proportion and architectural theory le modulor, neil eldem

Proportion and Architectural Theory

A critical enquiry on Le Corbusier’s approach to mathematical systems of proportion; and how did this influenced his creativity and his interpretation of the Golden Section into the Modulor.

Is the Modulor: True; or Useful; or Reconcile?

Neil Eldem BA (Hons),DipArch Associate Member of Royal Institute of British Architects RIBA PartII Architect

Except where stated otherwise, this dissertation is based entirely on the author’s own work

Acknowledgements I oblige a debt of gratefulness to my dissertation tutor Alan Powers. Whom I feel privileged to have had as my tutor. Thank you Alan for the benefit of your encyclopaedic knowledge, your infectious energy and enthusiasm and for the insightful guidance you have provided me. I would express my gratefulness and appreciations to Howard Gilby who gave me the opportunity to study at Greenwich University. Special thanks to those all authors of all the materials I have been reading and the individuals who make the effort to freely share their knowledge, experience and media. Thank you all....

For the memory of my father and love of my mother

“I dedicate this study of beauty to my beloved family, who gave me the benefit and the privilege to be loved and supported by.”

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Contents Cover Title Page Acknowledgements Content Page & Word Count List of Figures and their sources Epigram Introduction Chapter 1 Chapter 2 Conclusion Bibliography

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List of Figures:

Figure number Figure details Source of information

Figure 1.

Vitruvian man, Leonardo da Vinci, Cover page, layer 1

Thought and Art, Web source

Figures 2,3

Le Corbusier’s concept of body proportion, illustrated with the Vitruvian man Cover page, layer 2

Foundation of Le Corbusier

Figure 4.

Le Modulor ,the Modulor ribbon

Le Corbusier, the Modulor, Faber & Faber , 1954

Figure 5.

Le Modulor, the modulor vertical body proportion


Figure 6.



Figure 7.


Foundation of Le Corbusier

Figure 8. The Parthenon, Athena, Greece

Wikipedia, Web Encyclopaedia. Image library

Figure 9. The theory of the golden spiral and the link to belt of Orion.

Wikipedia, Web Encyclopaedia. Image library

Figure 10. Flower with 3 petals Google image search

Figure 11. Daisy with 13 successive petals. Google image search

Figure 12. Illustration of daisy pack. Google image search

Figures 13. 14. Illustration of Fibonacci numbers in the pack of the daisy.

Google image search

Figure 15. The Museum of Harmony and the Golden Section.

The Museum of Harmony and the Golden Section. Image gallery

Figure 16. Painting of Mona Lisa, by Leonardo Da Vinci.

Web source, joma.org/monalisa

Figure 17. Painting of Saint Jerome, by Leonardo Da Vinci.

Web source, joma.org/saintjerome

Figure 18.

Vitruvian man, by Leonardo da Vinci,

Thought and Art, Web source

Figure 19.

The Ancient Egyptian Pyramids Google image search

Figure 20.

The Ancient Egyptian Pyramid illustration of Phi

Google image search

Figure 21.

La Chaux-de-Fonds Brooks Le Corbusier’s Formative Years

Figure 22.

1908 Edouard Jeanneret Brooks Le Corbusier’s Formative Years

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Figure 23.

Le Cabanon, Roquebrune-Cap-Martin

http://www.fondationlecorbusier.asso.fr/ fondationlc_us.htm

Figure 24.

Le Modulor ,the Modulor measures


Figure 25.

Le Corbusier with Le Modulor related model.

http://tesugen.com/pictures/le-corbusier-chandigarh.jpg

Figure 26.

Le Corbusier in the Atelier at 35 rue de Sevres,

http://3.bp.blogspot.com/corbusier.jpg

Figure 27.

Villa La Roche-Jeanneret, Paris,

www.panoramio.com/photos/original

Figure 28.

.Internal view of Villa La Roche www.flickr.com/villalaroche

Figure 29.

.Le Corbusier’s drawings of Villa Stein.


Figure 30.

.Le Corbusier’s drawings of Villa Stein.


Figures 31.32.

Le Corbusier’s drawings of Villa Stein floor plans


Figure 33.

1914 Dom-Ino project http://www.fondationlecorbusier.asso.fr/ fondationlc_us.htm

Figure 34. Dom-Ino housing Brooks Le Corbusier’s Formative Years

Figure 35. Dom-Ino housing Brooks Le Corbusier’s Formative Years

Figure 36. Dom-Ino housing Ruegg Le Corbusier before Le Corbusier

Figure 37. Pilotis at the Unité Adams Columns

Figure 38. Béton brut at the Unité Marseille.

Le Corbusier in Detail Flora

Figure 39. Sectional view of the Unité http://www.villes-en-france.org/histoire/ aimacorbu/corbui.jpg

Figure 40. Main communal Corridor at Unité

By James Raw,

Figure 41. Main communal Corridor at Unité

Anonymously taken from web search

Figure 42. The Facade of the Unité


Figure 43. The aerial view of the Unité


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My dream is to set up, on building sites which will spring up all over our country one day, `grid of proportions`, drawn on the wall or made of strip iron, which will serve as a rule for the whole project, a norm offering an endless serious of different combinations and proportions; the mason, the carpenter, the joiner will consult it whenever they have to choose the measures for their work; and all things they make different and varied as they are, will be united in harmony. That is my dream!

