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GOLDEN TRIANGLE

A golden triangle is an isosceles triangle where the ratio of the length of one of the equal sides to the base of the triangle is the golden ratio.  The three angle of a golden triangle are 36, 72 and 72 degrees.  In terms of radians, these are p/5, 2p/5, and 2p/5.

The triangles formed on the 5 tips of a pentagram are golden triangles.  A regular decagon can be subdivided into 10 equal golden triangles with one vertices of each triangle at the center of the decagon.

Golden triangles can be dissected into smaller triangles that are in the form of golden gnomons and golden triangles.  It can be shown that successive points dividing a golden triangle into golden gnomons and triangles lie on a logarithmic spiral
 

More Mathematical Recreations

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