Ubiquitous Urbanism, Studio Hadid/ Schumacher, Columbia University, 1993, layering process: inflection/ interarticulation

Grid Definition : 

• Structural grid, modular grid; a regular framework of reference lines to which the dimensions of major structural components of the plan of a building are fixed.
•  in town planning, a checkerboard network of intersecting streets and avenues forming the basic layout of a city or town.

Grid Line Definition : 
One of the lines marking a structural, modular or layout grid of a building,  to which dimensions are coordinated.

Grid Plan Definition : 
An urban plan type in which streets are laid out in an orthogonal network, forming a pattern of approximately rectangular blocks; also called a checkerboard plan, checkerboard plan, chessboard plan or gridiron plan.

Grids in Graphic design : 
The most flexible foundation to support the designer working in two and three dimensions is that of the grid. The grid divides a two-dimensional or three-dimensional space into smaller compartments. The fields or compartments may be the same or different in size.


Space caught in the net of order. 

The Greeks 

The Greek city of (Miletus):
It's plan was to first articulate the value of the grid as an expression of social order and rationality.


Hippodamus of Miletus
Hippodamus of Miletus is the leader and most famous city planner. Aristoteles is the best resource for us to learn about him. Aristoteles says these about him "long haired, extraordinary personality and has ideas about the ideal city". He had specially planed Athens (Piraeus).

Athens (Piraeus), the most famous cities of the time was completely rebuilt by Hippodamus in symmetric. Streets intersecting each other in parallel and straight. Hippodamus rebuilt Miletus where he was born according to this plan. Then the plan was applied in Thurio and Rhodes in southern Italy.

According to Hippodamus, Agora was the first and the most important building in a city. As Agora was the life center of a city a few perpendicular blocks are left for it. After that gymnasium, stadium, theater and official buildings were located. Then the settled areas were located. There is no information about the separate settlements for aristocrats, soldiers and poor people. But the poor people were out of the city and far from these places. Underground sewage system was applied the entire city and there were drainpipes. They were built separately then the roads, streets and city walls. Main doors of City walls were open to an important street.



The Romans : 

The grid of the Roman towns were derived from miltary camps and was organized around two principal streets, set at right angles to each other and called the Cardo Maximus (north-south) and Decumanus Maximus (east west).

At their intersection was the Forum or marketplace, the Basilica or law court, the Curia or meeting hall, and a Capitolium for official state worship, dating from Hadrian's reign (AD 117-138).

This system was expanded across Europe to impose order om occupied territory.




The Beaux-Arts : 

The first concreted attempt to promote the use of an abstract grid of dimensions to coordinate the plans, sections and elevations of buildings in France by Jean-Nicolas-Louis Durand.
 He was an important figure in Neoclassicism, and his system of design using simple modular elements anticipated modern industrialized building components.

He used the basic architectural meter as the module, this was measured as the center to center distance between columns, rather than as a column diameter, which had been proportionally related to the human body.



Germany : 
The method of Jean-Nicolas-Louis Durand was popular in Germany by Neoclassicist architects such as Karl Friedrich Schinkel, and Leo von Klenze, and it inspired the attempt to create a comprehensive dimensional guidance for architects by Ernst Neufert a German architect who is known as an assistant of Walter Gropius, as a teacher and member of various standardization organizations, and especially for his essential handbook Architects' data.



The International style and the Machine age : 

This idea was very appealing universally where grids are used as means of coordinating the dimensions of a building and the elements which are built and assembled in a factory leaving little room for adjustment on site.

The modernist free plan :
The grid became means of allowing freedom in the organization in space.
Open plan :
Schematic plans. Projects by L. Mies van der Rohe, Brick Country House

Schematic plans. Projects by L. Mies van der Rohe. a: Brick Country House, 1924. b: Core House, 1951-1952 [Colombo, L. F., 2015. Orig.: MoMA NY]

