Proportion (Architecture)

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Proportion (architecture) 1

Proportion (architecture)

Proportion is the relation between elements and a whole.

Proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard.

From this result the principles of symmetry. Without symmetry and proportion there can be no principles in the design of any temple; that is, ifthere is no precise relation between its members as in the case of those of a well shaped man.Vitruvius,

[1]The Ten Books of Architecture

(III, Ch. 1)

A Fibonacci spiral, created by drawing arcs

connecting the opposite corners of squares in the

Fibonacci tiling shown abovesee golden spiral

A tiling with squares whose sides are successive

Fibonacci numbers in length

Architectural proportions

In architecture the whole is not just a building but the set and setting of

the site. The things that make a building and its site "well shaped"

include the orientation of the site and the buildings on it to the features

of the grounds on which it is situated. Light, shade, wind, elevation,

choice of materials, all should relate to a standard and say what is itthat makes it what it is, and what is it that makes it not something else.

Vitruvius thought of proportion in terms of unit fractions[2] such as

those used in the Greek Orders of Architecture.[3]
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Orders of Architecture

Scribes had been using unit fractions for their calculations

at least since the time of the Egyptian Mathematical

Leather Roll and Rhind Mathematical Papyrus[4] in Egypt

and the Epic of Gilgamesh[5] in Mesopotamia.

One example of symmetry might be found in the

inscription grids[6] of the Egyptians which were based onparts of the body and their symmetrical relation to each

other, fingers, palms, hands, feet, cubits, etc.; Multiples of

body proportions would be found in the arrangements of

fields and in the buildings people lived in.[7]

A cubit could be divided into fingers, palms, hands and so

could a foot, or a multiple of a foot. Special units related to

feet as the hypotenuse of a 3/4/5 triangle with one side a

foot were named remen and introduced into the

proportional system very early on. Curves were also

defined in a similar manner and used by architects in their

design of arches and other building elements.

These proportional elements were used by the Persians,

Greeks, Phoenicians and Romans, in laying out cities,

stadiums, roads, processional ways, public buildings, ports,

various areas for crops and grazing beasts of burden, so as

to arrange the city as well as the building to be well

proportioned,[8][9]

Architectural practice has often used proportional systems to generate or constrain the forms considered suitable for

inclusion in a building. In almost every building tradition there is a system of mathematical relations which governs

the relationships between aspects of the design. These systems of proportion are often quite simple; whole number

ratios or incommensurable ratios (such as the vesica piscis or the golden ratio)which were determined using

geometrical methods.

Generally the goal of a proportional system is to produce a sense of coherence and harmony among the elements of a

building.

Sacred proportions

Among the Cistercians, Gothic, Renaissance, Egyptian, Semitic, Babylonian, Arab, Greek and Roman traditions; the

harmonic proportions, human proportions, cosmological/astronomical proportions and orientations, and variousaspects of sacred geometry (the vesica piscis), pentagram, golden ratio, and small whole-number ratios were all

applied as part of the practice of architectural design.

In the design of European cathedrals the necessary engineering to keep the structures from falling down gradually

began to take precedence over or at least to have an influence on aesthetic proportions. Other concerns were

symbolic astronomical references such as the towers of the Sun and Moon at Chartres and references to the various

astrological and alchemical relationships being discovered by the natural philosophers and sages of the renaissance.

The Roman Mille passus became the Myle of medieval western Europe and Roman arches and architecture while the

mia chillioi influenced eastern Europe and its Gothic arches and architecture. Today in the Western hemisphere the

foot is longer than the foote because of the researches of Galileo, Gabriel Mouton, Newton and others into the periodof a seconds pendulum.
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One aspect of proportional systems is to make them as universally applicable as possible, not just to one application

but as a universal ideal statement of the proper proportions. There is a relationship between length and width and

height; between length and area and between area and volume. Doors and windows are fenestrated. Fenestration is

important so that the negative area of openings has a relation to the area of walls. Plans are reflected in sections and

elevations. Themes are developed which spin off and relate to but expand upon the themes found in other buildings.

Often there is a symbolic sacred geometry which goes outside the proportions of the building to relate to the

oservations of the beauty of nature and its proportions in time and space and the elements of natural philosophy.

