two equal segments would be 1:1. These ratios are not equal, therefore no proportion is present. There is only one way to form a proportion from a simple ratio, and that is through the golden section. Plato wants one to discover a special ratio such that the whole to the longer equals the longer to the shorter. He knows this would result in his favorite bond of nature, a continuous geometric proportion. The inverse also applies, the shorter to the longer equals the longer to the whole. PLATOS DIVIDED LINE 2 ca b ca ac b 2 acb /1 2 /1 2 2 ca b ca ac b 2 acb /1 2 /1 2 2 ca b ca ac b 2 acb /1 2 /1 2 2 ca b ca ac b 2 acb /1 2 /1 2 2 ca b ca ac b 2 acb /1 2 /1 2 2 ca b ca ac b 2 acb /1 2 /1 2 2 ca b ca ac b 2 acb /1 2 /1 2 The reason he uses a line instead of just numbers, is that Plato realized that the answer is an irrational number that can be geometrically derived in a line but cannot be expressed as a simple fraction. Solving this problem mathematically, and assuming golden value of 1.6180339...(for the whole), and the lesser golden value of 0.6180339...(for the shorter). These are referred to as ___ fye the Greater and ___ fee the lesser respectively. Notice the both their product and their difference is Unity. Furthermore, the square of the Greater is 2.6180339, + 1. Notice also that each is the others reciprocal, so that is 1/ To avoid confusion, they will generally be referred to as The Greater, meaning ___ the mean as Unity (1), and the Lesser being 1/ ___

PAGE 27

19 PHI ON THE PLANE Moving from the one-dimensional line onto the twodiscover. Starting with a square, and arc centered on the midpoint of its base swung down from an upper corner Importantly, the small rectangle which we have added to the square is also a golden rectangle. Continuing this technique creates a pair of these smaller golden rectangles. Conversely, removing a square from a golden rectangle leaves a smaller golden rectangle, and this process can Figure X: Golden triangle). Figure 3 Figure 2: Phi Ratios

PAGE 28

20 MATHEMATICS: GOLDEN SECTION to follow through history. Despite its use in ancient Egypt in extreme and mean ratio. The earliest known published essay works on the subject is by Luca Pacioli [1445-1517 described by Leonardo Da Vinci, as the monk drunk on beauty. Da Vinci according to tradition having created the term sectio aurea or golden section. Figure : Golden Spiral Figure 4 : Golden Circle

PAGE 29

21 So why has the golden section retained its lure throughout the centuries? One of the eternal questions asked by philosophers concerns how the One becomes Many. What is the nature of separation, or division? IS there a way in which parts can retain a meaningful relationship to the whole? Posing this question in allegorical terms, Plato in The Republic asks the reader to take a line and divide it unevenly. Under a pythagorean oath of silence not to reveal the secrets of the mysteries, Plato posed questions in hopes of provoking an insightful response. This line begins to lead us to the golden section. rabatment :: to take the short side of the rectangle and make a square out of it The side of the square is a strong component to include in a composition. The viewers eye senses the structure and feels a sense of harmony. This is called the rabatment of the rectangle. occult center :: literally hidden from the eye, not necessarily having any paranormal references. The occult spiral. Figure 6 : Rabatment and the Occult Center

PAGE 30

22 LE CORBUSIER Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion. He saw this system as a continuation of the long tradition of Vitruvius, Leonardo da Vincis Vitruvian Man, the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture. In addition to the golden ratio, Le Corbusier based the system on human measurements, Fibonacci numbers, and the double unit. He took da Vincis suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human bodys height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modulor system. Le Corbusiers 1927 Villa Stein in Garches, France rectangular ground plan, elevation, and inner structure all closely approximate golden rectangles. Le Corbusier placed systems of harmony and proportion at the centre of his design philosophy, and his faith in the mathematical order of the universe was closely bound to golden section and Fibonacci the series, which he described as: ... rhythms apparent to the eye and clear in their Figure : Villa Stein in Garches

PAGE 31

23 the learned. Figure : Diagram of Golden Section Properties, Villa Stein.

PAGE 32

24 Nature widely expresses the golden section through a very simple series of whole numbers. The astounding Fibonacci series: 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377. ..is both additive, as each number is the sum of the previous two, and multiplicative, as each number approximates the previous number multiplied by the golden section. The ratio becomes more accurate as the numbers increase. Inversely, any number divided by its smaller neighbor approximates Phi, alternating as more or less than ___ forever closing in on the divine limit. Each Fibonacci number is the approximate geometric mean of its two adjacent numbers, appears to have been known to the ancient Egyptians and Greeks. Ultimately Eduoard Lucas in the 19th century named the series after Leonardo da Pisa, who made the series 2 ca b ca ac b 2 acb /1 2 /1 2 MATHEMATICS :: THE FIBONACCI SEQUENCE

PAGE 33

25 famous from his solution of a problem regarding breeding of rabbits over a years time, see diagram in Figure X. The solution being directly related to the Fibonacci sequence. Fibonacci numbers occur in the family trees of bees, stock market patterns, hurricane clouds, self-organizing DNA nucleotides, and in chemistry. A turtle has 13 horn plates on its shell, 5 centered, 8 on the edges, 5 paw pins, and 34 backbone segments. There are 144 vertebrae in a Gabon Snake, a hyena has 34 teeth and a dolphin 233. Many spiders have 5 pairs of extremities, 5 parts to each extremity, and a belly divided into 8 segments carried by its 8 legs. Emerging as a science in the 19th century, Figure : Fibonacci spiral inscribed in rectangle 1 1 2 3 5 8 13

PAGE 34

26 phyllotaxis has been extended to the spiral patterns of pine cones, cacti aereoles, and other patterns exhibited in plants, as seen in Figures X, X, + X In the 15th century, Da Vinci observed that the spacing of leaces was often spiral in arrangement. Kepler [1571-1630] later noted the majority occur in leaf arrangement. Figure : Golden Angle

PAGE 35

27 ABSTRACT CASE STUDY 1 :: MATHEMATICAL ORDERING SYSTEMS HYPOTHESIS The works of architect Richard Meier, though varied on the surface, possess inherent similarities in the underlying design order by the way they are sited and integrated into the context by use of mathematical ordering that form will follow the process of site analysis and laying down this framework. This use of grid and modules for site planning creates a sensitive relationship to the context on both macro and micro levels. The grid and module are mathematical ordering properties which are used in many facets of the design process. This case study will look at the projects of different programs and their use of the grid and/or module and how it is used to strengthen the relationship to the site and to generate form in their respective designs. METHODOLOGY strategies will be used to gain an understanding of how the grid and module were employed in site integration and if, indeed, they were they basis for form generation.