Le Corbusier

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In the Ancient world it was believed that the nature has got a harmonies beauty governed by mathematical rules and laws, and that the nature regulates everything in its order. During the Renaissance the Ancient Golden Ratio and Golden Section were used nearly in every building and also in paintings and some other arts. This brought the Golden Ratio into a new world of questions and understandings. However, In the light of scientific revolutions of the seventeen century, and the empiricist philosophy that followed from it was shaken. The universal values that had formerly provided the objective foundation of proportion system were rejected in the absence of such values; art was bound to fall back on individual subjective

judgement.1

It seems rather disappointing that the debate loses its importance; because power of the golden section and mathematical order of laws such that they keep their significance even in the twentieth century and the philosophical ground for using mathematical ordering systems in art and architecture remains valid.

I expand my research on Le Corbusier and his ‘Le Modulor’ by debating his ‘nature is ruled by mathematics and masterpieces of art...’ expressed the laws of nature and themselves proceed from those laws’ and that by arguing his endless effort believing in the mathematical order of forms and his endeavour to develop a universal tool that can be a reference and that used to a simple or mass production of our needs. 2

1. R. Wittkower, The changing concept of proportion, in he the Idea and Image, Studies in the Italian Renaissance, Thames & Hudson, 1978, pg 117,122

2. Le Corbusier, The Modulor, Faber & Faber, 1961,pg29-30

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Figure 5. Le Corbusier, Le Modulor, Faber & Faber, 1961,

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Chapter 1

Le Corbusier believed that the golden section holds the definitive proportions of human body, and it can be constructed geometrically by finding ‘the place of right angle’ slightly off-centre with a double square. He believed that nature is ruled by mathematics and master pieces of art and he added that ‘only nature is inspiring and true and should be the support of human endeavour’.

Departing from ‘traces regulateurs’ in mid 1940s, Le Corbusier developed a more flexible system of proportion, a scale of dimensions by using height of a six feet man and constituting two interwoven progression. He stated that his aim was to make a measuring instrument that was more subtle, more organic and better attuned to human dimensions rather than either metric system or the system of feet and inches. 3

Inspired by Leonardo da Vinci’s human proportion; Le Corbusier explicitly used the golden ratio and experimented in order to develop his own catalogue of measures combines a blue serious of numbers the total Golden Section in height and a red serious of numbers - height of the navel-resulting a sequence of measures starts from 27 cm and ends 226 cm.

However, Richard Padovan believes that the primary relation between nature, art and mathematics is a matter of believe and faith and perception rather than reason or experiential facts and knowledge. He considers that Le Corbusier wanted to tell the story as an exciting voyage of discovery, and his book Le Modulor is rather an autobiographical than a system of measures and proportions, as he is perpetually laying false trails, designed to make him appear even more innovative and original than he really was.4

Figure 6 . Le Corbusier’s concept of proportion, proportion showing the vertical human body scale

Table 1. Blue and Red Series

Blue measures (m) 2.26 3.66 5.92 9.57 15.49 25.07

Red measures (m) 1.83 2.96 4.79 7.74 12.53 20.28

Figure 7. Le Corbusier’s study of proportion showing the vertical human body scale

3. Richard Padovan, Proportion, Science Philosophy Architecture Spon Press 1999, pg.321

4. H.A. Brooks, Le Corbusier Formative Years, University of Chicago Press, 1997,p 245-7

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Planning in proportions caused by aesthetic reasons in Le Corbusier’s Le Modulor. He works up to this later treatise with different proportional systems in his early years of employment at Behrens and study of Lauweriks' designs in the manifesto ‘Vers une architecture’. Written in a prophetic tone like all of his books, delivers speeches as it from a different time and world, as a predictive visionary.

Using "tracés regulateurs", measure-ruler, Le Corbusier tries to control the geometrical system of design, as it always façades in his examples. The geometrical figures of the measure-ruler themselves are at the architect's liking, but Le Corbusier presents only a few, and his examples strongly resemble those in Auguste Choisy's history of architecture, who also delivers Le Corbusier's figures5.

In his most important tract, Le Modulor (1948), Le Corbusier mentions his model, when he tells a story of discovery with postcards in his small Paris apartment, which he states should have happened in 1909. Then he narrates the development of his own system of measures, Le Modulor, beginning with an order by the office for standardization in Vichy-France (AFNor) in 1943. Till then he seemed to have organised designs for façades and paintings in a spontaneous and unsystematic manner by means of tracés regulateurs and Golden Mean, although post festum perhaps; the examples in possibly only then, through Neufert's Bauordnungslehre, did Le Corbusier receive the inspiration to systematize and organize consequently his tracés regulateurs idea 6

Before investigating the system of proportion and Le Corbusier’s universal measures of proportion sets out in Le Modulor explicitly, first I will look at theory of beauty and proportion with its relation to human sentiments and their influence in art and architecture in conjunction with golden ratio.