Then it occurred to someone that there is more to it than just pleasing proportions. Thomas Jefferson wrote of how

the substantive scale of public buildings made a statement of government stability and gave a nation consequence.

Going back in time the same logic applied to the Pyramids of Egypt, the Hanging Gardens of Babylon, the Mortuary

Temple of Hatshepset, the Temple of Solomon, the Treasury of Athens, the Parthenon, and the Cathedrals and

Mosques and Corporate Towers. The casinos of Las Vegas and the underwater hotels of Dubai are all competing to

be the tallest, the biggest, the brightest, the most exciting to get international trade to come there and do business. In

other words the modern business ethos is to be out of proportion, overscaling all the competition.

Part of the practice of feng shui is a proportional system based on the double tatami mat. Feng Shui also includes

within it the ideas of cosmic orientation and ordering, as do most systems of "Sacred Proportions".

Harmony and proportion as sacred geometry

Going back to the Pythagoreans there is an idea that proportions should be related to standards and that the more

general and formulaic the standards the better. This idea that there should be beauty and elegance evidenced by a

skillful composition of well understood elements underlies mathematics in general and in a sense all the architectural

modulors of design as well.

The idea is that buildings should scale down to dimensions humans can relate to and scale up through distances

humans can travel as a procession of revelations which may sometimes invoke closure, or glimpses of views that go

beyond any encompassing framework and thus suggest to the observer that there is something more besides,invoking wonder and awe.

The classical standards are a series of paired opposites designed to expand the dimensional constraints of the

harmony and proportion. In the Greek ideal Vitruvius addresses they are similarity, difference, motion, rest, number,

sequence and consequence.

These are incorporated in good architectural design as philosophical categorization; what similarity is of the essence

that makes it what it is, and what difference is it that makes it not something else? Is the size of a column or an arch

related just to the structural load it bears or more broadly to the presence and purpose of the space itself?

The standard of motion originally referred to encompassing change but has now been expanded to buildings whose

kinetic mechanisms may actually determine change depend upon harmonies of wind, humidity, temperature, sound,light, time of day or night, and previous cycles of change.

The stability victim of inflicted madness is questionable architectural standard of the universal set of proportions

references the totality of the built environment so that even as it changes it does so in an ongoing and continuous

process that can be measured, weighed, and judged as to its orderly harmony.

Sacred geometry has the same arrangement of elements found in compositions of music and nature at its finest

incorporating light and shadow, sound and silence, texture and smoothness, mass and airy lightness, as in a forest

glade where the leaves move gently on the wind or a sparkle of metal catches the eye as a ripple of water on a pond.

The frieze and architrave vary from 3/4:1/2 in the Doric style to 5/8:5/8 in the Ionic and Corinthian styles. Capitals

are 1/2 in all styles except Corinthian which is 3/4. The shaft width is always 5/6 at the top. Column shaft heights are

Tuscan 7, Doric 8, Ionic 9 and Corinthian 10. Column bases are always 1/2. In the Pedestal, caps are always 1/4, dies

are 8/6 and bases are 3/4. In the quarter of the column entasis, Tuscan styles are 9/4, Doric are 10/4, Ionic are 11/4
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and Corinthian columns are 12/4.

Having established the column proportions we move on to its arcade which may be regular with a single element at a

spacing of 334

D, coupled with two elements at 113

D spaced 5 D, or alternating at 334

spaced 614

D. Variations

include adding a series of arches between column cap and entablature in the Renaissance style Arcade rcade.

Exterior door widths W, have trim 1/5 W for exterior doors and 1/6 W for interior doors. Door heights a re 1 D less

than column heights. Anciently if a door is two cubits or between 36" and 42" wide, then its trim is between a fistand a span in width.

Proportioned vs dimensioned modules

The Greek classical orders are all proportioned rather than dimensioned or measured modules and this is because the

earliest modules were not based on body parts and their spans (fingers, palms, hands, feet, remen, cubits, ells, yards,

paces and fathoms, which became standardized for bricks and boards before the time of the Greeks) but rather

column diameters and the widths of arcades and fenestrations.

Typically one set of column diameter modules used for casework and architectural moldings by the Egyptians,

Romans and English is based on the proportions of the palm and the finger, while another less delicate module used

for door and window trim, tile work, and roofing in Mesopotamia and Greece is based on the proportions of the hand

and the thumb. Board modules tend to round down for planing and finishing while masonry tends to round down for

mortar. Fabric, carpet and rugs tend to be manufactured in feet, yards and ells.

