Editing Right triangle (section)

===Kepler triangle===
Let  <math>H,</math> <math>G,</math> and <math>A</math> be the [[harmonic mean]], the [[geometric mean]], and the [[arithmetic mean]] of two positive numbers <math>a</math> and <math>b</math> with <math>a > b.</math> If a right triangle has legs <math>H</math> and <math>G</math> and hypotenuse <math>A,</math> then<ref>Di Domenico, A., "The golden ratio — the right triangle — and the arithmetic, geometric, and harmonic means," ''Mathematical Gazette'' 89, July 2005, 261. Also Mitchell, Douglas W., "Feedback on 89.41", vol 90, March 2006, 153–154.</ref>
:<math>
\frac{A}{H} = \frac{A^{2}}{G^{2}} = \frac{G^{2}}{H^{2}} = \phi, \qquad
\frac{a}{b} = \phi^{3},
</math>

where <math>\phi = \tfrac12\bigl(1 + \sqrt{5}\bigr)</math> is the [[golden ratio]]. Since the sides of this right triangle are in [[geometric progression]], this is the [[Kepler triangle]].