- Proportion (architecture)
**Proportion**is the relation between elements and a whole.**Architectural proportions**In

architecture the whole is not just abuilding but the set and setting of thesite . The things that make a building and its site "well shaped" include theorientation of the site and the buildings on it to the features of the grounds on which it is situated.Light ,shade ,wind ,elevation , choice ofmaterials , all should relate to astandard and say what is it that makes it what it is, and what is it that makes it not something else.Vitruvius thought of proportion in terms of

unit fractions [*(Gillings ref. 16)*] such as those used in the Greek Orders of Architecture. [*(R. A. Cordingley ref. 30)*] [*(Andrew George Ref 4)*] in Mesopotamia.One example of symmetry might be found in the inscription grids [

*(Gillings ref 16)*] of the Egyptians which were based on parts 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. [*(Somers Clarke and R. Englebach ref.17)*]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 namedremen 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, [

*(Herodotus ref. 24)*] [*(Claudius Ptolomy ref. 25)*]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 easily constructed geometric shapes (such as the

vesica piscis or thegolden ratio ).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 various aspects ofsacred 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 variousastrological andalchemical relationships being discovered by the naturalphilosophers andsage s of therenaissance .The Roman Mille passus became the Myle of medieval western Europe and

Roman archs and architecture while the mia chillioi influenced eastern Europe and its Gothicarch es and architecture. Today in the Western hemisphere the foot is longer than the foote because of the researches ofGalileo ,Gabriel Mouton ,Newton and others into the period of a secondspendulum .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 symbolicsacred 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 ofnatural philosophy .Then it occurred to someone that there is more to it than just pleasing proportions.

Thomas Jefferson wrote of how the substantive scale ofpublic buildings made a statement ofgovernment stability and gave anation consequence.Going back in time the same logic applied to the

Pyramids of Egypt , theHanging Gardens of Babylon , theMortuary Temple of Hatshepset, theTemple of Solomon , theTreasury ofAthens , theParthenon , and theCathedrals andMosque s andCorporate Towers . The Casinos of Las Vegas and theunderwater hotels ofDubai 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

Pythagorean s there is an idea that proportions should be related to standards and that the more general and formulaic thestandards 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 todimensions humans can relate to and scale up through distances humans can travel as a procession of revelations which may sometimes invokeclosure , 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 aresimilarity ,difference ,motion ,rest ,number ,sequence andconsequence .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 ornight , and previouscycles ofchange .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 bemeasure d,weigh ed, andjudged as to its orderly harmony.Sacred geometry has the samearrangement ofelements found in compositions ofmusic and nature at its finest incorporatinglight andshadow ,sound andsilence ,texture andsmoothness ,mass and airylightness , as in a forest glade where the leaves move gently on thewind or asparkle ofmetal catches the eye as aripple ofwater on a pond.**Classical orders**The

classical order s [*R. A. Cordingley ref. 30*] here illustrated by theTemple of Hephaestus in Athens, showing columns with Doric capitals are largely known through the writings ofVitruvius , particularly "De Archetura" (The Ten Books of Architecture) and studies of classical architecture by Renaissance architects and historians. Within a classical order elements from the positioning oftriglyph s to the overall height and width of the building were controlled by principles of proportionality based on column diameters. Typically Ionic column bases are molded and about 1/2 the diameter of the column. They reduce in detail from theTemple of Artemis ofEphesus built c 560 BC and theHeraion of Samos c 550 BC to elongated detail in theTemple ofAthena c 535 BC, then begin to soften their lines in the Temple of Nike at Apteros c 342 BC and begin to emphasise circular rounds in the north porch of theErechteum c 421 BC. This establishes the elements of the form which remains virtually unchanged through the Temple of Fortuna c 40 BC, theBaths of Diocletian AD 306, and the classical Greek orders ofAndrea Palladio in the 16th century. Long before the Greeks international trade and commerce led to standardization of units and the facilitation of calculations inunit fractions throughout the civilized world. In architectural terms, the dimensions of structural elements likepost s, beams,column s,arch es,opening s andfenestration s constructed of wood and stone were slowly standardized as regards the expectedload andspan so that a given dimension could support a given load withoutfailure .By way of contrast to the elongated Ionic order, Doric orders never became so slender as to require a base but do have entasis as the

column shaft tapered upwards like a degree of the earth's surface. The column shafts of the Doric order are alwaysflute d and twenty flutes is the usual number. The columncapital has anabacus square in plan and a roundedechinus which supports it. The Doric entablature has a deep plainarchitrave , largeTriglyph s in thefrieze and a series of mutles in thecornice sloping as the roof rafters of a wooden structure. The greatest change in thedentil edentablature from Ionic through Corinthian is in the addition of thefrieze and scrolledmodillion s to thecyma in Corinthian styles.The proportions of entablature to

