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history/modulor/20130805-182648.txt
editor : alpha [82.249.167.200] 2013/08/05 18:26:48 _h1 modulor vs foot/inch _p Following the strange and complex (and unused) [[Modulor|http://ww3.ac-poitiers.fr/arts_p/b@lise14/pageshtm/page_7.htm]], a personal reflexion about usual dimensions based on simple "human" combinations of two values coming from the ancient days : the foot, (≠30cm) and the inch (≠2.5cm) ? _h3 the modulor {center {show {@ src="http://marty.alain.free.fr/risc/data/grains/echelles/modulor_1.jpg" height="150" width="600" title="Usual dimensions with Le Corbusier"}} {show {@ src="http://marty.alain.free.fr/risc/data/grains/echelles/modulor_2.jpg" height="150" width="600" title="Série Rouge et Série Bleue from Le Corbusier"}} {show {@ src="http://marty.alain.free.fr/risc/data/grains/echelles/modulo.jpg" height="150" width="600" title="Usual dimensions with the Imperial System ... and Alain Marty's 5%"}} {show {@ src="http://mamo.fr/wp-content/uploads/2013/04/modulor4-640x284.jpg" height="240" width="1000" title="Usual dimensions with Le Corbusier"}} } _p The "Série Rouge" and "Série Bleue" imagined by Le Corbusier follow the Fibonacci serie. The ratio of two Fibonacci numbers tends to the Golden Number : {pre Ø = (1+sqrt(5))/2 = {/ {+ 1 {{lambda (x) return Math.sqrt(x)} 5}} 2} } _p Le Corbusier built the "Série Rouge" on the value 1.13cm which should be the umbilic's height of a 6 feet heigth man. And the "Série Bleue" on the value 2.26cm (2*1.13cm) which is the height reached by his hand when the arm is raised up. Why not !! The result is a set of numbers difficult to use. And they are actually unused ! {pre {@ style="float:left;width:150px;margin:5px;"} FIBONACCI 1: 2/1 3: 3/2 5: 5/3 8: 8/5 13: 13/8 21: 21/13 34: 34/21 55: 55/34 89: 89/55 144: 144/89 233: 233/144 SERIE ROUGE sur m = 1.13cm * m Ø Ø Ø * m Ø Ø * m Ø m / m Ø / m Ø Ø / m Ø Ø Ø SERIE BLEUE with M = 2.26cm * M Ø Ø Ø * M Ø Ø * M Ø M / M Ø / M Ø Ø / M Ø Ø Ø } {pre {@ style="float:left;width:180px;;margin:5px;"} {/ 2 1} {/ 3 2} {/ 5 3} {/ 8 5} {/ 13 8} {/ 21 13} {/ 34 21} {/ 55 34} {/ 89 55} {/ 144 89} {/ 233 144} SERIE ROUGE {* 1.13 1.618 1.618 1.618} {* 1.13 1.618 1.618} {* 1.13 1.618} 1.13 cm {/ 1.13 1.618} {/ 1.13 1.618 1.618} {/ 1.13 1.618 1.618 1.618} {* 2.26 1.618 1.618 1.618} {* 2.26 1.618 1.618} {* 2.26 1.618} 2.26 cm {/ 2.26 1.618} {/ 2.26 1.618 1.618} {/ 2.26 1.618 1.618 1.618} } {pre {@ style="float:left;width:200px;;margin:5px;"} -> Ø = {/ {+ 1 {{lambda (x) return Math.sqrt(x)} 5}} 2} 1' = 30.48cm, 1" = 2.54cm ≠ 30cm ≠ 2.5cm ≠ 4.775 = 16' - 1" [{- {* 16 0.30} {* 1 0.025}}] ≠ 2.950 = 10' - 2" [{- {* 10 0.30} {* 2 0.025}}] ≠ 1.825 = 6' + 1" [{+ {* 6 0.30} {* 1 0.025}}] ≠ 1.125 = 4' - 3" [{- {* 4 0.30} {* 3 0.025}}] ≠ 0.700 = 2' + 4" [{+ {* 2 0.30} {* 4 0.025}}] ≠ 0.425 = 1' + 5" [{+ {* 1 0.30} {* 5 0.025}}] ≠ 0.250 = 1' - 2" [{- {* 1 0.30} {* 2 0.025}}] ≠ 9.575 = 32' - 1" [{- {* 32 0.30} {* 1 0.025}}] ≠ 5.900 = 20' - 4" [{- {* 20 0.30} {* 4 0.025}}] ≠ 3.650 = 12' + 2" [{+ {* 12 0.30} {* 2 0.025}}] ≠ 2.250 = 7' + 6" [{+ {* 7 0.30} {* 6 0.025}}] ≠ 1.400 = 5' - 4" [{- {* 5 0.30} {* 