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history/modulor/20130806-080614.txt
editor : alpha [82.65.69.145] 2013/08/06 08:06:14 _h2 the 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]], this is 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 follows the Fibonacci serie. Generating the numbers of [[Fibonacci|http://fr.wikipedia.org/wiki/Suite_de_Fibonacci]] is simple : {b F(n) = F(n-1) + F(n-2)} and this sequence has a remarquable property : the ratio of two successive Fibonacci numbers tends to the Golden Number : {pre Ø = (1+sqrt(5))/2 = {/ {+ 1 {{lambda (x) return Math.sqrt(x)} 5}} 2}, the root of x{sup 2} + x - 1 = 0 which is equivalent to (a+b)/a = a/b when a=1 and b=x : « two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to their maximum » } _p The "Golden Rectangle" - whose sides are in the golden ratio - is considered as an harmonic figure. Playing with squares generates a beautiful "spiral curve" : {center {show {@ src="data/spirale-fibonacci.jpg" height="300" width="1000" title="Fibonacci Spiral in a Golden Rectangle"}}} _p Le Corbusier built the "Série Rouge" on the value 1.13cm which should be the umbilic's height of an "ideal" 6 feet heigth man. And he built 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 goal was to have in hands a set of "magic" numbers which were supposed to help the conceptors. _p Below is a subset of these numbers rewritten in an approximation of feet and inches. {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}}] } _p The result is actually a set of numbers rather stranges and difficult to memorize and to use. And they are unused ! Note : contrary to Fibonacci, Le Corbusier had copyrighted his "discovery". No regret ! _h3 foot and inch _p Beside the Metric System, the Imperial System and the Modulor System, 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 successor of the Modulor. And you ? _p More to see here : [[RISC/GRAINS|http://marty.alain.free.fr/risc/?view=grains]]. {center {show {@ src="http://marty.alain.free.fr/risc/data/grains/immeuble/trame.jpg" height="180" width="1000" title="Using 30cm ≠ 1 foot / Alain Marty architect"}} {show {@ src="http://marty.alain.free.fr/risc/data/grains/immeuble/detail.jpg" height="180" width="1000" title="Using 2.5cm ≠ 1 inch / Alain Marty architect"}} {show {@ src="http://marty.alain.free.fr/risc/data/grains/nyls/nyls_1.jpg" height="350" width="1000" title="A house composed on 30cm/2.5cm by Alain Marty architect | The Catalan Canigou in the distance"}} }