Talk:Proportion (architecture)

Design using proportion

Design by the use of architectural proportion differs from space planning using benchmarks for the sizes of spaces. In modern architecture proportions are of little interest so long as there is enough room for a given function in a given space. Many Cad programs use blocks or objects which have the modulor sizes manufacturers have determined best suit their production. These differ depending on whether the materials have structural constraints or are designed for a particulor function. For example: Pre built cabinets generally have standard dimensions based on a 3" modulor. The spacing of joists for modulor 8' plywood is based on even divisions of a sheet. Ceiling tiles are generally based on a 2'x2' modulor and floor tiles a 1'x1' modular.

What would be different if they were based on on non modulor architectual proportions such as those found in the Greek Orders of Architecture and Medieval cathedrals is more dependence of curves and sections of curves that have harmonic relationships with other elements and break down to a human scale.Rktect 15:17, 16 July 2007 (UTC)

Remen as a Proportion to other units

The proportion of foot to remen can be either 4:5 making it the hypotenuse or 3:4 making it the side of a right triangle. If the remen is the hypotenuse of a 3:4:5 triangle then the foot is one side and the quarter another so the proportions are 3:4 quarter to foot, 4:5 foot to remen and 3:5 quarter to Remen. The quarter is 1/4 yard. The foot is 1/3 yard. The remen is

The remen may also be the side of a square whose diagonal is a cubit The proportion of remen to cubit is 4:5

The proportion of palm to remen is 1:5

The proportion of hand to remen is 1:4

The proportion of palm to foot is 1:4

The proportion of hand to foot is 1:3

The table below demonstrates a harmonious system of proportion much like the musical scales, with fourths and fifths, and other scales based on geometric divisions, diameters, circumferences, diagonals, powers, and series coordinated with the canons of architectural proportion, Pi, phi and other constants..

In Mesopotamia and Egypt the Remen could be divided into different proportions as a similar triangle with sides as fingers, palms, or hands. The Egyptians thought of the Remen as proportionate to the cubit or mh foot and palm.

They used it as the diagonal of a unit rise or run like a modern framing square. Their relatedseked gives a slope. Its convenient to think of remen as intermediate to both large and small scale elements.

Even before the Greeks like Solon, Herodotus, Pythagorus, Plato, Ptolomy, Aristotle, Eratosthenes, and the Romans like Vitruvius, there seems to be a concept that all things should be related to one another proportionally.

Its not certain whether the ideas of proportionality begin with studies of the elements of the body as they relate to scaling architecture to the needs of humans, or the divisions of urban planning laying out cities and fields to the needs of surveyors.

In all cultures the canons of proportion are proportional to reproducable standards.

In ancient cultures the standards are divisions of a degree of the earths circumference into mia chillioi, mille passus, and stadia.

Stadia, are used to lay out city blocks, roads, large public buildings and fields

Fields are divided into acres using as their sides, furlongs, perches, cords, rods, fathoms, paces, yards, cubits, and remen which are proportional to miles and stadia

Buildings are divided into feet, hands, palms and fingers, which are also systematized to the sides of agricultural units.

Inside buildings the elements of the architectural design follow the canons of proportion of the the inscription grids based on body measures and the orders of architectural components.

In manufacturing the same unit fraction proportions are systematized to the length and width of boards, cloth and manufactured goods.

The unit fractions used are generally the best sexigesimal factors, three quarters, halves, 3rds, fourths, fifths, sixths, sevenths, eighths, tenths, unidecimals, sixteenths and their inverses used as a doubling system

Greek Remen generally have long, median and short forms with their sides related geometrically as arithmetric or geometric series based on hands and feet.