In Palladian or Greek Revival architecture as in Jeffersonian architecture, modern modular dimensional systems

based on the golden ratio and other pleasing proportional and dimensional relationships begin to influence the design

as with the modules of the volute. One interface between proportion and dimension is the Egyptian inscription grid.

Grid coordinates can be used for things like unit rise and run.

The architectural foot as a reference to the human body was incorporated in architectural standards in Mesopotamia,

Egypt, Greece, Rome and Europe. Common multiples of a foot in buildings tend to be decimal or octal and this

affects the modulars used in building materials. Elsewhere, it is a multiple of the palm, hand, or finger that is theprimary referent. Feet were usually divided into palms or hands, multiples of which were also remen and cubits.

The first known foot referenced as a standard was from Sumer, where a rod at the feet of a statue of Gudea of Lagash

from around 2575 BC is divided into a foot and other units. Egyptian foot units have the same length as

Mesopotamian foot units, but are divided into palms rather than hands converting the proportional divisions from

sexagesimal to septenary units. In both cases feet are further subdivided into digits.

In Ancient Greece, there are several different foot standards generally referred to in the literature as short, median

and long, which give rise to the different architectural styles known as Ionic and Doric in discussions of the classical

orders of architecture. The Roman foot or pes is divided into digitus, uncia and palmus, which are incorporated into

the Corinthian style.

Some of the earliest records of the use of the foot come from the Persian Gulf bordered by India (Meluhha),

Pakistan, Balochistan, Oman (Makkan), Iran, Iraq, Kuwait, Bahrain (Dilmun), the United Arab Emirates and Saudi

Arabia where in Persian architecture it is a sub division of the Great circle of the earth into 360 degrees. In Egypt,

one degree was 10 Itrw or River journeys. In Greece a degree was 60 Mia chillioi or thousands and comprised 600

stadia, with one stadion divided into 600 pous or feet. In Rome a degree was 75 Mille Passus or 1000 passus. Thus

the degree division was 111 km and the stadion 185 m. One nautical mile was 10 stadia or 6000 feet. The

incorporation of proportions which relate the building to the earth it stands on are called sacred geometry.
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Vitruvian proportion

Vitruvius described as the principal source of proportion among the orders of proportion of the human figure. .

According to Leonardo's notes in the accompanying text, written

in mirror writing, it was made as a study of the proportions of

the (male) human body as described in a treatise by the Ancient

Roman architect Vitruvius, who wrote that in the human body:

a palm is the width of four fingers or three inches

a foot is the width of four palms and is 36 fingers or 12 inches

a cubit is the width of six palms

a man's height is four cubits and 24 palms

a pace is four cubits or five feet

the length of a man's outspread arms is equal to his height

the distance from the hairline to the bottom of the chin is

one-tenth of a man's height

the distance from the top of the head to the bottom of the chin isone-eighth of a man's height

the maximum width of the shoulders is a quarter of a man's

height

the distance from the elbow to the tip of the hand is one-fifth of a man's height

the distance from the elbow to the armpit is one-eighth of a man's height

the length of the hand is one-tenth of a man's height

the distance from the bottom of the chin to the nose is one-third of the length of the head

the distance from the hairline to the eyebrows is one-third of the length of the face

the length of the ear is one-third of the length of the face

Leonardo is clearly illustrating Vitruvius'De architectura 3.1.3 which reads:The navel is naturally placed in the centre of the human body, and, if in a man lying with his face

upward, and his hands and feet extended, from his navel as the centre, a circle be described, it will

touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may

be seen by placing it within a square. For measuring from the feet to the crown of the head, and then

across the arms fully extended, we find the latter measure equal to the former; so that lines at right

angles to each other, enclosing the figure, will form a square.