5. H.A. Brooks, Le Corbusier

Formative Years, University of Chicago Press, 1997,p 65

6. Herz-Fischler, Roger. 1998. A Mathematical History of the Golden Number. Mineola, NY: Dover. P 213

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Search for the beauty

Since early time of human, artists have been searching for the divine and the sacred proportion and various aspects of geometric and mathematical order, visual impacts of its beauty and mutual harmony that indeed have been coded in our god given divine creation; as it has believed, and proportion is the first and principal subject of architectural theory. Which pronounces the best aesthetic, function and meaning within us, a reflection of God himself in human, the perfection of God, the God within, his image within us?

The Greek geometer, Pythagoras was especially interested in the golden section, and proved that it was the basis for the proportions of the human figure. He showed that the human body is built with each part in a definite golden proportion to all the other. Hence, in a sense to believe that the whole

Figure 8. The Parthenon was perhaps the best example of a mathematical approach to art. Once its ruined triangular pediment is restored, the ancient temple fits almost precisely into a golden rectangle further classic subdivisions of the rectangle align perfectly with major architectural features of the structure

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content of the universe and the nature directly projected into the human mind by God; and is this illusion of the human sentiments give rise to beauty and its understanding or; a real phenomenon of the human mind reflecting primary resources of the real consciousness of the men receives from God.

In the Ancient world and today the inspiration and enthusiasm for golden proportion, golden aesthetic, golden beauty and its harmony and golden module has always been a question; which the answer hidden beneath our lives, in our feelings and in our motions, in our activities in our refined responses to; and understanding of the nature and environment we live in. The search for coherent and consistence beauty and its precise measures which constitutes the harmonic codes of nature; the objects that it is perfect with its identity of proportion and unity of the elements combines the beauty that a human eye

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the observer’s perspective. From this we can understand the phenomenon of beauty, cannot be given in a fixed rule. Thus changes according to the

movements and motions of human beings4 and their

cultural conditioning.

Although the human eye is subject to such subjective empirical recognition of harmonic beauty and relation, is there any universal law of mathematical system that constitute a true order of proportions, which defines and forms the perfect proportion and the ratio in our creation and in nature?

Figure 10. Probably most of us have never taken the time to examine very carefully the number or arrangement of petals on a flower. If we were to do so, several things would become apparent. First, we would find that the number of petals on a flower is often one of the Fibonacci numbers.

Are there any general rules of proportion distinguish one from another to determine our wishes into a definite proportional satisfaction?

Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics. The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself, yielding the sequence 0, 1, 1, 2, 3, 5, 8, etc. In mathematical terms, it is defined by the following recurrence relation

Figure 11. The petals of this daisy consist of successive expression of the Fibonacci numbers, in total 13.

Figure 12. The pack of the daisy spirals counter-clockwise successively and consists of the Fibonacci numbers of total 13.

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Figure 13. Illustration of Fibonacci numbers in the pack of the daisy.

In the close-packed arrangement of tiny florets in the core of a daisy blossom, we can see the phenomenon in almost two-dimensional form. The eye sees twenty-one counter-clockwise and thirty-four logarithmic or equiangular spirals. In any daisy, the combination of counter-clockwise and clockwise spirals generally consists of successive terms of the Fibonacci sequence.

Figure 14. Illustration of Fibonacci numbers in the pack of the daisy.

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Consequently, this question also applies in the arrangements of nature, art and order of forms and elements and it infuses and combines all structures, forms, proportions in both space and human being; or is this a natural order of the universe, where it shapes its forms and elements by its own rule? And is this the natural ratio that nature offers and produces such regulated relations and orders within objects in response to each other, and all the emanations of the nature is subject to collective relations of harmonic ratios?

L.B Alberti explains everything that in nature produces is regulated by the law of concinnittas*; and her chief concern is that whatever she produces

should be absolutely perfect`9. To take it to different

extend, `There is inherent in nature, a hidden harmony that reflects itself in our minds under the illustration of simple mathematical laws. That then is the reason why events in nature are predictable by combination of observation and mathematical

analyse`10 The perception of a human eye does

recognise the perfect harmonic beauty and understands the essence of its proportion, coincidently, the nature is also regulates and creates her law of equilibrium and symmetry by mathematical awareness and rules; to which those objects’ creations are regulated by mathematical instruct, geometrical truth and precision, thus the human intelligence tries to understand the phenomenon of the elements regulated or created by nature. Therefore, that part of the human and its characteristic individual approach and understanding of forms, shapes and its aesthetic may translates the object in a such way, and perhaps the nature is only reflected as in a mirror by the human and its complex creation or the human is echoed on the nature’s mirror, or;

Figure 15. The Museum of Harmony and the Golden Section. The iconic central staircase, view taken from upper floor at Vatican Library

* Concinnittas: Elegantly and skilfully joining of several things in beauty of style. In the Ancient world it represented a terminology, which indicates a particular awareness in order of forms and harmony of mathematical elements and its rhythm.