PAGE 36

28 ANALYSIS To best understand the employment of these mathematical ordering properties of grid and module it is in the 2006 Unabridged Dictionary: ::a rectangular system of coordinates used in locating the principal elements of a plan ::a basic system of reference lines for a region, generally consisting of straight lines intersecting at right angles. ::a standard or unit for measuring ::the dimensions of a structural component used as a unit of measurement or standard for determining the proportions of the rest of the construction ::a standardized, often interchangeable component of a system or construction that is grid (X,Y) module (X,Y,Z)

PAGE 37

29 Richard Meier, 1990 LeCorbusiers ideologies, Richard Meier employs a primarily rationalist style, using mostly white to emphasize the geometrical forms (Futugawa 23). His method of using Richard Meier, his grids are not always orthogonal. As in the case of the Atheneum, a visitor center found in New Harmony, Indiana, Meier said the organizing grids could have been even diagonal. The grids begin to shift and overlap to inform the user of the buildings organization. The use of this ordering system allowed for the grid of the town nearby and the river to be addressed in the orientation and layout of the building and in the way one moves through the spaces when looking at the exhibits (Futagawa 24). While the building is very sculptural it remains very systematized and navigable. The relationships of each faade to the condition materiality and the way you move through that wall. The building expresses itself through the differences amongst its exterior walls, as one can begin to see in Meiers preliminary sketch of the site in Figure 2. The river side Wabash River banks nearby. The town side, which also has the entry, is more open and inviting. This allows one to understand that this is the point of transition to enter. On

PAGE 38

30 the forest side the building closes up more at the edge. Each particular place is dealt with sensitively. Meier asserts that the Atheneum is a good example of user perception of how the shifting of grids creates a buildings organization and generates form (Futugawa 26). The Getty Center in Los Angeles, California, is an example of Meiers use of the grid and geometries to bring a large project together cohesively and relate it to a site. The strongest visual example of the grid and module is evident throughout the site and expressed in every material used. There is a 3x3 module for the materials, which is employed for the faades and is used in multiples for all of the materials and modular pavers. The grids of both plan and elevation are aligned so that all control joints meet at the same points. In Figure 4, one could count from the picture that the square window has a 3x3 dimension as the travertine cladding has an 18x18 dimension here, therefore the linear window must also have a height of 18 and we can

PAGE 39

31 know that its length will be some whole number multiple of 18. In Figure 5, the ribbon windows are 18 squares and meet the 18 travertine cladding, while the skylights are 3x3. Here you can see that even Meiers intangible building material, light, conforms to the grid in the shadow it makes on the wall and beam in a 3 x 3 fashion. The complex is aligned on two natural ridges on the site which intersect at a 22.5 degree angle. One lines up with the street grid off Los Angeles and the second, with the swing of the San Diego Freeway as it turns north. The master plan for the project responds to this natural topography and the sites orientation within the urban fabric of Los Angeles. The whole complex is organized on an orthogonal grid aligned with one of these two ridgelines. The public functions such as the museum and galleries happen on one axis, while the private sectors of align with the other datum on the more private, western side of the site. The Research Institute faces towards the ocean and mimics the costal edge in the facade of the museum.

PAGE 40

32

PAGE 41

33 Figure 24: EXTERIOR SPACES: Placement and proportion CONCLUSION The analysis, diagrams, and photographs constitute enough evidence of the grid and module, the presence of mathematical ordering properties and a strong visual and contextual link to the site. This case study has proven that these are design tools which can assist in large comprehensive projects to relate to the site and generate aesthetically pleasing forms. This theory will again need to be tested when applied to the scale and type of this thesis project in the context of downtown tampa. Meiers intent with these geometries is made more evident through a series of sketches he did for the project illustrating the various applications of the grid and regulating lines as can be seen in Figures 22-24

PAGE 42

34 CASE STUDY 2 :: THE FIBONACCI SEQUENCE IN DESIGN ABSTRACT HYPOTHESIS Complexity and richness can be accomplished without ornamentation, through the incorporation of geometries and dimensions based on the Fibonacci sequence. The Fibonacci sequence is an approximation of the golden section used to bring organization and visual harmony to a pattern or design. This study will investigate the use of these geometries and determine if and how it is used to add layers of meaning and complexity to the Rivergate Tower in Tampa, Florida. METHODOLOGY Analysis of plans and diagrams and primary research of samples of design theory, via e-mail correspondence and by phone with the architect, will be used to discern how the Fibonacci sequence was used to add a level of richness to the building

PAGE 43

35 ANALYSIS In an age where each city looks more like every other city and mans alienation from nature mounts daily, this project represents a resistance. Designed to draw in the curious, its structure invokes complex mathematics. The Rivergate Tower represents a lighthouse, guarding the entrance to the city. Two beams of light shoot from the roof into the night sky, amplifying the lighthouse effect. A notch at the buildings top represents a locking into the city grid, and the adjacent cubes mimic city blocks. Every aspect of its design is linked to the ancient mathematical series, the Fibonacci Sequence. qualities of Tampa, sought to understand, respect, singular to this city, to this place and to this time. Architect Harry Wolf, hired in the 1980s to create a home for NCNB Bank, wanted the tower to be viewed as a grand entryway into the city on the river. With the understanding that there would always be a taller building added to the skyline in the future, he wanted the building to be distinct. Something special, connected to its space. The two cubes were designed to mimic an urban grid and its harsh edges. The buildings limestone exterior is a material natural to Florida. The cylinder is linked to the urban grid approximate the height of the base of the building of lighthouse or citadel guarding to the entrance to

PAGE 44

36 Figure 26: Diagram of pattern constructed from the rabatment grid of Fibonacci numbers Through the use of geometric, number, proportion and material there is an aspiration to connect this building to time, place and culture. Needing a way to organize his design, Wolf chose the Fibonacci sequence. As a result, the buildings exterior the cubes are a geometric pattern based on the sequence.

PAGE 45

37 He chose the Fibonacci number series to bring a sense of elegant organization to its design. Wolf also paid attention to the calendar, placing 365 paving stones around the markings represent days and months. The idea is to make the building both simple and rich at the same time, Wolf said. Its intended to be a book you read on many levels. It is the coincidental geometry of the river, as shown in Figure X as it intersects the grid of the city that is the anchoring element to link together land and built-form. The precedence of the Islamic geometry in the Moorish traditions of Florida give insight into the division of the geometry, as well as the geometric veil that is stretched over the entire site. Grass, pavement, water and trees are interlaced to the onion-domed, University of Tampa across the river. geometric order, to inform and suffuse the building-

PAGE 46

38 to generate grid applied in plan and section of meaning. At each state of proximity, through modulation of scale, proportion and detail, the design seeks to re-establish the importance of the Wolf won at least three major design awards for the building. He said he hopes his design evokes the curiosity of those who pass by. It looks like no other building there or anywhere else, Wolf said. And if theyre curious, maybe theyll go inside and see the wonderful thing. s CONCLUSION This building clearly is a successful design, bother formally and functionally and that is achieved in large part due to the layer of mathematics employed in its planning and design.

PAGE 47

39 SITE SELECTION The most important needs in the site of the Graduate School of Art + Design are location and views. Primary goals would be proximity to the Tampa Arts District for opportunity to engage in joint exhibitions and allow for off-campus research and experience. An urban location would facilitate ease of transportation, using non-vehicular and mass transit options. Also the ability to walk to off-campus and art and culture destinations. Additionally, an urban location would support the goal of involving the public in exhibitions and events at the school and allow for the multi-story zoning. A location close to the park would make the public involvement easier as well as provide the students additional outdoor space to research and gain inspiration.

PAGE 48

40 SITE ANALYSIS :: GENERAL Macro location Latitude: +27.94722 (275649.992N) Longitude: -82.45861 (822730.996W) Time zone: UTC -5 hours Country: Florida, United States Continent: Americas Sub-region: Northern America Altitude: ~10 ft Micro location Tampa Armature Works 1910 N. Ola Ave, Tampa 33602 Neighborhood: Tampa Heights SITE DOCUMENTATION The intent of this thesis is to design a building and plan a site that has a strong connection to the context by means of regulating lines and connection to context and grids; and achieves form through the geometries of analysis and mathematical ordering properties such as the grid and module. The proposed building type is an Urban School of Art + Design, at the graduate level.