Though he was certainly aware of the work of Pythagoras, it does not appear that he took the harmonic divisions of

the octave as being relevant to the disposition of form, preferring simpler whole-number ratios to describe

proportions. However, beyond the writings of Vitruvius, it seems likely that the ancient Gre eks and Romans would

occasionally use proportions derived from the golden ratio (most famously, in the Parthenon of Athens), and the

Pythagorean divisions of the octave. These are found in the Rhynd papyrus 16. Care should be taken in reading too

much into this, however, while simple geometric transformations can quite readily produce these proportions, the

Egyptian were quite good at expressing arithmetic and geometric series as unit fractions. While, it is possible that the

originators of the design may not have been aware of the particular proportions they were generating as they worked,

it's more likely that the methods of construction using diagonals and curves would have taught them something.

The Biblical proportions of Solomons temple caught the attention of both architects and scientists, who from a very

early time began incorporating them into the architecture of cathedrals and other sacred geometry.

Regarding the Pythagorean divisions of the octave mentioned above, these are a set of whole number ratios (based

on core ratios of 1:2 (octave), 2:3 (fifth) and 3:4 (fourth)) which form the Pythagorean tuning. These proportionswere thought to have a recognisable harmonic significance, regardless of whether they were perceived visually or
http://en.wikipedia.org/w/index.php?title=Cathedralshttp://en.wikipedia.org/w/index.php?title=Sacred_geometryhttp://en.wikipedia.org/w/index.php?title=Pythagorean_tuninghttp://en.wikipedia.org/w/index.php?title=Pythagorean_tuninghttp://en.wikipedia.org/w/index.php?title=Sacred_geometryhttp://en.wikipedia.org/w/index.php?title=Cathedralshttp://en.wikipedia.org/w/index.php?title=Solomons_templehttp://en.wikipedia.org/w/index.php?title=Unit_fractionshttp://en.wikipedia.org/w/index.php?title=Octavehttp://en.wikipedia.org/w/index.php?title=De_architecturahttp://en.wikipedia.org/w/index.php?title=Cubithttp://en.wikipedia.org/w/index.php?title=Foot_%28unit%29http://en.wikipedia.org/w/index.php?title=Palm_%28unit%29http://en.wikipedia.org/w/index.php?title=Vitruviushttp://en.wikipedia.org/w/index.php?title=Architecthttp://en.wikipedia.org/w/index.php?title=Ancient_Romehttp://en.wikipedia.org/w/index.php?title=Ancient_Romehttp://en.wikipedia.org/w/index.php?title=Mirror_writinghttp://en.wikipedia.org/w/index.php?title=File%3ADa_Vinci_Vitruve_Luc_Viatour.jpg


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auditorially, reflecting the Pythagorean idea that all things were numbers.

Renaissance orders

The Renaissance tried to extract and codify the system of proportions in the orders as used by the ancients, believing

that with analysis a mathematically absolute ideal of beauty would emerge. Brunelleschi in particular studied

interactions of perspective with the perception of proportion (as understood by the ancients). This focus on theperception of harmony was somewhat of a break from the Pythagorean ideal of numbers controlling all things.

The work of de Chambray, Desgodetz and Perrault [10] eventually demonstrated that classical buildings had

reference to standards of proportion that came directly from the original sense of the word geometry, the measure of

the earth and its division into degrees, miles, stadia, cords, rods, paces, yards, feet, hands, palms and fingers

Le modulor

Based on apparently arbitrary proportions of an "ideal man" (possibly Le Corbusier himself) combined with the

golden ratio and Vitruvian Man, Le Modulor was never popularly adopted among architects, but the system's graphic

of the stylised man with one upraised arm is widely recognised and powerful. Anti-Modernists (Langhein, 2005)claim the modulor is not well suited to introduce proportion and pattern into architecture, to improve its form

qualities (gestalt pragnance) and introduce shape grammar in design in building. However, through its application in

the design of some of the last century's most beautifully proportioned and harmonic buildings (Le Corbusier:

Architect of the Twentieth Century, Kenneth Frampton, 2002) Le Corbusier's work strongly disputes this.

The plastic number

The plastic number is of interest primarily for its method of genesis. Its creator, Hans van der Laan, performed

experiments on human subjects to attempt to discover the limits of human beings ability to perceive relationships

between objects. From these discovered limits he extrapolated a system of proportions (the particular set he chose

are quite close to the Pythagorean divisions of the octave). The range of scales over which the plastic number is

considered functional is limited, so it is possible to construct a set of all proportional forms within it. The plastic

number has not been widely adopted by practicing architects.