9. L.B Alberti, On the Art of Building in Ten Books, MIT Press, 1988, pg. 302-3

10. H. Weyl, lecture, quoted in M. Kline, Mathematics: The loss of Certainty, Oxford University Press, 1980, pg.347

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‘The mind regains from nature that which mind has put out into nature’, or both are the divine resources and the mathematics of the nature and the harmony, its rules and law reflection and expansion of the nature. ‘The two great subjects of the naturalistic art-the human body and the landscape – each provide an outstanding example of empathy’s projection of human object in a such way, and perhaps the nature is only reflected as in a mirror by human and its complex creation or human is echoed on the nature’s mirror, or else: into

natural.’11 These arguments which are thought

manifestly by Berkeley to prove that colours and tastes only exists in the mind, and I can therefore add that also the beauty and proportion with equal right also exist only in mind and may with the same equal force be brought to prove the same thing of extension, figure, and motion together with sentiments.12 Figure 16. Mona Lisa, by Leonardo da Vinci, illustrated with

the Golden Section.

Figure 17. Painting of Saint Jerome, by Leonardo Da Vinci.

A golden rectangle fits so neatly around the central figure that it is often said the artist deliberately painted the figure to conform to those proportions. "Geometrical Recreations"

Leonardo da Vinci's illustrations in De Divina Proportione (On the Divine Proportion) and his views that some bodily proportions exhibit the golden ratio has led some scholars to speculate that he incorporated the golden ratio in his own paintings. Some suggest that his Mona Lisa, for example, employs the golden ratio in its geometric equivalents.[24] Whether Leonardo proportioned his paintings according to the golden ratio has been the subject of intense debate. The secretive Leonardo seldom disclosed the bases of his art, and retrospective analysis of the proportions in his paintings can never be conclusive.

11. H. Weyl, lecture, quoted in M. Kline, Mathematics: The loss of Certainty, Oxford University Press, 1980, pg.347

12. G. Berkeley, the Principle of Human Knowledge, pg. 69

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Figure 18. Leonardo Da Vinci’s Illustration of the human body inscribed in the circle and the square derived from a passage about geometry and human proportions

This interrelationship of modularity and geometry is also found in the detailed analysis of the proportions of the human body Vitruvius presents his canon, the famous figure of a man in circle and square, in support of his claim that "no Temple can have a rational composition without symmetry and proportion, that is, if it has not an exact calculation of members like a well-shaped man" So the body is a model by virtue of its perfection of symmetrical shaping first and foremost and not in its inherent proportions, which is often misunderstood; The human body, as an example of modular creation from nature, is chosen by Vitruvius as a paradigm for the required rules of proportion.13

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The existing of wholeness is something real in the world, whether we choose to see it or pay attention to it or not, its mathematical structure which exist in space, and we recognise by ourselves and in our terms that it is sensible way to go forward, and that it is congruent with our deepest sensation of art and beauty and justice, which effect structure of

buildings. 14

On the other hand, to reduce beauty to geometrical truth and exactness would produce work that is

insipid and disagreeable15 Edmund Burke argues

further that ‘Method and exactness, the soul of proportion, are found rather prejudicial than

serviceable to the cause of beauty’.16

Padovan debates this that the reduction of artistic decisions and involvements to matters of taste had deeper causes, than the severing of the link between art and beauty of the visual proportion. According to Wittkower, towards the nineteen and twenty centuries the replacement of the objective or universal standards in the judgement of art by subjective and personal ones. As the objective grounds of judgement slipped away, it was natural to turn inwards: to study the mental progress of the individual artist or the individual viewer. ‘Beauty

came to lie firmly in the eye of beholder’.17

Beauty is no quality in things themselves; it exits merely in the mind which contemplates them; and each mind perceives a different beauty. One person may even perceive deformity, where another is sensible of beauty; and every individual ought to acquiesce in his own sentiment, without pretending

to regulate those of others. 18

13. Marcus Frings, "The Golden Section in Architectural Theory", Nexus Network Journal vol. 4 no. 1

14. Christopher Alexander, The Nature of Order, Book One, the Phenomenon of Life, The Centre for Environmental Structure, 2002, pg.442

15. D. Hume, ‘of the standard of taste’ in Essay, Moral, Political and Literary, Oxford University Press, 1963, p 236

16. E. Burke, a Philosophical Enquiry into the Origin of our Ideas of the Sublime and beautiful, 1756, Oxford University Press, 1990, pg 86


18. D. Hume, ‘of the standard of taste’ in Essay, Moral, Political and Literary, Oxford University Press, 1963, p 124-5

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Human sentiments and perceptive of the beauty

Padovan agrees Hume’s approach and explanations to each mind perceives of different beauty, and he qualifies this view to: Though it be certain that the beauty and deformity are not qualities in objects, but belong to the sentiment, internal or external, it must be allowed, that there are certain qualities in objects which are fitted by nature to produce those particular feelings. However, Padovan believes that this qualities cannot be said are due to a universal

laws pervading or sustaining the natural world.19

Padovan considers subjectivity has its own roots in philosophy, which than its attention from the interpretation of the physical world to the study of our mental process, and particularly of the grounds of human knowledge. Thus, he adds that the shift from the physical to the psychological sphere, from outer to inner world, had important consequences for the theory of proportion in art.