PAGE 49

41 SITE ANALYSIS :: GENERAL Climate Temperature: moderate, 59-79; ideal for outdoor studio and display spaces Precipitation: moderate Solar Orientation: southern Zoning and Uses: The south side of Tampa Heights is centrally located within the city and very accessible a larger market than the immediate neighborhood, in

PAGE 50

42 SITE ANALYSIS :: GENERAL combination with the accessible Hillsborough River afford the community some very good opportunities. Florida Avenue is a bustling business area, in part, because the city has made it an impact fee free zone from Columbus to Martin Luther King, Jr. Blvd. The mixed use development projects proposed in 2001 for South Tampa Heights have now been built and there is now a pleasant waterfront character to the community that everyone can enjoy for living, working, parks, waterfront access and marinas. Tampa Heights is now part of the Citys trolley system and there is easy access for us to all of the business and entertainment facilities in downtown Tampa and portions of Tampa and Florida Avenues have been transformed into two-way pedestrian friendly streets.

PAGE 51

43 Space for studio views to downtown and of riverfront. Sound Sources Positive: Sounds of nature, water, and people are pleasing. construction is not desirable and would need to be screened or avoided. Access Public Transportation: The accessible bus routes and proximity of the Marion Transit Center would provide adequate access. Bicycle access: This is quite important for students, bike lanes are present on both major veins accesing the site. Pedestrian Access: This is the most important method of access, new sidewalks would need to be layed from Tampa St. to the site. Vehicular: This would be the facultys main transit method, it is very important and there is adequate access present. Views warehouses, library reading areas and entry spaces, bookstore, caf, and sculpture garden would all provide engaging views to pedestrians and students alike. Positive Out: Surrounding natural conditions, the skyline, proximal historic Tampa neighborhood are desirable views for students and faculty.

PAGE 52

44 Negative In: These would be the service functions and possibly classrooms. Negative Out: The interstate, power substations, and parking structures/lots would be views that would not be desirable and would be screened. Landscape Tree Cover: necessary for shade so as to be able to work outside for larger portions of the school year. Landscaping: also necessary to provide privacy for students and screen negative views and sound sources. C. With renovated housing, transit and interstate access, this site and its surrounding area are well positioned to become a community cornerstone and a major gateway to Downtown Tampa. This site with it proximity to the downtown grid, Tampa Museum of Art, Tampa University and Blake Arts High School is optimal. Additionally, the proposed riverwalk gives the opportunity for increased community interest in facility and joint exhibition and events. It is positioned on the river at the bend with view corridors down the river in two directions and of the downtown skyline. The climate of Tampa is moderate year round, with a 72 degree average temperature and southern sun. The activity and noise immediately around the site is mostly positive: Blake

PAGE 53

45 Arts High School, the river, Tampa Water Works Park. The interstate noise is the closest negative and is relatively far enough away. By positioning the project at the corner of the site and opening out to river will maximize possibility for dynamic intersecting and radial regulating lines, a street corner presence, and opening view corridors out to the river, city and eventually the riverwalk.

PAGE 54

46 SITE ANALYSIS :: GENERAL BOUNDARIES AREA 2815 PERIMETER 306984 SQ FT ~7 ACRES

PAGE 55

47 SITE ANALYSIS :: GENERAL W M A R T I N L U T H E R K I N G B L V D I 2 7 5 N B O U L E V A R D I 2 7 5 W V I R G I N I A A V E W I N D I A N A A V E N O L A A V E W P L Y M O U T H S T W A L F R E D S T W C O L U M B U S D R W F R A N C E S A V E W R O S S A V E W P A L M A V E E 7 T H A V E E E S T E L L E S T N M A S S A C H U S E T T S A V E N F L O R I D A A V E N H I G H L A N D A V E N M O R G A N S T N C E N T R A L A V E N T A M P A S T N C E N T R A L A V E E 2 6 T H A V E W O H I O A V E E F L O R I B R A S K A A V E E G L A D Y S S T T A M P A H E I G H T S N e i g h b o r h o o d M a p & B o u n d a r i e s N e i g h b o r h o o d & C o m m u n i t y R e l a t i o n s O f f i c e 1 0 2 E 7 t h A v e n u e T a m p a F L 3 3 6 0 2 L o c a t e d a t t h e H i s t o r i c F r e e L i b r a r y T e l : ( 8 1 3 ) 2 7 4 7 8 3 5 F a x : ( 8 1 3 ) 2 7 4 5 6 9 6 w w w t a m p a g o v n e t / n e i g h b o r h o o d s 8 E M a r t i n L u t h e r K i n g B l v d t o t h e N o r t h I 2 7 5 t o t h e E a s t I 2 7 5 / H i l l s b o r o u g h R i v e r t o t h e S o u t h N B o u l e v a r d t o t h e W e s t TAMPA HEIGHTS NEIGHBORHOOD MAP + BOUNDARIES :: E Martin Luther King Blvd to the North :: I-275 to the East :: I-275/Hilsborough River to the South :: N Boulevard to the West W M A R T I N L U T H E R K I N G B L V D I 2 7 5 N B O U L E V A R D I 2 7 5 W V I R G I N I A A V E W I N D I A N A A V E N O L A A V E W P L Y M O U T H S T W A L F R E D S T W C O L U M B U S D R W F R A N C E S A V E W R O S S A V E W P A L M A V E E 7 T H A V E E E S T E L L E S T N M A S S A C H U S E T T S A V E N F L O R I D A A V E N H I G H L A N D A V E N M O R G A N S T N C E N T R A L A V E N T A M P A S T N C E N T R A L A V E E 2 6 T H A V E W O H I O A V E E F L O R I B R A S K A A V E E G L A D Y S S T T A M P A H E I G H T S N e i g h b o r h o o d M a p & B o u n d a r i e s N e i g h b o r h o o d & C o m m u n i t y R e l a t i o n s O f f i c e 1 0 2 E 7 t h A v e n u e T a m p a F L 3 3 6 0 2 L o c a t e d a t t h e H i s t o r i c F r e e L i b r a r y T e l : ( 8 1 3 ) 2 7 4 7 8 3 5 F a x : ( 8 1 3 ) 2 7 4 5 6 9 6 w w w t a m p a g o v n e t / n e i g h b o r h o o d s 8 E M a r t i n L u t h e r K i n g B l v d t o t h e N o r t h I 2 7 5 t o t h e E a s t I 2 7 5 / H i l l s b o r o u g h R i v e r t o t h e S o u t h N B o u l e v a r d t o t h e W e s t

PAGE 56

48 SITE ANALYSIS :: GENERAL USF School of Fine Arts SITE :: Proposed Graduate School of Art + De sign Tampa Downtown Arts District MACRO LOCATION HILLSBOROUGH AVE. DALE MABRY HWY Tampa Intl. Airport LUTZ TEMPLE TERRACE USF School of Fine Arts SITE :: Proposed Graduate School of Art + Design Tampa Downtown Arts District MACRO LOCATION HILLSBOROUGH AVE. DALE MABRY HWY Tampa Intl. Airport LUTZ TEMPLE TERRACE Historic Seminole Heights

PAGE 57

49 SITE ANALYSIS :: GENERAL SITE 1 2 3 5 4 6 7 8 9 10 Points of Interest within walking distance to the USF Graduate School of Art + Design are: 1 :: Blake Magnet High School for the Visual, Communicative + Performing Arts 2 :: Riverfront Park 3 :: University of Tampa 4 :: Marion Street Transit Center 5 :: Tampa Bay Performing Arts Center 6 :: Tampa Museum of Art 7 :: Historic Tampa Theatre 8 :: Retail + Commerce 9 :: St. Petersburg Times Forum 10 :: Florida Aquarium MICRO LOCATION

PAGE 58

50 SITE ANALYSIS :: GENERAL Figure 42: Macro analysis of the existing context buildings. Figure 43: Micro analysis of the existing context buildings