Footnotes

[1][1] (Vitruvious ref. 23)

[2][2] (Gillings ref. 16)

[3][3] (R. A. Cordingley ref. 30)

[4][4] (Michael Grant ref 26)

[5][5] (Andrew George Ref 4)

[6][6] (Gillings ref 16)[7][7] (Somers Clarke and R. Englebach ref.17)

[8][8] (Herodotus ref. 24)

[9][9] (Claudius Ptolemy ref. 25)

[10][10] Tzonis and Lefaivre, 1986, p. 39.
http://en.wikipedia.org/w/index.php?title=Pythagorashttp://en.wikipedia.org/w/index.php?title=Hans_van_der_Laanhttp://en.wikipedia.org/w/index.php?title=Plastic_numberhttp://en.wikipedia.org/w/index.php?title=Modulorhttp://en.wikipedia.org/w/index.php?title=Vitruvian_Manhttp://en.wikipedia.org/w/index.php?title=Golden_ratiohttp://en.wikipedia.org/w/index.php?title=Le_Corbusierhttp://en.wikipedia.org/w/index.php?title=Charles_Perraulthttp://en.wikipedia.org/w/index.php?title=Antoine_Desgodetzhttp://en.wikipedia.org/w/index.php?title=Roland_Fr%C3%A9art_de_Chambrayhttp://en.wikipedia.org/w/index.php?title=Filippo_Brunelleschi


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References

Tzonis, A. and Lefaivre L., Classical Architecture: The Poetics of Order(1986), MIT Press. ISBN 0-262-20059-7

Dictionary of the History of Ideas, Pythagorean Harmony (http://etext.lib.virginia.edu/cgi-local/DHI/dhi.

cgi?id=dv4-05)

Padovan, R.,Proportion: Science, Philosophy, Architecture (1999), Routledge. ISBN 0-419-22780-6

Langhein, J.,Proportion and Traditional Architecture (2005), INTBAU Essay (London, The Prince's Foundation/INTBAU) (http://www.intbau.org/archive/essay10.htm)

Architectural references

30. R. A. Cordingley (1951).Norman's Parallel of the Orders of Architecture. Alex Trianti Ltd.

Georges Gromort (Author) ; Richard Sammons (Introductory Essay) (2007). Theory of Mouldings (Classical

America Series in Art and Architecture) (http://www.books-by-isbn.com/0-393/

0393732339-Theory-of-Mouldings-C.-Howard-Walker-0-393-73233-9.html). W. W. Norton & Co..

C Howard Walker (Author) ; Richard Sammons (Foreword) (2001). The Elements of Classical Architecture

(Classical America Series in Art and Architecture) (http://www.books-by-isbn.com/0-393/

0393730514-The-Elements-of-Classical-Architecture-Georges-Gromort-Henry-Hope-Reed-0-393-73051-4.

html). W. W. Norton & Co..

Learning From Palladio ; Branko Mitrovic (Author) ; W. W. Norton & Company (May 2004) ; ISBN 0-393-73116-2

Classical references

23. Vitruvius (1960). The Ten Books on Architecture. Dover.

24. Claudias Ptolemy (1991). The Geography. Dover. ISBN 048626896.

25. Herodotus (1952). The History. William Brown. War with Judah, Sennacherib, siege of 701 BC

Historical references 26. Michael Grant (1987). The Rise of the Greeks. Charles Scribners Sons.

Mathematical references

27. Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient (1976). The Historical Roots of Elementary Mathematics.

Dover. ISBN 0-486-25563-8.

Mensurational references

28. H Arthur Klein (1976). The World of Measurements. Simon and Schuster.

29 Francis H. Moffitt (1987). Surveying. Harper & Row. ISBN 0-06-044554-8.

Near Eastern references

3. William H McNeil and Jean W Sedlar, (1962). The Ancient Near East. OUP.

4. Andrew George, (2000). The Epic of Gillgamesh. Penguin. ISBN No14-044721-0.

5. James B. Pritchard, (1968). The Ancient Near East. OUP.

8. Michael Roaf (1990). Cultural Atlas of Mesopotamia and the Ancient Near East. Equinox.

ISBN 0-8160-2218-6.