Zaha Hadid Architects, One North Masterplan, Singapore

Reference :
100 Ideas that Changed Architecture: Richard Weston
Dictionary of Architecture and Building Construction (2008)
https://magical-steps.com/blog/hippodamus-of-miletus/
http://www.athenapub.com/medit7.htm
https://www.archdaily.com/881889/neufert-the-exceptional-pursuit-of-the-norm/59f673c2b22e3829dc00022a-neufert-the-exceptional-pursuit-of-the-norm-image
http://www.vitruvius.com.br/revistas/read/arquitextos/16.185/5782/en
https://www.architectural-review.com/rethink/viewpoints/the-autopoiesis-of-architecture-dissected-discussed-and-decoded/8612164.article

Get The Book on Amazon : 

Aldo Rossi | Illustration

Aldo Rossi | Teatro del Mondo

Le Corbusier :
"He argued that by following the Engineer's Aesthetic the architect could achieve a platonic grandeur that would resonate on a sounding-board possessed by everyone. This was inspired by the law economy of economy and governed mathematical calculation based on the universal aesthetic of the machine age."

The Idealist view was derived from Plato, and its interpretation continues to exercise philosophers.

It's easier to describe it's impact on architecture, by arguing that all object in the physical realm are imperfect variations of ideal versions that exist in the realm of ideas Plato gave rise to traditional representation of the ideal form.  (Look up Utopia)

Sir Christopher Wren on Idealism:
"There are two causes of beauty - natural and customary. Natural is from geometry consisiting in uniformity, that is equaliy and proportion. Customary beauty is begotten by the use, as familiarity breeds a love for things not in themselves lovely. Here lies the great occasion of errors, but always the true test is natural or germetrical beauty. Geometrical figures are naturally more beauful than irregular ones : the square, the circle are the most beautiful, next to the parallelogram and the oval. There are only two beautiful positions of straight lines, perpendicular and horizontal; this is the form of nature and consequently necessity, no other than upright being firm  "

Emphasis :
Form, Proportion, Symmetry. 
influencing works of architects such :  Leon Battista Alberti and Andrea Palladio.

Villa Capra "La Rotonda"

Santa Maria Novella

Winckelmann on Ideal Forms :
"He rejected the sensual nature of art and advocated an idealized expressionless beauty based on pure form, free of secondary elements such as color and texture - Le Corbusier 'Law of Rippon' (A French whitewash) as means of revealing the formal qualities of architecture"


Read more - "The Mathematics of the ideal villa , by Colin Rowe"
Wheres he compared Le Corbusier early work with Palladio.


Forms Free of Imperfection. 
- 100 Ideas that Changed Architecture Book by Richard Weston

References :
Public Domain, https://commons.wikimedia.org/w/index.php?curid=5315960
100 Ideas that Changed Architecture: Richard Weston - Amazon.com
https://amzn.to/3opHEeM
By No machine-readable author provided. JoJan assumed (based on copyright claims). - No machine-readable source provided. Own work assumed (based on copyright claims)., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=409060

Get the Book on Amazon : 

1_Piero della Francesca - Flagellation of Christ (c.1455-60) Showcasing a Pictorial space using perspective.

Buildings built around the proportions of the human figure. 

Mid-fifteenth century

• - General curriculum (studia humanitatis)
• - New world view  
• 
  

2 _ 16th century portrait of Giovanni Pico della Mirandola.

3_10 Books of Architecture by Vitruvius

4_Leonardo Da Vinci's Vitruvian man

5_Classical order of Classical Greek and Roman architecture (Columns)

References : 
--100 Ideas that Changed Architecture by Richard Weston:
Image 1 : Public Domain, https://en.wikipedia.org/w/index.php?curid=2030007 Image 2 : By Italian School, Anonymous - WestminsterCollege.edu, Public Domain, https://commons.wikimedia.org/w/index.php?curid=6676044 Imge Image 4 : https://www.emaze.com/@ALIFRLZR/Leonardo-Da-Vinci

John Lewis department store in Leicester, UK Foreign Office Architects

Ornament disguised as a pictogram and making the best possible use of modern technology is making a comeback and is no longer a crime. 

Definition : 
Two- or three-dimensional decoration, sculpture, carving etc. for the surfaces or spaces of a building or other object.
The need for ornament appears to be a universal one. an aspect of human condition which can be found in the caves of prehistoric man, in the pyramids and tombs of Ancient Egypt, the temples of Greece, the Middle Ages, the geometric ornamentation of Islam, and the patterned wall papers and textiles of today. 

