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...
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