Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A Kepler triangle is a right triangle with edge lengths in geometric progression. Triangles with such ratios are named after the German mathematician and astronomer Johannes Kepler (1571–1630), who first demonstrated that this triangle is characterised by a ratio between short side and hypotenuse equal to the golden ratio.Kepler constructed it differently. In a letter to his former professor Michael Mastlin, he wrote, "If on a line which is divided in extreme and mean ratio one constructs a right angled triangle, such that the right angle is on the perpendicular put at the section point, then the smaller leg will equal the larger segment of the divided line."

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