• The Egyptian bd is 300 mm and its remen is 375 mm. the proportion is 1:1.25
• The Ionian pous and Roman pes are a short foot measuring 296 mm their remen is 370 mm
• the Old English foot is 3 hands (15 digits of 20.32 mm) = 304.8 mm and its remen is 381 mm
• The Modern English foot is 12 inches of 25.4 mm = 304.8 mm and its remen is 381 mm (15")
• The Attic pous measures 308.4 mm its remen is 385.5
• The Athenian pous measures 316 mm and is considered of median length its remen is 395 mm
• Long pous are actually Remen (4 hands) and pygons
• See cubit for the discussion of the choice of division into hands or palms
• See the table below for proportions relative to other ancient Mediterranean units

Roman Remen generally have long, and short forms with their sides related geometrically as arithmetric or geometric series based on fingers palms and feet.

By Roman times the Remen is standardized as the diagonal of a 3:4:5 triangle with one side a palmus and another a pes. The Remen and similar forms of sacred geometry formed the basis of the later system of Roman architectural proportions as described by Vitruvius.

Generally the sexagesimal (base-six) or decimal (base-ten) multiples have Mesopotamian origins while the septenary (base-seven) multiples have Egyptian origins.

Unit Proportions to Greek Remen

Unit	Finger	Culture	Metric	Palm	Hand	Foot	Remen	Pace	Fathom
(1 ŝuŝi	1 (little finger)	Mesop	14.49 mm		.2	0.067	0.05
1 ŝushi	1 (ring finger)	Mesop	16.67 mm		.2	0.67	0.05
1 shushi	1 (ring finger)	Mesop	17 mm		.2	0.67	0.05
1 digitus	1 (long finger)	Roman	18.5 mm	.25		0.0625	0.04
1 dj	1 (long finger)	Egyptian	18.75 mm	.25		0.0625	0.04
1 daktylos	1 (index finger)	Greek	19.275 mm		.2	0.067	0.04
1 uban	1 (index finger)	Mesop	.2		.2	0.067	0.04
1 finger	1 (index finger)	Old English	20.32 mm		.2	0.067	0.045
1 inch	(thumb)	English	25.4 mm			0.083	.067
1 uncia	(thumb or inch)	Roman	24.7 mm	.25		0.083	.067
1 condylos	2 (daktylos)	Greek	38.55 mm	.5		2	.1
1 palaiste, palm	4 (daktylos)	Greek	77.1 mm	1		0.25	.2
1 palaistos, hand	5 (daktylos)	Greek	96.375 mm		1	0.333	.25
1 hand	5 (fingers)	English	101.6mm		1	0.333	.25
1 dichas,	8 (daktylos)	Greek	154.2 mm	2		0.5	.4
1 spithame	12 (daktylos)	Greek	231.3 mm	3		.75	.6
1 pous, foot of 4 palms	16 (daktylos)	Ionian Greek	296 mm	4		1	.8
1 pes, foot	16 (digitus)	Roman	296.4 mm	4		1	.8
1 uban, foot	15 (uban)	Mesop	300 mm		3	1	.75
1 bd, foot	16 (dj)	Egyptian	300 mm	4		1	.8
1 foote(3 hands)	15 (fingers)	Old English	304.8 mm		3	1	.75
1 foot, (12 inches)	16 (inches)	English	308.4 mm		3	1	.75
1 pous, foot of 4 palms	16 (daktylos)	Attic Greek	308.4 mm	4		1	.8
1 pous, foot of 3 hands	15 (daktylos)	Athenian Greek	316 mm	4		1	.8
1 pygon, remen	20 (daktylos)	Greek	385.5 mm	5	1.25	1.25	1
1 pechya, cubit	24 (daktylos)	Greek	462.6 mm	6		1.5	1.1