PAGE 59

51 SITE ANALYSIS :: CLIMATE Natural light is ideal for outdoor painting and photography and for lighting any studio spaces. Tampa has a high number of sunny days throughout the year. This diagram shows the sun path, solar elevation angle and solar azimuth throughout the day and annually for Tampa. July 1 2008 June 21 December 21 Annual variation Equinox (March and September) Sunrise Sunset 00:02 03:05 06:08 09:11 12:14 15:17 18:20 21:23 Figure 44: Solar Azimuth Diagram

PAGE 60

52 SITE ANALYSIS :: CLIMATE Figure 46: Clearness Chart Average Hours of Daylight SUNRISE SUNSETLENGTHCHANGEDAWNDUSKLENGTHCHANGE TODAY 6:5020:22 13:32 6:2420:48 14:24 +1 DAY 6:5120:22 13:31 -00:016:2520:47 14:22 -00:02 +1 WEEK 6:5420:18 13:24 -00:086:2920:43 14:14 -00:10 +2 WEEKS 6:5820:12 13:14 -00:186:3320:37 14:04 -00:20 +1 MONTHS 7:0619:57 12:51 -00:416:4220:21 13:39 -00:45 2 MONTHS 7:2019:22 12:02 -01:306:5719:46 12:49 -01:35 3 MONTHS 7:3718:51 11:14 -02:187:1319:15 12:02 -02:22 6 MONTHS 7:2018:05 10:45 -02:476:5518:30 11:35 -02:49 0 1 2 3 4 5 6 7 kWh/m2/day JANUARYMARCH MAY JULYSEPTEMBERNOVEMBER Insolation :: Average Solar Radiation Intensity Irradiance 0.44 0.46 0.48 0.50 0.52 0.54 0.56 Clearness (0-I) JANUARY APRIL JULY OCTOBER Average Monthly Clearness I= Irradiance Ratio Average Clearness Index Insolation :: Average Solar Radiation Intensity

PAGE 61

53 SITE ANALYSIS :: CLIMATE 2.16 3.05 3.18 1.52 3.18 5.45 7.09 7.30 5.87 2.40 1.80 2.18 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 in JANUARY MARCH MAY JULY SEPTEMBERNOVEMBER Average Monthly Precipitation Precipitation 6.7 6.7 6.3 3.7 6.4 11.8 14.8 16.6 12.0 6.3 5.8 6.3 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 days JANUARY MARCH MAY JULY SEPTEMBERNOVEMBER Average # of Wet Days Monthly Precipitation >0.1mm 59.72 62.19 65.37 68.74 74.52 78.08 79.41 79.14 77.50 72.81 67.35 61.43 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 degrees F JANUARYMARCH MAY JULYSEPTEMBERNOVEMBER Average Temperature Air Temperature

PAGE 62

54 SITE ANALYSIS :: CLIMATE The majority of the months the prevailing winds come from the NNE direction. During May-August winds are primarily east-west. The average windspeeds and waterfront location allow for substantial cooling breezes during most of the year. 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 mph JANUARY MARCH MAY JULY SEPTEMBERNOVEMBER Average Monthly Wind Speed Wind Speed

PAGE 63

55 SITE ANALYSIS :: SURROUNDING INFLUENCES HISTORIC DISTRICT TAMPA HEIGHTS The sites location in a historic district is a positive and revitilization of residential amenities. Several historic properties located nearby give additional close cultural destinations.

PAGE 64

56 SITE ANALYSIS :: SURROUNDING INFLUENCES The immediate context is primarily mediumdensity residential and the waterfront. The frontage along Tampa Street, between Palm Avenue and 7th Avenue is designated Heavy Commercial (HC24).

PAGE 65

57 SITE ANALYSIS :: SURROUNDING INFLUENCES

PAGE 66

58 SITE ANALYSIS :: ACCESS Transportation in the area is ample. The site has easy access by foot and public transportation means. Achieved by means of proximity to: Hartline Transit Hub, the majority of bus lines terminate in downtown and Florida Ave. and Tampa St. are major veins of transit

PAGE 67

59 SITE ANALYSIS :: ACCESS There is also vehicular and water access to the site. Water access would be an integral method for the riverwalk and tourist transportation.

PAGE 68

60 PROGRAMMING + PREDESIGN ANALYSIS the rather than the nature of the design solution. Site Area: 306,984 SF (~7 acres) Building Type: Graduate School Total # of Students: 1200 Total # of Faculty: 60 Total # of Staff: 40 form solely for forms sake. Functionality : The building must function well as a learning establishment and riverwalk terminus. Social : The layout must allow for interaction between students in various studios and interdisciplinary interaction. The faculty needs to have privacy but not be isolated from the studio culture. Cultural : Create a symbolic presence at the corner of the river and at the gateway to the Tampa Arts District. Utilize the existing Tampa Armature Works building, either as a faade or as materials. Temporal : As a type of learning center that is heading towards increased involvement in the technologic world, the building should provide for and plan for future advancements in technology. It should establish permanence of building PRIMARY VALUES Institution : Most important, is to provide security and a learning environment for students, secondarily to provide certain amenities and spaces to the general public. Meaning : To achieve form with purpose, through geometry, patterns and proportional relationships, not

PAGE 69

61 Communication Design lllustration is the art of picture-making for the purpose of communicating ideas and information Graphic Design is total information design, where pictures as well as words are created and designed to convey messages Advertising Art is a more focused combination of visual and verbal information design to create a message that moves consumers to action Fine Art This degree includes: painting + drawing; 3D + ceramics The goal is exploring the complex relationships between form, process, material and content. Photography + Digital Imaging The creative utilization of technology, digital imaging, animation, artist's books, interactive installations, performance and experimental video art. Entertainment Design Computer generated imagery (CGI) and video game design FIELDS OF STUDY internal change and evolution of the curriculum demands. SPECIFIC FACILITY AND EQUIPMENT REQUIREMENTS Printmaking Uses traditional processes (lithography, etching, etc), photo-digital printmaking and poster making. Communication Design Facilities must include proximity to computer labs and studios. Digital Imaging/Media: This would include a media cage which houses departmental photographic and electronic media equipment available for checkout to registered students. In addition to a variety of medium-format and large-format cameras, camcorders, audio recorders and microphones, tripods and lighting equipment, students can also reserve time in private darkrooms, the digital printing service bureau, a private lighting studio and an advanced electronic media lab

PAGE 70

62 production software as well as an array of digital audio production hardware. Fine Art: Studios, gallery space, ceramic, metal and wood shops Entertainment Design: Computer labs and studios. Photography + Film: A 15-station open Macintosh lab; Adobe, Macromedia and other software for digital imaging, sound, animation, web and video production and post-production. Needs a shooting studio with lights and sweeps. Digital cameras, lighting equipment, tripods, and microphones available for checkout Smart Gallery wired and wireless project room to develop and present electronic and interactive sculpture, installation and performance Printmaking Provide print studios that include: etching presses and lithography presses and numerous stones; automated and manual screen presses of various sizes and two graphics darkrooms. General Facilities Library Gallery Media Presentation Space Classrooms Smart Lecture wired and wireless room for mixed media education and presentations Public Program large lecture spaces for community projects and classes Studios General Semi-Private

PAGE 71

63 SPACE LIBRARY FUNCTION housing of book stacks viewing of electronic media research classes place for research and study SPATIAL RELATIONSHIPS ACTIVITY LEVEL VERY HIGH OCCUPANCY 500 AREA 45000SF EQUIPMENT shelves and racks for book/media/periodical storage tables/counters and chairs for study and reading DESIGN CONSIDERATIONS sunlight. Ample archive storage space accessible. Flexible furniture arrangements provided. Smart wired RIVERWALK GALLERY LIBRARY RECEPTION CAFE