4 0.025}}] ≠ 0.850 = 3' - 2" [{- {* 3 0.30} {* 2 0.025}}] ≠ 0.525 = 2' - 3" [{- {* 2 0.30} {* 3 0.025}}] } _h3 foot and inch _p It appears that in the architectural domain, usual dimensions can be easily reached by a simple combination of feet and inches in the approximation {b 1 foot = 30.48cm ≠ 30cm} and {b 1 inch = 2.54cm ≠ 2.5cm}. Examples : _ul a seat : 45cm = 1.5' _ul a table : 75cm = 2.5' _ul a kitchen work desk : 90cm = 3' _ul a man : 180cm = 6' _ul a woman : 165cm = 5.5' _ul a standard door's dimensions : 210cmx90cm = 7'x3' _ul ceiling's heights : 225cm = 7'6", 240cm = 8', 250cm = 8'4", 270 = 9' _ul a little room : 270cmx270cm = 9'x9' and a better one : 360cmx360cm = 12'x12' _ul passage unit : 60cm = 2' (which is also the step of the man who walks) _ul stairs formula : 2h+g in [60,65] : for g = 30cm = 1' h must be between 15cm = 0.5' and 17.5cm = 0.5' 1" _ul thickness of a standard plasterboard : 12,7mm = 1/2". Other thickness are 4/12" and 8/12". Two plasterboards makes one inch (1/2"+1/2"), and improve the acoustic behaviour of the partition. With two plasterboards with different thickness (4/12" + 8/12"), the frequencies of resonance will be different and the filter better. Thinking to this in the Metric System is very difficult, not in the Imperial System ! _ul more to say about the ducts diameters and so on ... _p So, with this simple set : {b [2.5,30]}, it is possible to generate a serie of useful related values : {pre 30 / 2 = 15 / 2 = 7.5 / 3 = 2.5 (or 1/2'=6", 1/4'=3", 1/12'=1") then 2.5 | 5 | 7.5 | 10.0 |12.5 | 15 | 17.5 | 20.0 | 22.5 | 25 | 27.5 | 30 and 45 | 60 | 75 | 90 | 105 | 120 | 135 | 150 | 165 | 180 | 195 | 210 |.. and also 50 = 45 + 5 = 1.5'2", 100 = 90 + 10 = 3'4", ..... } _p These values are easy to memorize and combine, and are compatible with the values coming from the Metric System (12.5, 25.0, 100, ...). This system coming with a ligth approximation of the foot and the inch makes the junction between the "Imperial System" and the "Metric System" in respect to the old measures of the ancient days ... _h3 the ancient days _p All these considerations look so "Middle Age" and at least not reasonable at all ! And if so, why are the foot and the inch used in the Modern Computer Technologies ? Why are the dimensions of a screen, of a pixel, of a font, of a page, are given in inches and not in centimeters ? Is it because of the predominance of the USA in these technologies. Whatever it may be, my experience as an architect confirmed the fact that it is a very good tool for conception in architecture, even if the dimensions are finally written in centimeters. The conceptual background is made of feet and inches. The Modulor was an attempt to fight against the Metric System, inappropriated in the building construction. But it was too complex, the Le Corbusier's "Série Rouge" and "Série Bleue" can't be easily used and they are not used. I think that the idea of a "little smart modulor" made on gentle combinations of feet and inches can be an acceptable and useful follower of the Modulor. And you ? _p More to see here : [[RISC/GRAINS|http://marty.alain.free.fr/risc/?view=grains]].