There are two aspects/ schools of thoughts that are basically for and against ornamentation, as in the current time 21 century, a decline in the use of ornaments are noticed due to the minimalist movement and idealism architects seem to be adapting, ornaments are to be an integral part of the building and not a secondary element (Ornament is crime) .

Can ornaments answer the question of identity in architectural design and be an important structural element of the design ?
Few architects seem to have found a middle ground when it comes to using ornaments integrated in the design vs. it being a stick on the design kind of statement. 

Advocates of the Modern architecture took two broad approaches to the problematic issue of ornament, they either eliminated it (Pure space and true construction) thus empowering the values of the machine age, or devise a new contemporary ornamental vocabulary. 

Architects such as  Antoni Gaudi, Friedensreich Hundertwasser, Jean Nouvel's works are illustrated here to showcase the modern implementation of ornaments in architectural design.

The use of ornaments in Greek orders

Antoni Gaudí:
"What I saw in Barcelona – Gaudí – was the work of such strength, such faith, of an extraordinary technical capacity, manifested during a whole life of genius; of a man who carved the stones before his eyes in well thought out pattern. Gaudí is the ‘builder’ of the turn of the century, a man adept with stone, iron and brick. His glory is seen today in his country. Gaudí was a great artist; only those who move the sensitive hearts of gentle people remain. But they are mistreated in the course of their lives, misunderstood or accused of sin toward the mode of the day. Architecture’s significance is shown when there dominates evidence of lofty intentions that triumph over all the problems in the line of fire (structure, economy, technique, utility). Thanks to interior preparation, architecture is the fruit of character – just that, a manifestation of character." – Le Corbusier 


Antoni Gaudí helped the Catalan architecture to worldwide fame and reputation. Gaudí was also an architect and designer with a special ability to synthesise their own tradition and the courage to new technical solutions. He understood to integrate creative and plastic elements in his buildings.

Casa Milà

Casa Batlló

Friedensreich Hundertwasser:
Friedensreich Hundertwasser (1928–2000) was an Austrian painter, architect, and sculptor best known for his architecture characterized by colorful, ornamental, and biomorphic shapes. He initially gained acclaim for his paintings, but later became more renowned for his unique architectural styling.

The green citadel of Magdeburg, Germany

Maishima Incineration Plant in Osaka

Jean Nouvel:
Jean Nouvel born in 1945 is a French architect. Nouvel studied at the École des Beaux-Arts in Paris and was a founding member of Mars 1976 and Syndicat de l'Architecture. He has obtained a number of prestigious distinctions over the course of his career, including the Aga Khan Award for Architecture (technically, the prize was awarded for the Institut du Monde Arabe which Nouvel designed), the Wolf Prize in Arts in 2005 and the Pritzker Prize in 2008.

Philharmonie de Paris

Institut du Monde Arabe

Louvre Abu Dhabi

References  :

-By Unknown, scan by sidonius 16:34, 7 November 2006 (UTC) - Meyers Kleines Konversationslexikon. Fünfte, umgearbeitete und vermehrte Auflage. Bd. 1. Bibliographisches Institut, Leipzig und Wien 1892., Public Domain, https://commons.wikimedia.org/w/index.php?curid=1348314
-https://en.wikiquote.org/wiki/Antoni_Gaud%C3%AD
-https://lightslant.wordpress.com/2011/07/23/phantom-balconies/
-http://www.amusingplanet.com/2013/07/friedensreich-hundertwassers-strange.html
-http://barcelona.de/en/barcelona-antoni-gaudi.html
-http://www.amusingplanet.com/2013/07/friedensreich-hundertwassers-strange.html

Etienne-Louis Boullée | Cenotaph for Newton

Difference between definitions in English and German :

Principles of Gestalt

1. English : Ambiguous meaning, it can mean shape and idea or essence. 
2. German : (Gestalt : an organized whole that is perceived as more than the sum of its parts.) censorial perception, the form as the idea of something. 