1 cubit of 17.6" 6 palms	25 (fingers)	Egyptian	450 mm	6		1.5	1.3
1 cubit of 19.2" 5 hands	25 (fingers)	English	480 mm		5	1.62	1.3
1 mh royal cubit	28 (dj)	Egyptian	525 mm	7		2.33	1.4
1 bema	40 (daktylos)	Greek	771 mm	10		2.5	2
1 yard	48 (finger)	English	975.36 mm	12		3	2.4
1 xylon	72 (daktylos)	Greek	1.3878 m	18		4.55	3.64
1 passus pace	80 (digitus)	Roman	1.542 m	20		5	4	1
1 orguia	96 (daktylos)	Greek	1.8504 m	24		6	5		1
1 akaina	160 (daktylos)	Greek	3.084 m	40		10	8	2
1 English rod	264 (fingers)	English	5.365 m	66		16.5	13.2		1
1 hayt	280 (dj)	Egyptian	5.397 m	70		17.5	14		3
1 perch	1,056 (fingers)	English	20.3544 m	264		66	53.4		11
1 plethron	1,600 (daktylos)	Greek	30.84 m	400		100	80	20
1 actus	1,920 (digitus)	Roman	37.008 m	480		120	96	24	20
khet side of 100 royal cubits	2,800 (dj)	Egyptian	53.97 m	700		175	140	35
iku side	3,600 (ŝushi)	Mesop	60m		720	240	180	48	40
acre side	3,333 (daktylos)	English	64.359 m	835		208.71	168.9
1 stade of Eratosthenes	8,400 (dj)	Egyptian	157.5 m	2100		525	420	84	70
1 stade	8,100 (shushi)	Persian	162 m		2700	900	525	85
1 minute	9,600 (daktylos)	Egyptian	180 m	2400		600	480	96	80
1 stadion 600 pous	9,600 (daktylos)	Greek	185 m	2400		600	480	96	80
1 stadium625 pes	9,600 (daktylos)	Roman	185 m	2400		625	500	100
1 furlong 625 pes	10,000 (digitus)	Roman	185.0 m	2640		660	528	132	88
1 furlong 600 pous	9900 (daktylos)	English	185.0 m	1980		660	528	132	88
1 Olympic Stadion 600 pous	10,000 (daktylos)	Greek	192.8 m	2500		625	500	100
1 furlong 625 fote	10,000(fingers)	Old English	203.2 m	2500		635	500	100
1 stade	11,520 (daktylos)	Persian	222 m	2880		720	576	144	120
1 cable	11,520 (daktylos)	English	222 m	2880		720	576	144	120
1 furlong 660 feet	10,560 (inches)	English	268.2 m	2640		660	528	132	110
1 diaulos	19,200 (daktylos)	Greek	370 m	4800		1,200	960	192	160
1 English myle	75,000(fingers)	Old English	1.524 km		15000	5,000	4000	800
1 mia chilioi	80,000 (daktylos)	Greek	1.628352 km	20,000		5,000	1000
1 mile	84,480 (fingers)	English	1.628352 km	21,120		5,280	4224	1056	880
1 dolichos	115,200 (daktylos)	Greek	2.22 km	28,800	7,200	5760	4800
1 stadia of Xenophon	280,000 (daktylos)	Greek	5.397 km	70,000		17,500	1400	3500
1/10 degree	560,000 (daktylos)	Greek	10.797 km	140,000		35,000	2800	7000
1 schϓnus	576,000 (daktylos)Z	Greek	11.1 km	144,000		36,000	288000	28800	24000
1 stathmos	1,280,000 (daktylos)	Greek	24.672 km	320,000		80,000	64000	16000
1 degree	5,760,000 (digitus)	Roman	111 km	1,440,000		360,000	288000	72000	60000

1 daktulos (pl. daktuloi), digit

= 1/16 pous

1 condulos

= 1/8 pous

1 palaiste, palm

= ¼ pous

1 dikhas

= ½ pous

1 spithame, span

= ¾ pous

1 pous (pl. podes), foot

≈ 316 mm, said to be 3/5 Egyptian royal cubit. There are variations, from 296 mm (Ionic) to 326 mm (Doric)

