Design Fundamentals I: AAID-101 Spring 2012: PROPORTION AND ORDERING SYSTEMS

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1 Design Fundamentals I: AAID-101 Spring 2012: PROPORTION AND ORDERING SYSTEMS

2 From the patterning of the seed in the sunflower

3 To the edges of the Universe

4 A spiral, created by drawing arcs connecting the opposite corners of squares creates a Golden Rectangle: Divine Proportions as defined by Nature and Mathematics

5 A tiling with squares whose sides are successive Fibonacci numbers in length

6 The Parthenon organized by the Golden Rectangle; relationships are as parts to the whole. Columns, Entablature and Pediment register horizontally and vertically.

7 Leonardo Da Vinci and Renaissance artists used the divine proportions to organize their paintings in a way that would put the focal point at the center of the square and all other important elements occurred at the intervals of the spiral Many modern industrial designers also use divine proportions in developing their product designs. Human beings relate to the system innately.

8 Vitruivian Man, Limits of the Sphere and Relationships of Center to Whole The navel is naturally placed in the centre of the human body, and, if in a man lying with his face upward, and his hands and feet extended, from his navel as the centre, a circle be described, it will touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square. For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square.

9 Le Modulor Le Corbusier The Modulor: Human Scale Relationships by Le Corbusier In the years 1942 to 1948, Le Corbusier developed a system of measurements which became known as "Modulor". Based on the Golden Section and Fibonacci numbers and also using the physical dimensions of the average human, Modulor is a sequence of measurements which Le Corbusier used to achieve harmony in his architectural compositions. Le Modulor was published in 1950 and after meeting with success, Le Corbusier went on to publish Modulor 2 in In many of Le Corbusier's most notable buildings, including the Chapel at Ronchamp and the Unité d'habitation, evidence of his Modulor system can be seen

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11 Modular Man as a scale reference and reminder that human occupation of proportionally harmonious space is the architect s ultimate goal

12 The sum of the parts equals the whole; the parts are related and create balance

13 Interior spaces also reflect the intention to keep the human scale relationships at all levels

14 Furniture and fenestration provide further reinforcement of the design principles while making the space efficient and functional

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17 From the smallest details come the most compelling moments of the spatial experience

18 The built environment is tailored to the human form

19 We use our bodies constantly without realizing our extents and limits. As designers, we must study the parameters of things we now take for granted

20 Arms length allows humans to reach, pull, extend, contract. Fingers work singularly or in unison to perform mundane or out of the ordinary tasks. Harmony is in the movement.

21 Since the proportions of the human body exhibit the same relationships seen in nature as translated to Fibonacci numbers and to the golden mean, golden rectangle, the modular and any other system, it is natural that we would respond to the harmonious relationships that we find in both the man-made and natural environments

22 From the macro scale of the entire body to the micro scale of the relationship of the elements of a face; eyes, nose, ears, mouth, forehead, chin. We can find the rules of symmetry, axis, horizontal and vertical registration; all within the golden rectangle.

23 Piet Mondrian: Composition II in red, blue and yellow 1930

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25 Piet Mondrian: Composition with blue, red and yellow 1942

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27 Piet Mondrian: Broadway Boogie Woogie 1943

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29 Drawing Template and Sketch

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31 Now you will construct your own Golden Rectangle and experiment with the geometries found within the harmonious proportions of this form, in order to create a composition that uses Ordering Systems: Axis, symmetry, hierarchy, rhythm and balance Compositional Systems: Layering, transparency, figure and ground and directionality