I See The Golden Section. It's Everywhere.

Geometry of Design is an interesting, quick read about some of the age-old design principles we see around us in nature, art, architecture, etc. The discussion is based on the Golden Section and application of it’s harmonious derivatives, such as root 2, 3, 4 and 5 rectangles.

For example, I didn’t realize sunflowers and pine cones had similar spiral growth patterns.

“Each seed in the pine cone belongs to [two] sets of spirals. 8 of the spirals move clockwise and 13 of the spirals move counterclockwise. The proportion of 8:13 is 1:1.625 which is very close to the golden section proportion of 1:1.618.

“Similar to the pine cone, each seed in the sunflower belongs to [two] sets of spirals. 21 spirals move clockwise, and 34 spirals move counterclockwise. The proportion of 21:34 is 1:1.619 […].”

Interestingly, it’s old news to… mathematicians.

“The numbers 8 and 13 as found in the pine cone spiral and 21 and 34 as found in the sunflower spiral are very familiar to mathematicians. They are adjacent pairs in the mathematical sequence called Fibonacci sequence. Each number in the sequence is determined by adding together the previous two: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… The ratio of adjacent numbers in the sequence progressively approaches golden section proportions of 1:1.618.”

Attempts to apply the Golden Section are also found in car design. VW Beetle fits squarely (pun intended) into a golden section rectangle, and the size and placement of its windows and tires is not random either.

Before this turns into a math lecture, go read the book! :)