PAGE 72

64 SPACE LIBRARY-CIRCULATION DESK FUNCTION service desk where materials are checked out from the library essentially the library hub SPATIAL RELATIONSHIPS ACTIVITY LEVEL VERY HIGH OCCUPANCY 300 AREA 425 SF EQUIPMENT circulation desk with shelving 3 chairs, 4 book trucks 2 circulation terminals, 1 self-check station, 1 printer, security device, telephones DESIGN CONSIDERATIONS Visibility to entry is very important. Ample circulation, to accomodate possible public use as well. CIRCULATION ENTRY MEDIA STOR. WORKROOM/ OFFICES

PAGE 73

65 SPACE LIBRARY-STACKS FUNCTION essentially the library hub ACTIVITY LEVEL VERY HIGH OCCUPANCY 300 AREA Art History + Fine Arts 10000 Photography 5000 Communicative Design 5000 Arts, Humanities, Soc. Sciences 10000 Approx. 400,000 volumes total EQUIPMENT shelves enough for 80% of volumes DESIGN CONSIDERATIONS visibility to entry ample circulation TERRACE STACKS STUDY AREAS READING ROOMS

PAGE 74

66 SPACE STUDIOS FUNCTION the studios are the essence of the school both class time and after-hours work space SPATIAL RELATIONSHIPS ACTIVITY LEVEL VERY HIGH OCCUPANCY 560 AREA 70800SF EQUIPMENT sinks drafting size desk or tables DESIGN CONSIDERATIONS ample daylighting MIN. 12 ceiling height STUDIOS FACULTY WORKROOM ENTRY COMP. LAB

PAGE 75

67 SPACE GALLERIES FUNCTION temporary and semi-permanent displays static work and interactive installations smaller gallery with temporary display would also serve as lobby gallery spaces that can become part of installation displays SPATIAL RELATIONSHIPS ACTIVITY LEVEL VERY HIGH OCCUPANCY LIBRARY RECEPTION SMALL: 65 MAIN: 265 AREA SMALL: 2000SF MAIN: 8000SF EQUIPMENT shelves, racks and cases (all movable) benches DESIGN CONSIDERATIONS direct daylighting desirable in temporary gallery indirect daylighting in main exhibition space good circulation cabling for new media GALLERY GALLERY GALLERY

PAGE 76

68 SPACE DIGITAL MEDIA PRESENTATION SPACE FUNCTION formal and informal presentations for large groups large lecture and seminar classes guest speakers SPATIAL RELATIONSHIPS ACTIVITY LEVEL MEDIUM OCCUPANCY RECEPTION 500 AREA 5000SF EQUIPMENT 500 movable, upholstered seats movable tables large screen computer/video whiteboard light and AV controls DESIGN CONSIDERATIONS no daylighting minimum ceiling height of 25 raised stage PRESENTATION SPACE PRESENTATION RIVERWALK Figure 62: Presentation spatial relationships

PAGE 77

69 School of Art + Design Building Program Site area 239,000 S.F. 5.5 acres Students 1000 Facult y 40 Ad j unct Professors 20 Staff 40 Total 1100 SPACE Mi n. Clg. Ht. NET S.F.QUAN. GROSS S.F. Occu p Load Media Presentation S p ace Seatin g 20'500015000500 Sta g e Area 15'5001500 Sound, Light and Video Systems 100011000 Storage 14'6001600 Total 47100500 Galler y -Exhibition S p ace s Perm. Exhibition Galler y 15'400028000400 Tem p Exhibition Galler y 15'100022000200 Scul p ture Garden 10000110000 Total 520000600 Collections Stora g e Paintin g s 100011000 Scul p ture 100011000 Works of Art 100011000 Pa p er and Photo g ra p h y 8001800 Total 438000 Librar y Stacks-Art Histor y 10000110000100 Stacks-Fine Arts + Photography 1000011000050 Stacks-Communicative 50001500050 Stacks-Arts, Humanities, Soc. Sciences 10000110000100 Di g ital Media 50001500050 Lar g e Print 500150010 Periodicals 30001300030 Reference 1251125 2 Listenin g Stations 251025010 Media Stora g e 5001500 Readin g Room 20510020 Stud y Areas 35120420020 Circulation Desk 4251425 3 Reserved Materials 1001100 Workroom + Office 2501250 6 Lobb y N/A* 1N/A* Terrace 500015000 Total 14954450451 Administration + Offices Rece p tion 4001400 6 Dean's Office 1601160 1 Asst. Dean's Office 1201120 1 Bookkee p in g Office 1501150 1 Conference Room 300130012 Student Services 3001300 6 Student Records 2001200 Dean's Office 1601160 Facult y Offices 10010100010 Ad j unct Work Room 2002400 8 Total 20319045 Classrooms General "smart" lecture room 120067200360 Public p ro g ram room 200024000120 Work Review Room 10004400040 Total 815200480 Com p uter Lab Primar y 300013000150 Secondar y 10001100050

PAGE 78

70 School of Art + Design Building Program Site area 239,000 S.F. 5.5 acres Students 1000 Facult y 40 Ad j unct Professors 20 Staff 40 Total 1100 SPACE Mi n. Clg. Ht. NET S.F.QUAN. GROSS S.F. Occu p Load Media Presentation S p ace Seatin g 20'500015000500 Sta g e Area 15'5001500 Sound, Light and Video Systems 100011000 Storage 14'6001600 Total 47100500 Galler y -Exhibition S p ace s Perm. Exhibition Galler y 15'400028000400 Tem p Exhibition Galler y 15'100022000200 Scul p ture Garden 10000110000 Total 520000600 Collections Stora g e Paintin g s 100011000 Scul p ture 100011000 Works of Art 100011000 Pa p er and Photo g ra p h y 8001800 Total 438000 Librar y Stacks-Art Histor y 10000110000100 Stacks-Fine Arts + Photography 1000011000050 Stacks-Communicative 50001500050 Stacks-Arts, Humanities, Soc. Sciences 10000110000100 Di g ital Media 50001500050 Lar g e Print 500150010 Periodicals 30001300030 Reference 1251125 2 Listenin g Stations 251025010 Media Stora g e 5001500 Readin g Room 20510020 Stud y Areas 35120420020 Circulation Desk 4251425 3 Reserved Materials 1001100 Workroom + Office 2501250 6 Lobb y N/A* 1N/A* Terrace 500015000 Total 14954450451 Administration + Offices Rece p tion 4001400 6 Dean's Office 1601160 1 Asst. Dean's Office 1201120 1 Bookkee p in g Office 1501150 1 Conference Room 300130012 Student Services 3001300 6 Student Records 2001200 Dean's Office 1601160 Facult y Offices 10010100010 Ad j unct Work Room 2002400 8 Total 20319045 Classrooms General "smart" lecture room 120067200360 Public p ro g ram room 200024000120 Work Review Room 10004400040 Total 815200480 Com p uter Lab Primar y 300013000150 Secondar y 10001100050

