Golden Triangle (mathematics)

Golden Triangle (mathematics)

A golden triangle, also known as the sublime triangle, is an isosceles triangle in which the smaller side is in golden ratio with its adjacent side:

Golden triangles are found in the nets of several stellations of dodecahedrons and icosahedrons.

Also, it is the shape of the triangles found in the points of pentagrams. The vertex angle is equal to

Since the angles of a triangle sum to 180°, base angles are therefore 72° each. The golden triangle can also be found in a decagon, or a ten-sided polygon, by connecting any two adjacent vertices to the center. This will form a golden triangle. This is because: 180(10-2)/2=144 degrees is the interior angle and bisecting it through the vertex to the center, 144/2=72.

The golden triangle is also uniquely identified as the only triangle to have its three angles in 2:2:1 proportion.