* Read more abut the principles of Gestalt patterns here  http://www.fusioncharts.com/blog/2014/03/how-to-use-the-gestalt-principles-for-visual-storytelling-podv/

Aristotle on Form :

he central image from Raphael's The School of Athens (1509-1511), depicting Plato (left) and Aristotle (right). Plato is depicted pointing upwards, in reference to his belief in the higher Forms, while Aristotle disagrees and points downwards to the here-and-now, in reference to his belief in empiricism.

*In a platonic conception of form by Aristotle, form is an ideal known to the mind through intelligence, not senses. It is linked to material things.


Renaissance architects on Form :

Elevation of the principal façade of the Panthéon, Paris

*They used form as a synonym for shape or for the Pythagorean idea of ratio and proportion.

Adolf Lose and Gottfried Semper on Form :

Muller House 1930 - Adolf Loos

*Form represents the means of resisting ornament, his idea was that any given material contained its own potential form.
The attitude was developed in the Deutsche Werkbund as a method of producing objects and building which were true to the form unexpressed in their material.


Modernists of the 20's century on Form: 

Farnsworth House | Mies van der Rohe

Constant Nieuwenhuys' New Babylon

Cedric Price | Fun Palace

Peter Eisenman | House X

• 1920's | Mies van der Rohe : "Form as goal is formalism".
  
• Hanned Meyer : Strove to negate any interest in form, thereby, demonstrating their preoccupation with the social value of their work.
  
• 1950's : The Situationists attempted o resist capitalism by thinking of architecture as formless | Constant Nieuwenhuys' New Babylon project envisaged the city as an ever changing ambiance through which the post-revolutionary individual can wander from one leisure to another in search of new sensations.
  
• 1960's Radical technology-based approach : A composed static form is not a legitimate objective of architectural design | Architects like Cedric Price through his Fin Palace project was a support structure capable of endless rearrangements.
  
• 1970's Peter Eisenman's early work was intended as a critique of functionalism, in his series of provocative house projects he developed spatial compositions from grammatical operations applied to elements such as planes and lines, only later resulting how the final form might be inhabited. 

References: 
-100 Ideas that Changed Architecture by Richard Weston:
-http://www.archdaily.com/63267/ad-classics-house-vi-peter-eisenman
-https://en.wikipedia.org/wiki/Constant_Nieuwenhuys
-http://www.bcchang.com/transfer/articles/2/18346584.pdf
-https://wratliffcgds2.wordpress.com/2012/03/19/structuralism-and-cardboard-architecture-14/


Photo references : 
By Raphael - Web Gallery of Art:   Image  Info about artwork, Public Domain, https://commons.wikimedia.org/w/index.php?curid=75881
https://www.premedhq.com/gestalt-principles
http://www.archdaily.com/544946/ad-classics-cenotaph-for-newton-etienne-louis-boullee
By Jacques-Germain Soufflot - Paris BNF, cabinet des estampes, Public Domain, https://commons.wikimedia.org/w/index.php?curid=555099
https://ksamedia.osu.edu/work/63842
http://www.worldarchitecturenews.com/project-images/2012/21461/cedric-price/reader-review-fun-palace.html?img=1

"The design of a temple depends on symmetry, the principles of which must be most carefully observed by the architect. They are due to proportion, in Greek ἁναλογἱα. Proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard. From this result the principles of symmetry. Without symmetry and proportion there can be no principles in the design of any temple; that is, if there is no precise relation between its members, as in the case of those of a well shaped man."

What is : Proportion ?

[Pythagorus and Plato on proportion] :
Pythagoras was the first to discover the diatonic scale in music, which led to the development of the system of proportions, having harmonious relationships such as the perfect fifth (3:2), minor seventh (16:9) and so on, this method is called the Pythagorean tuning which is a tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is 702 cents wide.
Pythagoras and Plato saw this as an evidence for an underlying harmony of nature, and a technique for achieving similar qualities in art.





[Vitruvius on proportion ]:
Chapter 1 : Vitruvius- The Ten Books of Architecture
ON SYMMETRY: IN TEMPLES AND IN THE HUMAN BODY

1. The design of a temple depends on symmetry, the principles of which must be most carefully observed by the architect. They are due to proportion, in Greek ἁναλογἱα. Proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard. From this result the principles of symmetry. Without symmetry and proportion there can be no principles in the design of any temple; that is, if there is no precise relation between its members, as in the case of those of a well shaped man.