PAGE 79

71 School of Art + Design Building Program Site area 239,000 S.F. 5.5 acres Students 1000 Facult y 40 Ad j unct Professors 20 Staff 40 Total 1100 SPACE Mi n. Clg. Ht. NET S.F.QUAN. GROSS S.F. Occu p Load Media Presentation S p ace Seatin g 20'500015000500 Sta g e Area 15'5001500 Sound, Light and Video Systems 100011000 Storage 14'6001600 Total 47100500 Galler y -Exhibition S p ace s Perm. Exhibition Galler y 15'400028000400 Tem p Exhibition Galler y 15'100022000200 Scul p ture Garden 10000110000 Total 520000600 Collections Stora g e Paintin g s 100011000 Scul p ture 100011000 Works of Art 100011000 Pa p er and Photo g ra p h y 8001800 Total 438000 Librar y Stacks-Art Histor y 10000110000100 Stacks-Fine Arts + Photography 1000011000050 Stacks-Communicative 50001500050 Stacks-Arts, Humanities, Soc. Sciences 10000110000100 Di g ital Media 50001500050 Lar g e Print 500150010 Periodicals 30001300030 Reference 1251125 2 Listenin g Stations 251025010 Media Stora g e 5001500 Readin g Room 20510020 Stud y Areas 35120420020 Circulation Desk 4251425 3 Reserved Materials 1001100 Workroom + Office 2501250 6 Lobb y N/A* 1N/A* Terrace 500015000 Total 14954450451 Administration + Offices Rece p tion 4001400 6 Dean's Office 1601160 1 Asst. Dean's Office 1201120 1 Bookkee p in g Office 1501150 1 Conference Room 300130012 Student Services 3001300 6 Student Records 2001200 Dean's Office 1601160 Facult y Offices 10010100010 Ad j unct Work Room 2002400 8 Total 20319045 Classrooms General "smart" lecture room 120067200360 Public p ro g ram room 200024000120 Work Review Room 10004400040 Total 815200480 Com p uter Lab Primar y 300013000150 Secondar y 10001100050

PAGE 80

72 School of Art + Design Building Program Site area 239,000 S.F. 5.5 acres Students 1000 Facult y 40 Ad j unct Professors 20 Staff 40 Total 1100 SPACE Mi n. Clg. Ht. NET S.F.QUAN. GROSS S.F. Occu p Load Total 24000200 Studios Communications Desi g n 12'1800814400192 Fine Art 12'1800814400192 Photo g ra p h y + Di g ital Ima g in g 12'15004600080 Printmakin g 12'1800814400192 3D Media/ Scul p ture 15'18002360048 Dedicated Pro j ect Studio 12'18002360048 Total 3256400704 Fabrication/Sho p s Wood/Metal Sho p 15'1000011000050 Ceramics 15'25001250020 Plaster/Fabrics/Plasti c 15'25001250020 Litho g ra p h y /Printin g 25001250020 Lar g e-Scale Installation Construction15'50001500025 Total 522500135 Photo/Film Labs Enlar g er Stations 5050250050 Private Darkrooms 10010100020 Nonsilver darkroom 200120010 Di g ital Scannin g + Printin g Facilit y 500150015 B/W + Color Photo Lab 15001150040 Film Editin g + E q mt. 30001300050 Total 648700185 Di g ital Ima g in g Recording Studio One 14'3601360 8 Control Room 550155014 Isolation Room 80180 1 Studio Two 14'3001300 5 Control Room 450145014 Isolation Room 80180 1 Central Machine Room 80180 Midi Studio 7501750 Director's Studio 1801180 3 Re p air Sho p 1001100 2 Archival Recordin g 2801280 2 Media Ca g e 100011000 Total 12421050 Bookstore Retail Area 15001150050 Retail Stockroom 4001400 Total 2190050 Caf Caf Area (addl. Seating outdoors) 15001150050 Kitchen 4001400 4 Total 2190054 Service and Maintenance Receivin g N/A* 1N/A* Loadin g Dock 4001400 Trash and Rec y clin g 2401240 Custodial 36062160 Communications, Data, Electrical E q ui p 140011400 Total 1042000 Total Total Net 2075503454 Wall thickness and structural @ 10% 20755 Buildin g Service E q ui p ment @ 10% 20755 Circulation @ 20% 41510 Total 290570SF Parking Student ( .5 s p aces p er ) 320500160000 Facult y + Staff ( 1 s p ace p er ) 32010032000 192000SF N/A*: non-assi g nable s p ace to come from gross % allotment of unassigned program space

PAGE 81

73 School of Art + Design Building Program Site area 239,000 S.F. 5.5 acres Students 1000 Facult y 40 Ad j unct Professors 20 Staff 40 Total 1100 SPACE Mi n. Clg. Ht. NET S.F.QUAN. GROSS S.F. Occu p Load Total 24000200 Studios Communications Desi g n 12'1800814400192 Fine Art 12'1800814400192 Photo g ra p h y + Di g ital Ima g in g 12'15004600080 Printmakin g 12'1800814400192 3D Media/ Scul p ture 15'18002360048 Dedicated Pro j ect Studio 12'18002360048 Total 3256400704 Fabrication/Sho p s Wood/Metal Sho p 15'1000011000050 Ceramics 15'25001250020 Plaster/Fabrics/Plasti c 15'25001250020 Litho g ra p h y /Printin g 25001250020 Lar g e-Scale Installation Construction15'50001500025 Total 522500135 Photo/Film Labs Enlar g er Stations 5050250050 Private Darkrooms 10010100020 Nonsilver darkroom 200120010 Di g ital Scannin g + Printin g Facilit y 500150015 B/W + Color Photo Lab 15001150040 Film Editin g + E q mt. 30001300050 Total 648700185 Di g ital Ima g in g Recording Studio One 14'3601360 8 Control Room 550155014 Isolation Room 80180 1 Studio Two 14'3001300 5 Control Room 450145014 Isolation Room 80180 1 Central Machine Room 80180 Midi Studio 7501750 Director's Studio 1801180 3 Re p air Sho p 1001100 2 Archival Recordin g 2801280 2 Media Ca g e 100011000 Total 12421050 Bookstore Retail Area 15001150050 Retail Stockroom 4001400 Total 2190050 Caf Caf Area (addl. Seating outdoors) 15001150050 Kitchen 4001400 4 Total 2190054 Service and Maintenance Receivin g N/A* 1N/A* Loadin g Dock 4001400 Trash and Rec y clin g 2401240 Custodial 36062160 Communications, Data, Electrical E q ui p 140011400 Total 1042000 Total Total Net 2075503454 Wall thickness and structural @ 10% 20755 Buildin g Service E q ui p ment @ 10% 20755 Circulation @ 20% 41510 Total 290570SF Parking Student ( .5 s p aces p er ) 320500160000 Facult y + Staff ( 1 s p ace p er ) 32010032000 192000SF N/A*: non-assi g nable s p ace to come from gross % allotment of unassigned program space

