In the Golden Maths posts I'll gather mathematical facts about the golden ratio/section/number. The series will not be very extensive, because the golden number only rarely pops up in mathematics. People are led to believe otherwise, but that is one of the many Golden Myths. The latter series will be bulky indeed.
We start with geometry, which is where the golden saga began. There are four items: the decagon, the pentagon, the icosahedron and the dodecahedron. Only the decagon leads unavoidably to the golden number. The proofs are short and elementary, and how could it be otherwise? The golden ratio is just an elementary application of the Pythagorean theorem!
In fact, all you'll ever need of golden geometry is in this illustration:
