Geometry of Design Elam, Kimberly.

Geometry of Design

Elam, Kimberly. (2001). The Geometry of Design. New York: Princeton Architectural Press.

The Geometry of Design is not a book about nature, physics, or even of design. Instead, it is a relatively short and simple overview of the role of geometry within nature -- whether it is the analysis after the fact from a human perspective or the way nature works that we find pleasant, the book explains the prevalence of the Golden Mean and other geometrical thermos within nature's design.

Proportion in Man and Nature - Proportion is all around us, it is in everything designed within the sphere of nature; a leaf, a shell, a flower. And these proportions are instinctively pleasurable for us, which is likely the reason why much of design and architecture is based on the very same principles of ratio, proportion, and structure. The basis for this design structure is the Golden Ratio, or 1:1.618. Since the Renaissance, this is the proportion that has been used by artists and architects to proportion their works for mass appeal. Fascinating, however, is just how many objects in nature follow this exact proportion.

Talking Points-

Nature is typically proportionate in design, showing smaller objects to be part of a greater whole.

Even animals show this same proportion, a fish for example, when split into individual rectangles, retains the 1:1.618 ratio.

Similarly, the human body in classical drawing (Leonardo, the Greeks, etc.) form similar ratios.

Preferred facial proportions also follow the ratio; faces that do not are often considered less pleasing.

Chapter 2 -- Architectural Proportions - Through a series of dynamic rectangles, humans have developed their entire building system off this ratio. The harmony of space, e.g. windows, doors, arches, etc., especially in public buildings (governmental locations, arenas, religious buildings), all serves both to inspire and make one comfortable.

Talking Points

Ancient architects were very concerned with the way a building was shaped, laid-out, and built. It had to conform to strict proportions in order to be appropriate from a symboligist viewpoint to its function.

Each architectural discovery and innovation resulted in a reestablishment of the principles of appropriate design (e.g. circular stained glass windows in cathedrals, etc.)

This tradition remained in effect for several centuries; progressing through styles like the Baroque, Gothic, Romantic, etc.

In 1931, a French architect, Le Corbusier, expanded this into a more complex merging of mathematics and geometry -- regulating lines. He believed "with regulating lines, you make God a recipe."

In a way, this invigorated the reemphasis on proportion and meaning to form a more 20-21st century way of applying the Golden ratio to modern construction and design.

Chapter 3- Golden Section- the Golden section of any rectangle is a ratio of the Divine Proportion. The Divine Proportion is derived from the division of a line segment into two segments such that the ratio of the whole segment is the same, as 1: 1.61803. This ratio can be found in any portion or sub-portion of a triangle, rectangle, or square in which lines are drawn to make right angles. Additionally, the golden section is unique in that when subdivided its reciprocal is a smaller proportional rectangle, and the area remaining is a square. This portion of the theory results in the ability to find the Golden section in spirals, circles, etc.

Talking Points

The power of the Golden section was seen as something metaphysical for much of history, prior to the generalized advancement and understanding of geometry.

The Golden section may be found within almost every natural structure once reduced to common angles.

The Golden section has a special relationship to the Fibonacci sequence. This is a mathematical sequence in which the first two numbers being 0 and 1, each subsequent number is a sum of the previous two numbers: 0, 1,1, 2 (1+1), 3 (2+1), 5 (3+2), etc.

Like the Golden section, the Fibonacci numbers are used to understand the way trees branch, leaves occur, fruit ripens, etc. -- it is a set of numbers that explains nature's patterns.

Subdividing shapes has no effect on their ratio or relationship to Fibonacci.

Chapter 4 -- Root Rectangles- the idea of the root angel reduction allows the Golden section to become more vital in several aspects of modern life. Not only does this impact modern design of furniture, technology, and appliances; it has a far larger and more robust meaning as we begin to understand the roots of organic chemistry and the structure of living organisms. One of the most interesting aspects of this behavior is that of the human's innate ability to follow some of the principles of the Fibonacci and Golden section rules without even realizing it. In a similar manner, one need only listen to a composition by Bach to find it emotionally pleasant, calming, and that something about it "seems to fit." One need not analyze the chords or structures to understand that it, too, operates off the Golden section ratio.

Talking Points

Root rectangles (and therefore Golden sections) may be created using any shape or combination of shapes; circles, ovals, trapezoids, or combinations.

Snowflakes and ice crystals are examples of hexagonal constructions of the Golden section and form the basis for inorganic chemistry.

If one takes a look at most design, from movie posters to magazine art, one can easily find the Golden section and divide the document into coherent triangles.

Furniture, too, is based on the principle of the Golden ratio; the curve proportion, the way the back of the chair or sofa fits the individual, and even the way the balance of the item interacts with the floor all become part of the Golden section.