The Glorious Golden Ratio by Alfred S. Posamentier

Author:Alfred S. Posamentier
Language: eng
Format: azw3, epub, mobi, pdf
Publisher: Prometheus Books
Published: 0101-01-01T00:00:00+00:00

and, on the other hand,

as well as

Unexpected appearances of the golden section such as these make it so intriguing. Sometimes when you do not actually expect the golden ratio to appear, it just does.

CURIOSITY 5

From our previous exploration of the golden section in polygons, we find it particularly ubiquitous in the pentagon, and consequently in the pentagram. It is now only fitting that we investigate the golden section's appearance in the regular hexagram: a six-pointed star in which each of the “points” is formed by an equilateral triangle and in which the center is a regular hexagon. We begin our search for the golden ratio in figure 5-6, with a regular hexagram. We will construct a circle with center D and radius DC to intersect the extension of line segment AB at point S. Curiously enough—among other sightings of the golden section—we find that point B partitions line segment AS in the golden ratio. Let us see why this actually is true.

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