This in a way driven by the human sentiments, that tries to understand the distinguish relation between the objects and its mathematical systems of order, rules and its relation with visual beauty in a way that the human sentiments are satisfied. Christopher Alexander defines the human feelings as it is nearly the same in all human and explains in Nature of Order `The human feelings are mostly the same from person to person, and mostly the same in person. Of course there is that part of human feeling where we are all

different`20 thus, what part of the human feelings do

recognise the beauty, the most same feelings or the less same feelings. Which part of human feelings and its characteristic individual approach and understanding of forms, shapes and aesthetics do define the object and its visual beauty and proportion

19. D. Hume, ‘of the standard of taste’ in Essay, Moral, Political and Literary, Oxford University Press, 1963, p 240

20. Christopher Alexander, The Nature of Order, Book One, the Phenomenon of Life, The Centre for Environmental Structure, 2002, pg.4

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Chapter 2

‘All this work on proportioning and measures is the outcome of a passion, disinterested and detached, an exercise, a game, a preoccupation and occupation, a need and a duty, a ceaseless facing up to life, a seeking after proof, a right to march forward, a duty to be straight and loyal, dealing in honest-to-goodness, clean merchandise.’21

Le Corbusier

Early ages and Influences

‘My childhood years were spent with my family and friends among nature. My father moreover was a fervent worshipper of the mountains and river which formed our landscape. We were constantly among the mountain tops; we were always in contact with the immense horizon....’22

In his young age, Edouard Jeanneret travelled to Europe occasionally and in 1907 to Paris where he had found a job in a French pioneer of reinforced concrete, Auguste Perret. From 1910 to 1911, he worked in Berlin for Peter Behrens architect where he met with Ludwig Mies van der Rohe. His experi- ences with Mies van der Rohe and the other architect

21. Le Corbusier, the Modulor, Faber & Faber , 1954, pg 80

22. Baker, G.H. (1984) Le Corbusier: An analysis of form. (1984). Hong Kong: Van pg 16

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ce

27

Figure 23. Le Cabanon, Roquebrune-Cap-Martin, Built in 1952 Le Corbusier’s desire to personally retain a sense of nature and simplicity in his life and his career long quest to encapsulate this in a functional modular dwelling.

Of the leaders of Modernism, Le Corbusier was the only one who put systems of harmony and proportion at the centre of his design philosophy. His faith in mathematical order of universe was closely

bound with the golden section and Fibonacci series26,

Le Corbusier describes the serious as: rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of Golden Section by

children, old men, savages and learned. 27

Le Corbusier in the Modular tried to explore the mathematical links in between objects in order to form a universal law where it can be a reference to mass production in post World War I, a standardization and systems of proportion and the Modulor to be at the centre of this, setting the rules of systems and production, fabrication and manufacturing. Therefore, he believed economic and technological circumstances and needs in post World War I, force to mass produce houses and the basic, well oriented simple and functional houses can only be achieved by adopting a perfect mathematical order of forms and functions, and thus where this

Table 3. Red and Blue series, Le Modulor

Red: 0.10 0.16 0.26 0.43 0.70 1.13 1.83

Blue: 0.12 0.20 0.33 0.53 0.86 1.40 2.26



28

relations and links have simplified in his principle that he tried to out bring in the Modulor, and if has any right to existence, will only be worthy something if it is applied on a mass scale in the

dimensioning of manufactured articles.28

If economical and technological forces require the house to be mass-produced like a motor car, has not the car been perfected by its standardization, and was ‘The Parthenon is a product of selection applied to an established standard. Already for a century the Greek temple had been standardized in all its parts.’

Standardization is imposed by the law of selection and is an economic and social necessity. Harmony is a state of agreement with the norms of our universe. Beauty governs all; she is purely human creation; she is the overplus necessary only men of the highest type. But we must first of all aim at the setting up of standards in order to face the problem of

perfection.’29

Post World War I imposed economical and social restrictions and the necessity of the mass production was inevitably essential, in the meantime the aesthetic should not be abandon completely and a universal law of order and proportion in mass production must be implemented in order to achieve the functionality in a sense of a rule for whole production. Le Corbusier wanted to invent a grid of proportion and its practical use and implementing it in a fairly consistence way to all production and standardization.

In 1951 at a conference ‘On Divine Proportion’ in Milan he heard the views of historians like Rudolf Wittkower on Vitruvian, Renaissance and other systems of proportion. Long before this he surely

Figure 24. Le Corbusier’s characteristic relations of modulor measures to the human body, from Le Modulor

Figure 25. Le Corbusier with Le Modulor related model.



29

knew of Leonardo da Vinci’s illustration of Vitruvian man inscribed in a circle, and was at least intuitively aware of concept of symbolic representation through cosmic geometries in past architecture.30

Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion and functionality. He saw this system as a continuation of the long tradition of Vitruvius, Leonardo da Vinci's "Vitruvian Man", the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture. In addition to the golden ratio, Le Corbusier based the system on human measurements, Fibonacci numbers, and the double unit. He took Leonardo's suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body's height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat. The Modulor combines squares and the Golden Section, yet it does not offer anything else than a system of numbers, and it does not go beyond the Golden Ratio. The blue series of numbers reference to -golden section of the total height- and a red series -height of the navel- results a sequence of measures starts from 27 cm to 226 cm and it carries over in the same principle.31

Although Le Corbusier wanted the Modulor used for all dimensioning, both vertical and horizontal, he explicitly based it on the vertical dimension and approximation of Fibonacci numbers. In some stages the serious of red and blue numbers for no reason losses its rules of combination and it becomes so hard and elastic to follow and as a result it loses its methodology and system.