parapet remain the same at 2:2 in all styles as do the proportions of cap, die and base at 1/4:1:3/4 in the parapet. In all styles the Cornice has the proportion of 3/4 but 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 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 3 3/4 D, coupled with two elements at 1 1/3 D spaced 5 D, or alternating at 3 3/4 spaced 6 1/4 D. Variations include adding a series of arches between column cap and entablature in the Renaissance style arcade, adding a keystone in the

archivolt in the Roman style arcade, and adding more detail in thePalladian arcade. 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" in width, then its trim is between afist and aspan in width.**Proportioned vs dimensioned modules**The Greek classical orders are all

proportion ed rather thandimension ed or measured modules and this is because the earliestmodule s were not based on body parts and their spans,finger s,palm (unit) s,hand s, feet,remen ,cubit s,ell s,yard s,pace s andfathom s which became standardized forbrick s, and boards, before the time of theGreeks , but rathercolumn diameters and the widths of arcades andfenestration s.Typically one set of column diameter modules used for casework and architectural

molding s by the Egyptians, Romans and English is based on the proportions of the palm and the finger, while another less delicate module used fordoor andwindow trim,tile work, androofing inMesopotamia andGreece is based on the proportions of the hand and the thumb.Board modules tend to round down for planing and finishing whilemasonry tends to round down for mortar.Fabric ,carpet and rugs tend to be manufactured in feet,yards andells .In Palladian or

Greek Revival architecture as inJefferson classic revival , 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 thevolute . One interface between proportion and dimension is the Egyptian inscription grid. Gridcoordinate s can be used for things like unitrise and run .The architectural

foot as a reference to thehuman 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 themodular s used in Building materials. Elsewhere it is amultiple of palms, hands and fingers which are the primary referents. Feet were usually divided into palms or hands, multiples of which were alsoremen andcubit s.The first known foot referenced as a standard was from

Sumer , where arod at the feet of a statue ofGudea ofLagash from around2575 BC is divided into a foot and other units.Egypt ian foot units have the same length as Mesopotamian foot units, but are divided into palms rather than hands converting theproportional division s fromsexagesimal toseptenary units. In both cases feet are further subdivided intodigits .In

Ancient Greece , there are several different foot standards generally referred to in the literature asshort ,median andlong which give rise to differentarchitectural style s known as Ionic, and Doric in discussions of theclassical order s of architecture. The Roman foot orpes 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 byIndia (Meluhha ),Pakistan ,Beluchistan ,Oman (Makkan),Iran ,Iraq ,Kuwait ,Bahrain (Dilmun ), theUnited Arab Emirates andSaudi Arabia where in Persian architecture it is a sub division of theGreat circle of the earth into 360 degrees. InEgypt , one degree was 10 Itrw orRiver journey s. In Greece a degree was 60 Mia chillioi or thousands and comprised 600stadia , with onestadion divided into 600pous 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. OneNautical mile was 10 stadia or 6000 feet. The incorporation of proportions which relate the building to the earth it stands on are calledsacred geometry .**Vitruvian proportion**Vitruvius described as the principal source of proportion among the orders the 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 Romanarchitect 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

* acubit 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 is one-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 faceLeonardo 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 Greeks 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 asunit 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 ofcathedrals and othersacred 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 proportions were thought to have a recognisable harmonic significance, regardless of whether they were perceived visually or 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 the perception of harmony was somewhat of a break from the Pythagorean ideal of numbers controlling all things.

Leonardo da Vinci's

Vitruvian Man is an example of a Renaissance codification of the Vitruvian view of the proportions of man. Divina proportione took the idea of thegolden ratio and introduced it to the Renaissance architects. Both Palladio and Alberti produced proportional systems for classically-based architecture.Alberti's system was based on the Pythagorean divisions of the octave. It grouped the small whole-number proportions into 3 groups, short (1:1, 2:3, 3:4), medium (1:2, 4:9, 9:16) and long (1:3, 3:8, 1:4).

