## Rabbit holes

Da Vinci

Divine proportion

Dodecahedron

Dymaxion

Euclid

Golden mean

Hexagon

Icosahedron

Icosidodecahedron

Making a lamp

Motivation

Octagon

Pentagon

Pacioli

Paper

Plato

Rhombicosido-

decahedron

Rhombicub-

octahedron

Symmetry

Truncation

Wood

Zometool

# The golden mean

© 2000 Contentment by design

Click an image to see a full size view.

These images are based on a description in

*Layout* by Allen Hurlburt.

Many of my lamps, including the Chiara lamp, make use of the golden mean—also known as the divine proportion—the aesthetically pleasing ratio revealed in these illustrations in the relationship between the width and height of the rectangle. The animated image on the right shows the actual sequence of construction:

- Begin with a right-angled triangle with one side twice the length of the other.
- Draw a circle centered on the vertex where the shorter side and hypotenuse meet, with a radius equal to the length of shorter side.
- Draw a second circle centered on the vertex where the longer side and hypotenuse meet, with a radius determined by the point where the smaller circle bisects the hypotenuse.
- The golden ratio is revealed by the point where the larger circle bisects the longer side (the ratio of the shorter to the longer segment is equal to the ratio of the longer to the whole side).
- Raise the longer segment up 90º to form the side of a golden rectangle.

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Quick links to the dens in this rabbit hole: