The ancient Greek mathematician Euclid in his foundational text Elements gave the first recorded definition of the golden ratio at around 300 B.C.
Euclid called the ratio we now refer to as Phi the “extreme and mean ratio”. He derived the ratio from from the following geometry which Leonardo da Vinci later referred to as “the Golden Triangle”.
the golden triangle
The pentagon forms five triangles each with angles 72/54/54 which in mod9 is 9/9/9.