PAGE 82

74 School of Art + Design Building Program Site area 239,000 S.F. 5.5 acres Students 1000 Facult y 40 Ad j unct Professors 20 Staff 40 Total 1100 SPACE Mi n. Clg. Ht. NET S.F.QUAN. GROSS S.F. Occu p Load Total 24000200 Studios Communications Desi g n 12'1800814400192 Fine Art 12'1800814400192 Photo g ra p h y + Di g ital Ima g in g 12'15004600080 Printmakin g 12'1800814400192 3D Media/ Scul p ture 15'18002360048 Dedicated Pro j ect Studio 12'18002360048 Total 3256400704 Fabrication/Sho p s Wood/Metal Sho p 15'1000011000050 Ceramics 15'25001250020 Plaster/Fabrics/Plasti c 15'25001250020 Litho g ra p h y /Printin g 25001250020 Lar g e-Scale Installation Construction15'50001500025 Total 522500135 Photo/Film Labs Enlar g er Stations 5050250050 Private Darkrooms 10010100020 Nonsilver darkroom 200120010 Di g ital Scannin g + Printin g Facilit y 500150015 B/W + Color Photo Lab 15001150040 Film Editin g + E q mt. 30001300050 Total 648700185 Di g ital Ima g in g Recording Studio One 14'3601360 8 Control Room 550155014 Isolation Room 80180 1 Studio Two 14'3001300 5 Control Room 450145014 Isolation Room 80180 1 Central Machine Room 80180 Midi Studio 7501750 Director's Studio 1801180 3 Re p air Sho p 1001100 2 Archival Recordin g 2801280 2 Media Ca g e 100011000 Total 12421050 Bookstore Retail Area 15001150050 Retail Stockroom 4001400 Total 2190050 Caf Caf Area (addl. Seating outdoors) 15001150050 Kitchen 4001400 4 Total 2190054 Service and Maintenance Receivin g N/A* 1N/A* Loadin g Dock 4001400 Trash and Rec y clin g 2401240 Custodial 36062160 Communications, Data, Electrical E q ui p 140011400 Total 1042000 Total Total Net 2075503454 Wall thickness and structural @ 10% 20755 Buildin g Service E q ui p ment @ 10% 20755 Circulation @ 20% 41510 Total 290570SF Parking Student ( .5 s p aces p er ) 320500160000 Facult y + Staff ( 1 s p ace p er ) 32010032000 192000SF N/A*: non-assi g nable s p ace to come from gross % allotment of unassigned program space

PAGE 83

75 Urban School of Art + Design Net Square Footages by Usage 3% 10% 2% 26% 3% 7% 2% 27% 10% 4% 2% 1% 1% 2% Media Presentation Space Gallery/Exhibition Collections/Storage Library Admin/Offices Classrooms Computer Lab Studios Fabrication/Shops Photo/Film Digital Imaging Bookstore Caf Service/Maintenance

PAGE 84

76 ADJUNCT WORK ROOM RECEPTION ASST. DEANS OFFICE CONFERENCE ROOM STUDENT SERVICES BOOKEEPING OFFICE STUDENT RECORDS ADMINISTRATION/OFFICES DEANS OFFICE ADJUNCT WORK ROOM LOUNGE TO STUDIOS FACULT Y OFFICES TO GALLERY ST AFF OFFICES ADMINISTRATION FACULTY + ADJUNCT ADJACENCY DIAGRAMS

PAGE 85

77 STAGE AREA SEATING TO GALLERY MEDIA PRESENTATION SPACE LOBBY SOUND, LIGHT AND VIDEO SYSTEMS STORAGE ADJACENCY DIAGRAMS

PAGE 86

78 ENTRY S T A C K S WORKROOM/ OFFICE MEDIA STORAGE S T U D Y A R E A LISTENING STATIONS LARGE PRINT PERIODICALS S T A C K S READING ROOMS REFERENCE TERRACE S T U D Y A R E A S T A C K S DIGITAL MEDIA CIRCULATION LIBRARY TO STUDIOS S T U D Y A R E A READING ROOMS ADJACENCY DIAGRAMS

PAGE 87

79 TO LIBRARY TERRACE STUDIOS COMM. DESIGN COMM. DESIGN COMM. DESIGN COMM. DESIGN COMM. DESIGN COMM. DESIGN COMM. DESIGN COMM. DESIGN FINE ART FINE ART FINE ART FINE ART FINE ART FINE ART FINE ART FINE ART PHOTO/ FILM PHOTO/ FILM PRINTMAKING PRINTMAKING 3D MEDIA/ SCULPTURE 3D MEDIA/ SCULPTURE TO PHOTO LAB DESIGNATED PROJECT STUDIO TO COMP. LAB STUDENT LOUNGE TO FACULTY WORK SPACE TO SHOP ADJACENCY DIAGRAMS

PAGE 88

80 S T A C K S URBAN SCHOOL OF ART + DESIGN LIBRARY RIVERWALK PEDESTRIAN BOULEVARD CAFE SCULPTURE GARDEN MEDIA PRESENTATION SPACE ADMIN. OFFICE GALLERIES HILLSBOROUGH RIVER STUDIOS FABRICATION/ SHOPS BOOKSTORE COMP. LAB CLASSROOMS PHOTO/FILM LABS DIGITAL LABS TO MAIN STREET ENTRY LEGEND ADJACENCY MAIN ENTRY OTHER ADJ. REQUIREMENT ADJACENCY DIAGRAMS

PAGE 89

81 SCHEMATIC DESIGN

PAGE 90

82

PAGE 91

83 SCHEMATIC DESIGN PLAN :: level 1

PAGE 92

84 PLAN :: level 2

PAGE 93

85 PLAN :: level 3

PAGE 94

86 PLAN :: level 4

PAGE 95

87 PLAN :: level 5

PAGE 96

88 PLAN :: level 6

PAGE 97

89 PLAN :: level 7

PAGE 98

90 PLAN :: aerial view

PAGE 99

91 ELEVATIONS Figure 86: View of the facade when looking east Figure 87: View of the facade when looking south

PAGE 100

92 ELEVATIONS Figure 88: View of the facacde when looking west Figure 89: View of the facade when looking north

PAGE 101

93

PAGE 102

94

PAGE 103

95

PAGE 104

96

PAGE 105

97

PAGE 106

98

PAGE 107

99

PAGE 108

100

PAGE 109

101

PAGE 110

102

PAGE 111

103

PAGE 112

104

PAGE 113

105 The investigation for this thesis began with the research of mathematical patterns and properties in design, and the proposal of a unit to be employed in the project. The selected module proposed that there was a aesthetically pleasing: the golden ratio. Equally important, it suggested that this proportion could enhance ones innate design process by presenting the surroundings in frames and forced perspectives that reinforced the geometries of layout and design. Some of these include: the rule of thirds, composition of a canvas, and the use of a grid. In beginning of the task of site planning for such vertically to form eight main golden rectangles. Using Fibonacci numbers as the dimension of intervals for the regulating lines, the site was easily turned into a framework angle of the river was drawn into the site to connect to Downtowns Arts District and embrace the shift in the citys street grid. The module of 34 x 55 was selected as the standard for student buildings, i.e. classrooms, lecture halls, studio spaces, galleries and the library. Smaller variations of this module were used as appropriate, though not a directly scaled down version off that rectangle but a golden rectangle of the next proportion, 21 x 34, 13 x 21, etc... Doorways and mullions were used to frame openings in the same fashion, so that views were constrained by these CONCLUSION

PAGE 114

106 proportions as well. The goal of the classrooms and lecture rooms was to provide enough of a view to stimulate interest but not too much as to distract from the teaching and learning process. Studio spaces however, were designed to allow for broad vistas, though framed and directed by golden ratios. The galleries and the libraries were designed for the inclusion of varying levels of natural light, with outward views treated as a secondary feature. Though some may argue that this imposition of views and perspectives would hinder the creative process, it was the goal of this project to present the views as inspiration and leave the rest of the building as a fairly simple canvas for the play of light and shadow, and transparency and opacity. modules is that the dimensions of at least one side of each of the adjacent modules would be equal, on the x, y or z axis, while the overall volume may differ in size. This makes the modules easy to juxtapose and interchange. In turn, this creates a versatile building arrangement for the accomodation of various functions. Should the focus of the school shift to a more research based curriculum, the library and lecture spaces could easily be expanded or additional modules could be added to the buildings framework, without compromisinng the original design concept. The same could be done if there was a need for more studio spaces or fabrication areas. Future uses could be accomodated by shifting the spaces and orientation.