Figure 26. Le Corbusier in the Atelier at 35 rue de Sevres, Paris in early 1950s.

30. W.J.R Curtis, Le Corbusier; Ideas and Forms, Phaidon, pg 164.


30

In order to have human scale normal living spaces should be no higher than a man can reach with his raised arm, - yet he never mentions nor applies any of his proportion and scale based on a women- a dimension first set at 2.20.32

Compared with Fibonacci numbers, this is 4 times of 55. Le Corbusier assumes the height of navel to be exactly midway between the sole of the foot and the tip of the raised hand, so it is 1.10 m, or 55x2 cm. The two measures are member of blue and red series respectively. The navel is assumed to divide a man’s height by the golden section, so the height must be 89x2 cm= 178. For the clarity his system, Le Corbusier then decides for no apparent reason to reduce the man’s height from 1.78 to 1.75. This small reduction has the effect of throwing out all the dimensions so that they become very complicated, involving millimeters, and lose all the connection with the Fibonacci series. 33

Where it is believed that Le Corbusier tried to unify metric and imperial dimensions, or make it rather easier to shift from one to another, as claims to be the tool of universal manufacturing in all over the world, referencing from the blue and red serious the height of the ideal man should be 1.78 m. Whereas Le Corbusier in his words states that ‘have you ever noticed that in English detective novels, the good-looking men, such as the policemen, are always six feet tall?’ When we look at the standard: 6 feet is equal to 1.82.88 cm, yet for no obvious reasons, in the blue and red series this measurement plays a margin between 1.75 - 1.78 cm. 34

Le Corbusier's 1927 Villa Stein in Garches exemplified the Modulor system's application. The villa's rectangular ground plan, elevation, and inner structure closely approximate the Golden Rect- angles. In his early houses, Le Corbusier tried to implement the principle of traces regulateurs, notably at the La Roche-Jeanneret in Paris.

Table 4.

Fibonacci: 8 13 21 34 55 89

Red: 0.16 0.26 0.42 0.68 1.10 1.78

Blue: 0.32 0.52 0.84 1.36 2.20 3.56



34. Wikipedia Web Encyclopaedia.

31

Figure 27. Villa La Roche-Jeanneret, Paris, a perspective drawing of the facade by Le Corbusier.

Figure 28. Internal view of Villa La Roche,

Le Corbusier was interested in a new architecture for the industrial age and developed the concept of a building as a ‘machine for living in’. The Villa la Roche was built with reinforced concrete for Le Corbusier’s brother and for banker and art collector Raoul la Roche.

32

However, to all Le Corbusier’s mathematical villas’ of the 1920s, the one that most clearly embodies what he calls The place of right angle”, which also leads on most directly to his final solution the Modulor is the Villa Stein at Garches, 1927.

This is one of five examples of his earlier works that he illustrates in his book Le Modulor to demonstrate his use of regulating lines and the golden section. “The impression of luxury is not provided by expensive materials, but simply by the arrangement of the interior and by proportioning. The design of the entire house governed by vigorous regulating lines that had effect of modifying the dimension of various parts- sometimes by one centimetre. Here mathematics brings reassuring verities: one does not stop working until one is certain to have achieved exactitude”. 35

In retrospect, nothing served to tie Le Corbusier more firmly to the Humanist tradition of the Renaissance than this villa, realised in 1927, for its from was patently predicated on Palladian types and rhythms.

Figure 29. "More usually known as the Villa Garches, this building started its life as the Villa de Monzie, according to the name of the original client, de Monize, who, as Minister of Culture, first invited Le Corbusier to design the Pavilion de l'Espirt before proceeding to


33

The deconstructed Palladian structure of this villa is brilliantly achieved on the ground and first floors ... where the means of vertical access are directly related to the narrow bays of the Palladian tartan grid of A-B1-A-B2-A. In this matrix the left-hand service stair is rotated 90 degrees and displaced out of its bay (B2). The gyration induced by this displacement initiates the asymmetrical configuration of the first floor, where the living volume "zigzags" between the kitchen situated on the left front and the inset terrace opening towards the garden at the right rear36

The example of the modular system application that Le Corbusier tired to implement is in Villa Stein, Garches, that the ground floor plan, the internal structure and the elevation of the villa is closely exemplifies the golden rectangular. Le Corbusier and his faith and believe in mathematical order and proportions of the elements brought a harmony and function as well as quality and luxury into his design.

Figure 30. Axonometric drawing of Villa Stein at Garches.

36. Kenneth Frampton, Modern Architecture 1920-1945, Thames & Hudson world of art, p295

34

Figure 31 . The ground and first floor of Villa Stein.

Figure32 . The second floor and the terrace of Villa Stein. A basic symmetry of the villa.

35

The villa can be seen as an abstract cube of form in which various geometric elements are freely disposed as a Purist painting. The tree dimensional grid, this Cartesian coordination system exists as an ideal order throughout the building even where elements are felt out or filled in over the column and floor grid. The idea developed from the 1914 Dom-Ino* System, gave birth to several new principle which Le Corbusier partially enunciated as the ‘five points of a New Architecture’. The house on pilotis which frees the ground for circulation; the roof garden allowed by a flat roof; the free plan and facade allowed the independent frame structure; the ribbon window which gives more light than that in

the load bearing wall.37

'...I have decided to make beauty by contrast. I will find its complement and establish a play between crudity and finesse, between the dull and the intense, between precision and accident. I will make people think and reflect, this is the reason for the violent, clamorous, triumphant polychrome of the facades.’ Le Corbusier... Figure 33.Le Corbusier’s Maison Dom-Ino. Free facade.