Palladio's system was based on similar proportions with the addition of the square root of 2 into the mix. 1:1, 1:1.414..., 3:4, 2:3, 3:5. [

*[*] .*http://www.aboutscotland.com/harmony/prop4.html Harmony and Proportion, J. Boyd-Brent*]The work of de Chambray, Desgodetz and Perrault [

*Tzonis and Lefaivre, 1986, p. 39.*] 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 thegolden ratio andVitruvian 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. The modulor is not well suited to introduce proportion and pattern into architecture (Langhein, 2005), to improve its form qualities (gestalt pragnance) and introduce shape grammar in design in building.**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.**ee also****Footnotes****References*** Tzonis, A. and Lefaivre L., "Classical Architecture: The Poetics of Order" (1986), MIT Press. ISBN 0-262-20059-7

* [*http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv4-05 Dictionary of the History of Ideas, Pythagorean Harmony*]

* 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/essay10.htm*]**Architectural References*** 30. R. A. Cordingley Section:Book reference after author|Year=1951|Title=Norman's Parallel of the Orders of Architecture|Publisher=Alex Trianti Ltd|ID=

**Classical References*** 23. Vitruvius Section:Book reference after author|Year=1960|Title=The Ten Books on Architecture|Publisher=Dover|ID=

* 24. Claudias Ptolemy Section:Book reference after author|Year=1991|Title=The Geography|Publisher=Dover|ID=ISBN 048626896

* 25. Herodotus Section:Book reference after author|Year=1952|Title=The History|Publisher=William Brown|ID= War with Judah, Sennacherib, siege of 701 BC**Historical References*** 26. Michael Grant Section:Book reference after author|Year=1987|Title=The Rise of the Greeks |Publisher=Charles Scribners Sons|ID=

**Mathematical References*** 27. Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient Section:Book reference after author|Year=1976|Title=The Historical Roots of Elementary Mathematics|Publisher=Dover|ID=ISBN 0486255638

**Mensurational References*** 28. H Arthur Klein Section:Book reference after author|Year=1976|Title=The World of Measurements |Publisher=Simon and Schuster|ID=

* 29 Francis H. Moffitt Section:Book reference after author|Year=1987|Title=Surveying|Publisher=Harper & Row|ID=ISBN 0060445548**Near Eastern References*** 3. William H McNeil and Jean W Sedlar, Section:Book reference after author|Year=1962|Title=The Ancient Near East|Publisher=OUP|ID=ISBN

* 4. Andrew George, Section:Book reference after author|Year=2000|Title=The Epic of Gillgamesh|Publisher=Penguin|ID=ISBN No14-044721-0

* 5. James B. Pritchard, Section:Book reference after author|Year=1968|Title=The Ancient Near East|Publisher=OUP|ID=ISBN

* 8. Michael Roaf Section:Book reference after author|Year=1990|Title=Cultural Atlas of Mesopotamia and the Ancient Near East|Publisher=Equinox|ID=ISBN 0-8160-2218-6

* 10. Gerard Herm Section:Book reference after author|Year=1975|Title=The Phoenicians|Publisher=William Morrow^ Co. Inc.|ID=ISBN 0-688-02908-6**Egyptological References*** 13. Gardiner Section:Book reference after author|Year=1990|Title=Egyptian Grammar|Publisher=Griffith Institute|ID=ISBN 0900416351

* 14. Antonio Loprieno Section:Book reference after author|Year=1995|Title=Ancient Egyptian|Publisher=CUP|ID=ISBN 0-521-44849-2

* 15. Michael Rice Section:Book reference after author|Year=1990|Title=Egypt's Making|Publisher=Routledge|ID=ISBN 0-415-06454-6

* 16. Gillings Section:Book reference after author|Year=1972|Title=Mathematics in the time of the Pharaohs|Publisher=MIT Press|ID=ISBN 0262070456

* 17. Somers Clarke and R. Englebach Section:Book reference after author|Year=1990|Title=Ancient Egyptian Construction and Architecture|Publisher=Dover|ID=ISBN 0486264858**Linguistic References*** 18. Marie-Loise Thomsen, Section:Book reference after author|Year=1984|Title=Mesopotamia 10 The Sumerian Language |Publisher=Academic Press|ID=ISBN 87-500-3654-8

* 19. Silvia Luraghi Section:Book reference after author|Year=1990|Title=Old Hittite Sentence Structure|Publisher=Routledge|ID=ISBN 0415047358

* 20. J. P. Mallory Section:Book reference after author|Year=1989|Title=In Search of the Indo Europeans |Publisher=Thames and Hudson|ID=ISBN 050027616-1

* 21. Anne H. Groton Section:Book reference after author|Year=1995|Title=From Alpha to Omega|Publisher=Focus Information group|ID=ISBN 0941051382

* 22. Hines Section:Book reference after author|Year=1981|Title=Our Latin Heritage|Publisher=Harcourt Brace|ID=ISBN 0153894687

*Wikimedia Foundation.
2010.*