1 pugon, Homeric cubit

= 1¼ podes

1 pechua, cubit

= 1½ podes ≈ 47.4 cm

1 bema, pace

= 2½ podes

1 khulon

= 4½ podes

1 orguia, fathom

= 6 podes

1 akaina

= 10 podes

1 plethron (pl. plethra)

= 100 podes, a cord measure

1 stadion (pl. stadia)

= 6 plethra = 600 podes ≈ 185.4 m

1 diaulos (pl. diauloi)

= 2 stadia, only used for the Olympic footrace introduced in 724 BC

1 dolikhos

= 6 or 12 diauloi. Only used for the Olympic foot race introduced in 720 BC

1 parasanges

= 30 stadia ≈ 5.5 km. Persian measure used by Xenophon, for instance

1 skhoinos (pl. skhoinoi, lit. "reefs")

= 60 stadia ≈ 11.1 km (usually), based on Egyptian river measure iter or atur, for variants see there

1 stathmos

≈ 25 km, one day's journey. May have been variable, dependent on terrain

For variant, the stadion at Olympia measures 192.3 m. With a widespread use throughout antiquity, there were many variants of a stadion, from as short as 157.5 m up to 222 m, but it is usually stated as 185 m.

The Greek root stadios means 'to have standing'. Stadions are used to measure the sides of fields.

In the time of Herodotus, the standard Attic stadion used for distance measure is 600 pous of 308.4 mm equal to 185 m. so that 600 stadia equal one degree and are combined at 8 to a mia chilioi or thousand which measures the boustredon or path of yoked oxen as a distance of a thousand orguia, taken as one orguia wide which defines an aroura or thousand of land and at 10 agros or chains equal to one nautical mile of 1850 m.

Several centuries later, Marinus and Ptolemy used 500 stadia to a degree, but their stadia were composed of 600 Remen of 370 mm and measured 222 m, so the measuRement of the degree was the same.

The same is also true for Eratosthenes, who used 700 stadia of 157.5 m or 300 Egyptian royal cubits to a degree, and for Aristotle, Posidonius, and Archimedes, whose stadia likewise measured the same degree.

The 1771 Encyclopædia Britannica mentions a measure named acæna which was a rod ten (Greek) feet long used in measuring land.

Cleanup—Wikify

This article has good material, but in style and format it does not conform to WP:MOS in many respects. It lacks a lead sentence that defines the topic of the article in its context. Much of what is in the lead section is disorganized, and much of its material belongs under appropriate headings. There are insufficient wikilinks, specially in the lead section. Also, the article must, first and foremost, address the needs of the general reader. For example, many readers will not know who Vitruvius (who must be linked in the lead!) is or when he worked. The citations need reworking to conform to WP:CITE. The use of "hard" (as opposed to automatically) numbered references is unacceptable, as it makes it too difficult for editors to add a reference? Also, the use of stray numbers throughout the text to refer to the numbered references does not conform to Wikipedia style, and more importantly may not be understood by the general reader. There are also many statements of opinion or conclusions that lack source citations. Finell (Talk) 21:52, 2 August 2007 (UTC)

Thanks for the helpful style references, that was a much better solution than reverting. I added a lead sentence (Though I wish the name of the article was something more along the lines of Architectural proportions) added some wikilinks; and replaced the hard numbers with a reflist but I still don't know how to get them to go directly to the numbered list of books and pages cited. In terms of making it better organized, I'd like to see it give more examples of how proportion was used in antiquity and more on why the use of proportiion has been almost entirely replaced with the use of modulors.Rktect 10:35, 13 August 2007 (UTC)

Wiki Education assignment: Architectural History

This article was the subject of a Wiki Education Foundation-supported course assignment, between 28 August 2023 and 8 December 2023. Further details are available on the course page. Student editor(s): StellaWitch (article contribs).

— Assignment last updated by StellaWitch (talk) 02:24, 4 October 2023 (UTC)