Kepler triangle

A Kepler triangle is a right triangle with edge lengths in geometric progression. The ratio of the progression is √𝜙, where 𝜙 is the golden ratio, and can be written: , or approximately 1 : 1.272 : 1.618. The squares of the edges of this triangle are also in geometric progression according to the golden ratio itself. Geometry has two great treasures: one is the theorem of Pythagoras, the other the division of a line into extreme and mean ratio. The first we may compare to a mass of gold, the second we may call a precious jewel.

Kepler triangle

A Kepler triangle is a right triangle with edge lengths in geometric progression. The ratio of the progression is √𝜙, where 𝜙 is the golden ratio, and can be written: , or approximately 1 : 1.272 : 1.618. The squares of the edges of this triangle are also in geometric progression according to the golden ratio itself. Geometry has two great treasures: one is the theorem of Pythagoras, the other the division of a line into extreme and mean ratio. The first we may compare to a mass of gold, the second we may call a precious jewel.