2. For the human body is so designed by nature that the face, from the chin to the top of the forehead and the lowest roots of the hair, is a tenth part of the whole height; the open hand from the wrist to the tip of the middle finger is just the same; the head from the chin to the crown is an eighth, and with the neck and shoulder from the top of the breast to the lowest roots of the hair is a sixth; from the middle of the breast to the summit of the crown is a fourth. If we take the height of the face itself, the distance from the bottom of the chin to the under side of the nostrils is one third of it; the nose from the under side of the nostrils to a line between the eyebrows is the same; from there to the lowest roots of the hair is also a third, comprising the forehead. The length of the foot is one sixth of the height of the body; of the forearm, one fourth; and the breadth of the breast is also one fourth. The other members, too, have their own symmetrical proportions, and it was by employing them that the famous painters and sculptors of antiquity attained to great and endless renown.



3. Similarly, in the members of a temple there ought to be the greatest harmony in the symmetrical relations of the different parts to the general magnitude of the whole. Then again, in the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centered at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square.

4. Therefore, since nature has designed the human body so that its members are duly proportioned to the frame as a whole, it appears that the ancients had good reason for their rule, that in perfect buildings the different members must be in exact symmetrical relations to the whole general scheme. Hence, while transmitting to us the proper arrangements for buildings of all kinds, they were particularly careful to do so in the case of temples of the gods, buildings in which merits and faults usually last forever.

5. Further, it was from the members of the body that they derived the fundamental ideas of the measures which are obviously necessary in all works, as the finger, palm, foot, and cubit. These they apportioned so as to form the "perfect number," called in Greek τἑλειον, and as the perfect number the ancients fixed upon ten. For it is from the number of the fingers of the hand that the palm is found, and the foot from the palm. Again, while ten is naturally perfect, as being made up by the fingers of the two palms, Plato also held that this number was perfect because ten is composed of the individual units, called by the Greeks μονἁδες. But as soon as eleven or twelve is reached, the numbers, being excessive, cannot be perfect until they come to ten for the second time; for the component parts of that number are the individual units.

6. The mathematicians, however, maintaining a different view, have said that the perfect number is six, because this number is composed of integral parts which are suited numerically to their method of reckoning: thus, one is one sixth; two is one third; three is one half; four is two thirds, or δἱμοιρος as they call it; five is five sixths, called πεντἁμοιρος; and six is the perfect number. As the number goes on growing larger, the addition of a unit above six is the ἑφεκτος; eight, formed by the addition of a third part of six, is the integer and a third, called ἑπἱτριτος; the addition of one half makes nine, the integer and a half, termed ἡμιὁλιος; the addition of two thirds, making the number ten, is the integer and two thirds, which they call ἑπιδἱμοιρος; in the number eleven, where five are added, we have the five sixths, called ἑπἱπεμπτος; finally, twelve, being composed of the two simple integers, is called διπλἁσιος.

7. And further, as the foot is one sixth of a man's height, the height of the body as expressed in number of feet being limited to six, they held that this was the perfect number, and observed that the cubit consisted of six palms or of twenty-four fingers. This principle seems to have been followed by the states of Greece. As the cubit consisted of six palms, they made the drachma, which they used as their unit, consist in the same way of six bronze coins, like our asses, which they call obols; and, to correspond to the fingers, divided the drachma into twenty-four quarter-obols, which some call dichalca others trichalca.


8. But our countrymen at first fixed upon the ancient number and made ten bronze pieces go to the denarius, and this is the origin of the name which is applied to the denarius to this day. And the fourth part of it, consisting of two asses and half of a third, they called "sesterce." But later, observing that six and ten were both of them perfect numbers, they combined the two, and thus made the most perfect number, sixteen. They found their authority for this in the foot. For if we take two palms from the cubit, there remains the foot of four palms; but the palm contains four fingers. Hence the foot contains sixteen fingers, and the denarius the same number of bronze asses.

