Experiment #33

Kepler Triangle

The astronomer Johannes Kepler (1571-1630) was very interested in the golden ratio. He wrote, "Geometry has two great treasures: one is the theorem of Pythagoras, the other the division of a line into mean and extreme ratios, that is , the Golden Mean. The first way may be compared to a measure of gold, the second to a precious jewel."

In a letter to a former professor he states the theorem, which I rephrase as:

If the sides of a right triangle are in geometric ratio, then the sides are

We recognize this as the sides of the Egyptian triangle, which is why its also called the Kepler triangle.

Project: Prove that If the sides of a right triangle are in geometric ratio, then the sides are