PAGE 115

107 This thesis aimed to explore the relationship between mathematics and architecture. Although the applications and uses of the proportioned, 3-dimensional experienced, the resultant spatial qualities will impart meaning and understanding at the subconscious level. Consequently, this subconscious meaning of architecture through mathematics, employed by Egyptian, Classical and Renaissance masters, can be replicated in a contemporary context.

PAGE 116

108 ENDNOTES 1 J.J. O’Connor and E.F. Robertson. “Mathematics and Art.” School of Mathematics and Statistics University of St. Andrews. http://www-history.mcs.st-andrews.ac.uk/ HistTopics/Art.html (accessed July 1, 2008). 2 J.J. O’Connor and E.F. Robertson. “Mathematics and Art.” School of Mathematics and Statistics University of St. Andrews. http://www-history.mcs.st-andrews.ac.uk/ HistTopics/Art.html (accessed July 1, 2008). 3 David C. Wang and Linda Groat. Architectural Research Methods. Canada: John Wiley & Sons, Inc., 2002.

PAGE 117

109 BIBLIOGRAPHY Mario Botta: Architetture 1960-1985 edited by Carlo Pirovano. Milano, Italia: Electra Editrice, 1985. Dimitriu, Livio and Mario Botta. “Architecture and Morality: An Interview with Mario Botta.” Perspecta 20, (1983): 119, http://www.jstor.org/stable/1567069 (accessed 15/06/2008). Futagawa, Yukio. GA DOCUMENT Extra 08: Richard Meier GA Document Extra., edited by Yukio Futagawa. Vol. 8. Tokyo, Japan: A.D.A. EDITA Tokyo Co., Ltd., 1997. Hershberger, Robert G. Architectural Programming and Predesign Manager edited by Wendy Lochner. New York: McGraw-Hill, 1999. O’Connor, J. J. and Robertson, E. F. “Mathematics and Art.” School of Mathematics and Statistics University of St. Andrews. http://www-history.mcs.st-andrews.ac.uk/ HistTopics/Art.html (accessed July 1, 2008). Padovan, Richard. Proportion: Science, Philosophy, Architecture New York: E & FN Spoon, 1999. Pizzi, Emilio, ed. Mario Botta: The Complete Works [Mario Botta: das Gesamtwerk] Translated by David Kerr, Bruce Almberg and Katja Steiner. Vol. 3 : 1990-1997. Basel: Birkhauser, 1998. Psarra, Sophia. “Geometry and Space in the Architecture of Le Corbusier and Mario Botta.” London, 1997 (accessed July 1, 2008). Salingaros, Nikos A. “Architecture, Patterns and Mathematics.” Nexus Network Journal I, (1999): 75. Schol eld, P. H. The Theory of Proportion in Architecture London: Cambridge University Press, 1958. Wang, David C. and Linda Groat. Architectural Research Methods. Canada: John Wiley & Sons, Inc., 2002. Williams, Harold M., Ada Louise Huxtable, Stephen D. Rountree, and Richard Meier. MAKING ARCHITECTURE: The Getty Center edited by Gloria Gerace. Los Angeles, CA: The J. Paul Getty Trust, 1997.

PAGE 118

110 BIBLIOGRAPHY edited by Carlo Pirovano. Milano, Italia: Electra Editrice, 1985. Dimitriu, Livio and Mario Botta. Architecture and Morality: An Interview with Mario Botta. Perspecta 20, (1983): 119, http://www.jstor.org/stable/156706 9 (accessed 15/06/2008). Futagawa, Yukio. GA GA Document Extra., edited by Yukio Futagawa. Vol. 8. Tokyo, Japan: A.D.A. EDITA Tokyo Co., Ltd., 1997. Hershberger, Robert G. Architectural Programming and Predesign Manager edited by Wendy Lochner. New York: McGraw-Hill, 1999. OConnor, J. J. and Robertson, E. F. Mathematics and Art. School of Mathematics and Statistics University of St. Andrews. http://www-history.mcs.st-andrews.ac.uk/ HistTopics/Art.htm l (accessed July 1, 2008). Padovan, Richard. Proportion: Science, Philosophy, Architecture New York: E & FN Spoon, 1999. Pizzi, Emilio, ed. [Mario Botta: das Gesamtwerk] Translated by David Kerr, Bruce Almberg and Katja Steiner. Vol. 3 : 1990-1997. Basel: Birkhauser, 1998. Psarra, Sophia. Geometry and Space in the Architecture of Le Corbusier and Mario Botta. London, 1997 (accessed July 1, 2008). Salingaros, Nikos A. Architecture, Patterns and Mathematics. I, (1999): 75. The Theory of Proportion in Architecture London: Cambridge University Press, 1958. Wang, David C. and Linda Groat. Architectural Research Methods. Canada: John Wiley & Sons, Inc., 2002. Williams, Harold M., Ada Louise Huxtable, Stephen D. Rountree, and Richard Meier. edited by Gloria Gerace. Los Angeles, CA: The J. Paul Getty Trust, 1997.


xml version 1.0 encoding UTF-8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd
leader nam 2200385Ka 4500
controlfield tag 001 002029671
005 20090918153549.0
007 cr mnu|||uuuuu
008 090918s2009 flu s 000 0 eng d
datafield ind1 8 ind2 024
subfield code a E14-SFE0002969
035
(OCoLC)437035023
040
FHM
c FHM
049
FHMM
090
NA2520 (Online)
1 100
Thom, Alison Marie.
0 245
Form and numbers :
b mathematical patterns and ordering elements in design
h [electronic resource] /
by Alison Marie Thom.
260
[Tampa, Fla] :
University of South Florida,
2009.
500
Title from PDF of title page.
Document formatted into pages; contains 110 pages.
502
Thesis (M.Arch.)--University of South Florida, 2009.
504
Includes bibliographical references.
516
Text (Electronic thesis) in PDF format.
520
ABSTRACT: In America, buildings are often constructed with the intent of being utile only 30-40 years. All over the world though, there are buildings that are hundreds of years old that are still very functional. Historically, architecture was a part of mathematics, and in many periods of the past, the two were indistinguishable. Architects were often required to be also mathematicians in ancient times. The idea of this thesis is to identify the relationship between mathematics and architecture and to reintroduce them in order to create a module for successful design Presence of mathematical boundaries help to attain visual consistency by relating a small scale to a larger scale. Spaces which meet these criteria are subconsciously realized as sharing critical qualities with natural and biological forms. Accordingly, they are perceived as more comfortable psychologically.Scaling coherence is a common element of traditional and vernacular architectures, but is often extensively deficient from contemporary architecture. Architecture has used proportional systems to create, or limit, the forms in building since its inception. In almost every building tradition, there exists a system of mathematical relations which governs the relationships between elements of design. These are often quite simple: whole number ratios or easily constructed geometric shapes. Many types of revival architecture have been employed in recent years, therefore it would be critical to identify why they have achieved a resurgence in popularity. However, historical allusions are generally superficial. No authentic scale or systems are used and the formerly unique qualities are not explored spatially. The attraction to, and association with, forms possessing harmonic proportions is a mitigating factor in design that needs to be addressed.The natural beauty stemming from proportion, mathematics, and the proper relationship of elements to the whole is what renders a building aesthetically and experientially pleasing to a human. Post-Modern architecture is all but going in the opposite direction of achieving this goal. The idea that a building should scale down to dimensions humans can relate to and reveal its stature in the experiential qualities must be extracted from traditional architecture and employed in contemporary techniques.
538
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
590
Advisor: Daniel Powers, M.Arch
653
Mathematics
Proportion
Grid
Architecture
Art
690
Dissertations, Academic
z USF
x Architecture and Community Design
Masters.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.2969