9. Therefore, if it is agreed that number was found out from the human fingers, and that there is a symmetrical correspondence between the members separately and the entire form of the body, in accordance with a certain part selected as standard, we can have nothing but respect for those who, in constructing temples of the immortal gods, have so arranged the members of the works that both the separate parts and the whole design may harmonize in their proportions and symmetry.

Leonardo Da Vinci - Vitruvian man

[Alberti on proportion] :

"We shall therefore borrow all our Rules for the Finishing our Proportions, from the Musicians, who are the greatest Masters of this Sort of Numbers, and from those Things wherein Nature shows herself most excellent and compleat." Leon Battista Alberti (1407-1472)

Music with Arithmetic, Geometry and Astronomy, made up the Quadrivium, the four ways, or liberal arts, advocated in the Middle Ages as essential for the education of the human being, (together with their outward expression in Grammar, Rhetoric and Logic; the Trivium). Although the educated person would often have learnt to master a musical instrument, it was the mathematical and proportional aspect of music which was held to be of most relevance. Actually playing music, and even composing, because in the creative moment instinctive faculties seemed to have the upper hand, were, at least up to the end of the Middle Ages, seen as inferior to the purity of theory alone.

In Chapter VI, Alberti develops the relationship between the proportions of numbers and the measuring of areas.
Methodically, he lists three types of area;
short, middle, and long.

Alberti's own summary:
Short: 1:1, 2:3, 3:4
Middling: 2:4. 4:9, 9:16
Long:1:3, 3:8, 1:4
"By the help of these Mediocrates the Architects have discovered many excellent Things, as well as with Relation to the whole Structure, as to its several Parts; which we have not Time here to particularize. But the most common Use they have made of these Mediocrates, has been however for their Elevations

[Andrea Palladio on proportion]:

Andrea Palladio (1508-80) was an Italian architect, one of the most influential architects of our time. Palladio was born November 8, 1508, in Padua, and trained as a stonemason. Palladio moved to Vicenza in his early twenties. Originally named Andrea di Pietro della Gondola, he was named Palladio (after Pallade the goddess of wisdom daughter of Zeus) by the Italian poet and patron Giangiorgio Trissino, who oversaw Palladio's architectural studies. Trissino took him to Rome, where Palladio studied and measured Roman architectural ruins; he also studied the treatises of Vitruvius, one of the most important of the Roman architects.
In and near Vicenza he designed many residences (Villas) and public buildings (Palazzi). He also planned several churches in Venice, San Francesco della Vigna, San Giorgio Maggiore, and Il Redentore. One of his last work was the Teatro Olimpico in Vicenza, completed after his death by architect Vincenzo Scamozzi. Palladio's own use of classical motifs came through his direct, extensive study of Roman architecture.

He freely recombined elements of Roman buildings as suggested by his own building sites and by contemporary needs. At the same time he shared the Renaissance concern for harmonious proportion, and his facades have a noteworthy simplicity, austerity and repose.

Palladio was the first architect to develop a systematic organization of the rooms in a house. He was also the first to apply to houses the pedimented porticos of Roman temples-formal porches defined by a shallow triangular gable (Timpano) supported by a row of columns. Both these features are exemplified in the Villa Almerico "The Rotonda".

Palladio's buildings were highly functional. Palladio was the author of an important scientific treatise on architecture, I Quattro Libri dell'Architettura (The Four Books of Architecture), which was widely translated and influenced many later architects. Its precise rules and formulas were widely utilized, especially in England, and were basic to the Palladian style, adopted by Inigo Jones, Christopher Wren, and other English architects, which preceded and influenced the neoclassical architecture of the Georgian Style.

Palladio married Allegradonna, daugther of Marcantonio, and had five children, Leonida, Marcantonio, Orazio, Silla and Zenobia. He died on August 19, 1580 in Vicenza, or probably at Maser (Treviso), while attending construction of the Tempietto of Villa Barbaro.

"Palladio Rotonda Plan" by Andrea Palladio (1508-1580)

When Andrea Palladio, (1508-1580), in The Four Books of Architecture, published in 1570, suggested seven sets of the most beautiful and harmonious proportions to be used in the construction of rooms he chose measurements which reflect musical consonances. He suggests;
- The Circle
-The Square;
-The Rectangle in ratios [3 : 4, 1 :2, 2: 3 , 3: 5]

A perfect example of the ratios Andrea Paladio preferred in his designs :
The Path From Villa Cornaro to Drayton Hall, by Carl I. Gable.

