The Kepler triangle is triangle with side lengths in proportion 
,
where 
is the golden ratio. It is therefore a reciprocal
proportion triangle. Surprisingly, it is also a right
triangle, which follows from the identity
 |
(1)
|
The Kepler triangle with side lengths 
, 1, and 
has angles
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
and area
 |
(5)
|