* Dom-Ino ‘The intuition works through unexpected Illuminations. Here in the year of 1914, we have the pure and total concept of

construction’38 Le Corbusier first foray toward reinforced concrete design began in 1914 with attempt to develop a patentable modular system, of reusable self supporting formwork, that would enable the frame of a basic housing unit to be economically constructed from reinforced

concrete.39

37. Oeuvre Complete, Volume I, 1910-1929, pg 128-9

38. Vogt,A.M. (1998) Le Corbusier, the Noble Savage Toward an Archaeology of Modernism, MIT Press, p 13

39. Allen Powers’ book, pg 214

36

Figure 34 Structure of ‘Dom-Ino’ housing.

Figure 35. Structure of ‘Dom-Ino’ housing.

Figure 36. Complex of ‘Dom-Ino’ housing.

‘Dom-Ino as a piece of equipment, analogues in its form and mode of assembly to a typical piece of product design. Such elements were seen by Le Corbusier as objects-types, whose forms had already become refined in response to typical needs.’ Kenneth Frampton.

37

Unite D’Habitation, Marseille

Le Corbusier was approached by Raoul Dautry, Minister of Reconstruction, who wanted him to study housing for Marseilles with a view to establishing relevant prototype for French mass-housing. The resulting Unite D’Habitation took seven years to complete and announced with full force both the architect’s urban philosophy and new devices like the brise-soleil and beton brut. The Unite drew together a lifetime’s research into the ideal community, but expressed these insights in a vocabulary linked to Le Corbusier’s other experiments of the late1940s as painter, sculptor, theorist, architect and planner.40

The Unité introduced the world to raw concrete - béton brut - with its texture defined by the wooden planks shaping it when it was poured. This unwitting prototype for the New Brutalism to follow came from necessity: not only was there insufficient steel in post-war France for a steel construction, but there was insufficient skilled labor for consistent, precise construction.

The building is the prototype for Le Corbusier’s Ville Radieuse. “Le Corbusier was given complete freedom of expression to try out his idea on modern middle-income housing. After twenty years of untiring preparation, the occasion arrived to put in

practice what has been resolved theoretically.”41

Figure 38. ‘Beton brut’ at Unite D’Habitation.

Figure 37. The Pilotis, the ground floor of Unite D’Habitation.

40. W.J.R Curtis, LE Corbusier; Ideas and Forms, Phaidon, pg 163

41. Le Corbusier 1910 – 65, Birkhäuser, p. 138)

38

Figure 39. The Unité D’Habitation, Marseille, 3D sectional view of floor spaces

The Marseille Unité D’Habitation brings together Le Corbusier's vision for communal living with the needs and realities of post-war France. Up to 1600 people live in a single-slab 'vertical village', complete with an internal shopping street halfway up, a recreation ground and children's' nursery on the roof, and a generous surrounding area of park land made possible by the density of the accommodation in the slab itself.

Most of Le Corbusier's 'five points of architecture' from the 1920s and the Villa Savoye are alive and well in the Unité: the strong pilotis creating circulation space beneath, the free facades now loud with a carefully orchestrated pattern of single- and double-height balconies generated from fifteen different types of apartment, and the roof terrace reclaiming the lost land beneath the building for recreation. The plan is no longer completely free: the partition walls between the apartments are load-bearing, freeing the facades, and providing strong sound-proofing between apartments - part of the building's success in combining privacy with communal living. But between these walls, the free plan has taken on a new dimension, to become a 'free volume'. In an ingenious use of space, two-story apartments interlock, so that an entrance corridor and elevator stop are required only at every third level.42

Figure 40. View of the Corridor. Wide and spacious rather unusual for communal living places.

42. James Raw, Essay on Unite D’Habitation, www.flickr.com

39

Figure 41 . 'Five points of architecture' the strong pilotis creating circulation space beneath,

On one side of the corridor you may enter an apartment's lower level, taking up one side of the building, and climb the stairs within the apartment to a double-aspect floor of bedrooms above; on the other side of the corridor you may enter the neighbouring apartment's upper level, and descend to the double-aspect floor below. As a result, apartments typically combine bright, double-height sitting rooms on one level, with long, narrow bedrooms on the other. "Le Corbusier's most influential late work was his first significant post-war structure—the Unite D’Habitation in Marseilles of 1947-52. The giant, twelve-story apartment block for 1.600 people is the late modern counterpart of the mass housing schemes of the 1920s, similarly built to alleviate a severe post-war housing shortage. Although the program of the building is elaborate, structurally it is simple: a rectilinear ferroconcrete grid, into which are slotted precast individual apartment units, like 'bottles into a wine rack' as the architect put it. Through ingenious planning, twenty-three different apartment configurations were provided to accommodate single persons and

Figure 42. 'Five points of architecture' the free facade allowed the independent frame structure; the ribbon window which gives more light than that in the load bearing wall.

40

Figure 43. Aerial View of The Marseille Unité D’Habitation

The Marseille Unité D’Habitation brings together Le Corbusier's vision for communal living with the needs and realities of post-war France. Up to 1600 people live in a single-slab 'vertical village', complete with an internal shopping street halfway up, a recreation ground and children's' nursery on the roof, and a generous surrounding area of park land made possible by the density of the accommodation in the slab itself.

families as large as ten, nearly all with double-height living rooms and the deep balconies that form the major

external feature." 43

Unite D’Habitation; Marseilles is the major example of Le Corbusier’s use of the Modulor. The overall dimensions of the building are 140x56x24 m, as to Padovan plays no role of what so ever in implementation of the Modulor and its proportion is an exact modulor measures. He states that ‘not only the smaller dimensions of individual cells but also the three major dimensions- the height, length and breadth of the whole building’ responses to modulor dimensions. The length of the building is 140 m where according to the Modulor this should be 142.84, the height is 56 where should be 54.56, and the breadth is 24 where it should be 25.07. Le Corbusier simply recognises the relation between these elements as a whole and simply ignores them for no obvious reason.

Although Le Corbusier wanted to incorporate the modulor measures impulsively as he believed to be the

43. Great Buildings, www.greatbuildings.com

41

most practical and the perfect response for living accommodation; as seeing these measurements in some instant comprising merely, he then selected randomly of those he believed close enough to his functionality and aesthetic of the building. Yet Padovan state that; the overall dimensions of the building are left outside the system. But if the use of a proportion system is to mean anything, it must be more than an arbitrary trimming of dimensions to fit a list of required measures.

Padovan speak further and argues as: an architectural composition, like a musical one, must express its measure-system determinately and unambiguously. Only if all its proportions are designed to be as clear as possible, and are extended to encompass the scheme as a whole, can one speak, with Le Corbusier, of architecture as ‘the first manifestation of a man creating his own universe, submitting to the laws of nature, the laws which govern our own nature, our universe However, in Toward a New Architecture Le Corbusier, in Unite D’Habitation, for the functionality and the vital elements of his design departs from his own laws of proportions.

42

Conclusion

I begun to this dissertation with rather knowing little; but eager and enthusiastic of the subject to learn and to explore further.

Le Corbusier gave the Golden Ratio a new breath and life, seeing that it has not occurred in the architectural theory since the Renaissance.

Having gone through both World Wars, Le Corbusier immediately realised the necessity of post war world that enquires a new language in architecture.

For no doubt that Le Corbusier with his tremendous life time achievement, believed that he eventually found the answer, that the system he had established would be a revolution in architecture and production throughout the world; and this revolution would have to rely on its own rules, its own merit, on its own system of proportion.

Some believed that he found the magical arrangement and method of architectural proportion and theory which succeeding both the metric and the foot-inch systems; However, he was no further than relying all the rules that he believed invented on the Golden Ratio and the Fibonacci numbers by interpreting them into the 20th Century’s Architecture world in his own way by giving it a modern make-up and texture.

Le Modulor was applied only on few buildings other than Le Corbusier’s own. Today the system is only a subject for student to explore and study, and it has lost its sparkling interest when it was first published in 1950.

Since the Ancient Greeks, the Golden Ratio has been a young and a powerful subject; it has encouraged people to find the secrets of it. However, it is perhaps us that who defined its secrets and then believe to it; and it is us who tries to find the no secret and eagerly denies that is all sceptics and not divine.

Did the Modulor failed, and its mathematical systems of proportion? Or it was just a source that Le Corbusier rely all his proportion on a six-feet-man body and chosen from it randomly?

Le Corbusier believed that ‘nature is ruled by mathematics, and so too art, which must conform to nature’s laws’, but he also described mathematics as ‘the majestic structure conceived by man to grant him comprehension of the universe’. It is clear that man created a framework to believe to it in order to make the world and its rules intelligible.

43

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ALEXANDER, C. The Nature of Order, Book One, the Phenomenon of Life, the Centre for Environmental Structure, California, (2002).

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Brooks H.A. Le Corbusier’s formative Years.(1997 p147). Chicago: University of Chicago Press Boesiger, W. Le Corbusier, The Complete Architectural Works Volume V (1946-1952) Thames and Hudson, London, (1953).

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Frings, M. "The Golden Section in Architectural Theory", Nexus Network Journal vol. 4 no. 1

Herz-Fischler, Roger. 1998. A Mathematical History of the Golden Number. Mineola, NY: Dover. Hume, H. ‘Of the Standard of Taste’ in Essay, Moral, Political and Literary, Oxford University Press, 1963,

Le Corbusier, Towards a New Architecture (Vers un architecture), Editions Cres, Paris 1923, Architectural Press, London, 1946

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Livio, Mario the Golden Ratio: The Story of Phi, the World's Most Astonishing Number

Le Modulor, Editions de l’Architecture d’aujour’hui, Boulogne sur Seine, 1950; Modulor 2 , Faber & Faber, London (1958).

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James Raw, Essay on Unite D’Habitation, www.flickr.com Wikipedia web Encyclopaedia. www.Wikipedia.co.uk

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proportion and architectural theory le modulor, neil eldem

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