Wordpress Blog - The Path From Villa Cornaro to Drayton Hall, by Carl I. Gable

 [Le Corbusier on proportion  [The Modulor]]:

Le Corbusier developed the Modulor in the long tradition of Vitruvius, Leonardo da Vinci's Vitruvian Man, the work of Leon Battista Alberti, and other attempts to discover mathematical proportions in the human body and then to use that knowledge to improve both the appearance and function of architecture. The system is based on human measurements, the double unit, the Fibonacci numbers, and the golden ratio. Le Corbusier described it as a "range of harmonious measurements to suit the human scale, universally applicable to architecture and to mechanical things".

With the Modulor, Le Corbusier sought to introduce a scale of visual measures that would unite two virtually incompatible systems: the Anglo Saxon foot and inch and the French metric system.Whilst he was intrigued by ancient civilisations who used measuring systems linked to the human body: elbow (cubit), finger (digit), thumb (inch) etc., he was troubled by the meter as a measure that was a forty-millionth part of the meridian of the earth.

In 1943, in response to the French National Organisation for Standardisation's (AFNOR) requirement for standardising all the objects involved in the construction process, Le Corbusier asked an apprentice to consider a scale based upon a man with his arm raised to 2.20 m in height. The result, in August 1943 was the first graphical representation of the derivation of the scale. This was refined after a visit to the Dean of the Faculty of Sciences in Sorbonne on 7 February 1945 which resulted in the inclusion of a golden section into the representation.

Le Corbusier’s Modulor Man

Le Corbusier used his Modulor scale in the design of many Buildings such as :

Church of Sainte Marie de La Tourette

Unité d'Habitation in Marseille

Carpenter Center for the Visual Arts

References :
-Vitruvius- The Ten Books of Architecture 
-100 Ideas that Changed Architecture by Richard Weston:

-https://en.wikipedia.org/wiki/Proportion_(architecture)
-http://www.fondationlecorbusier.fr/corbuweb/morpheus.aspx?sysId=13&IrisObjectId=7837&sysLanguage=en-en&itemPos=82&itemSort=en-en_sort_string1%20&itemCount=215&sysParentName=&sysParentId=65
-http://www.gutenberg.org/files/20239/20239-h/29239-h.htm
-http://www.aboutscotland.com/harmony/prop2.html
-http://www.aboutscotland.com/harmony/prop3.html
-http://www.ionone.com/arepalladio.htm
-https://draytonhall.wordpress.com/2011/08/09/the-path-from-villa-cornaro-to-drayton-hall-by-carl-i-gable/
-https://en.wikipedia.org/wiki/Modulor

Photo credits :
-http://www.fondationlecorbusier.fr/corbuweb/morpheus.aspx?sysId=13&IrisObjectId=7837&sysLanguage=en-en&itemPos=82&itemSort=en-en_sort_string1%20&itemCount=215&sysParentName=&sysParentId=65
- http://www.thecultureconcept.com/circle/le-corbusier-charles-edouard-jeannerets-modernist-style
- https://www.google.ae/search?q=Carpenter+Center+for+the+Visual+Arts&es_sm=93&source=lnms&tbm=isch&sa=X&ved=0CAcQ_AUoAWoVChMItaKw_dn7yAIVR9oaCh3umQLS&biw=1366&bih=623#imgrc=8H0mbIJDvcDokM%3A
- http://afasiaarchzine.com/2012/10/le-corbusier-3/
- "PalladioRotondaPlan" by Andrea Palladio (1508-1580) - I Quattro libri dell'Architettura (1570); Transferred from it.wikipedia; transferred to Commons by User:Marcok using CommonsHelper.. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:PalladioRotondaPlan.jpg#/media/File:PalladioRotondaPlan.jpg


Movie Credits:
-Introduction to Pythagorean Tuning- https://www.youtube.com/watch?v=GzUaViQk1LA
-Vitruvian Man | The Beauty of Diagrams - https://www.youtube.com/watch?v=GGUOtwDhyzc

Get the Book on Amazon: