# Talk:Proportion (architecture)

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## 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 schœìnus 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
= 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.