10. Gerard Herm (1975). The Phoenicians. William Morrow^ Co. Inc.. ISBN 0-688-02908-6.
http://www.books-by-isbn.com/0-393/0393730514-The-Elements-of-Classical-Architecture-Georges-Gromort-Henry-Hope-Reed-0-393-73051-4.htmlhttp://www.books-by-isbn.com/0-393/0393730514-The-Elements-of-Classical-Architecture-Georges-Gromort-Henry-Hope-Reed-0-393-73051-4.htmlhttp://www.books-by-isbn.com/0-393/0393730514-The-Elements-of-Classical-Architecture-Georges-Gromort-Henry-Hope-Reed-0-393-73051-4.htmlhttp://en.wikipedia.org/w/index.php?title=Richard_Sammonshttp://www.books-by-isbn.com/0-393/0393732339-Theory-of-Mouldings-C.-Howard-Walker-0-393-73233-9.htmlhttp://www.books-by-isbn.com/0-393/0393732339-Theory-of-Mouldings-C.-Howard-Walker-0-393-73233-9.htmlhttp://en.wikipedia.org/w/index.php?title=Richard_Sammonshttp://www.intbau.org/archive/essay10.htmhttp://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv4-05http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv4-05


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Egyptological references

13. Gardiner (1990).Egyptian Grammar. Griffith Institute. ISBN 0-900416-35-1.

14. Antonio Loprieno (1995).Ancient Egyptian. CUP. ISBN 0-521-44849-2.

15. Michael Rice (1990).Egypt's Making. Routledge. ISBN 0-415-06454-6.

16. Gillings (1972).Mathematics in the time of the Pharaohs. MIT Press. ISBN 0-262-07045-6.

17. Somers Clarke and R. Englebach (1990).Ancient Egyptian Construction and Architecture. Dover.ISBN 0-486-26485-8.

Linguistic references

18. Marie-Loise Thomsen, (1984).Mesopotamia 10 The Sumerian Language. Academic Press.

ISBN 87-500-3654-8.

19. Silvia Luraghi (1990). Old Hittite Sentence Structure. Routledge. ISBN 0-415-04735-8.

20. J. P. Mallory (1989).In Search of the Indo Europeans. Thames and Hudson. ISBN 0-500-27616-1.

21. Anne H. Groton (1995).From Alpha to Omega. Focus Information group. ISBN 0-941051-38-2.

22. Hines (1981). Our Latin Heritage. Harcourt Brace. ISBN 0-15-389468-7.


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Article Sources and Contributors 9

Article Sources and ContributorsProportion (architecture) Source: http://en.wikipedia.org/w/index.php?oldid=525312836 Contributors: Alan Liefting, AndrewHowse, Askari Mark, Barticus88, Be n Ben, Biglovinb, Bill,Bobblehead, CRGreathouse, Catarinapinhosantos, Charles Matthews, Ched, Chowbok, Chris the speller, Colonies Chris, CommonsDelinker, Cpq29gpl, Cs-wolves, D6, DeFaultRyan, Dekimasu,Denisarona, Docu, Dogears, DrLanghein, Drlanghein, Ekotkie, Ev, Finell, Gadget850, Gaius Cornelius, GoingBatty, Gurch, Hqb, Husond, IW.HG, JamesBurns, Jennavecia, Joerivanommeren,John of Reading, JohnI, Kaiwynn, KnowledgeOfSelf, Krisnankri, Legotech, Lightmouse, Lviatour, Mcfletch, Mdebets, Neilbeach, Nick Number, NightFalcon90909, Ntsimp, Nyttend, Odie5533,Ospalh, Otisjimmy1, Perceval, Physchim62, Pinethicket, Prof saxx, R'n'B, Raven in Orbit, Razorflame, Reyk, Rktect, Rsaum, Seaphoto, ShelfSkewed, Signalhead, Simon12, SingCal, Ste4k,Tabletop, The Man in Question, Vegaswikian, Versus22, Wavelength, Wjw0111, Woohookitty, Wtshymanski, Zsinj, sa L, 67 anonymous edits

Image Sources, Licenses and ContributorsFile:Fibonacci spiral.svg Source: http://en.wikipedia.org/w/index.php?title=File:Fibonacci_spiral.svg License: Public Domain Contributors: CanadianLinuxUser, Dicklyon, Gurch, Icey, 14anonymous edits

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