The Golden Ratio (1)
The golden ratio (or golden section) is one of the best-known rules of proportion in nature, mathematics and art. It dates back to ancient Greece and has a particularly harmonious effect on the human eye. In this new Scrolly series, you can find out more about this fascinating irrational number and the geometry associated with it.
In geometry, we consider construction methods that only require a compass and ruler. There are many such methods for dividing a distance using the golden ratio (φ). The following method is popular because of its simplicity.
Construct a straight line with the length of AB. Draw a circle around point B with half the length of the distance AB.
Now connect points A and C with a line. Now draw a radius around point C with the length CB.
The circle intersects the connection AC at point D.
A circle around A with the radius AD divides the distance AB in the ratio of the golden ratio (φ).
The distance AB with length 1 is now divided into two distances: the larger distance M (major) = 0.61803… and the smaller distance m (minor) = 0.38197…
There are many such methods for dividing a distance in the ratio of the golden ratio. Two procedures are mentioned here as examples.
Construction according to Euclid of Alexandria. He was a Greek mathematician who probably lived in Alexandria in the 3rd century BC.
This construction method was first discovered in 1982 by the American mathematician George Odom. The construction starts with an equilateral triangle.
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Veröffentlicht am 19.09.2026
Credits
Fotos: Jan Schwochow; getty images; Gelijkzijdige vijfhoek met vrouw bij een tempel, Sébastien Leclerc (I), 1669 - Rijksmuseum
Grafik und Animation: Jan Schwochow
Produktion: Schwochow Visual Stories GmbH
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