An almost-theorem in a regular 10-gon

Did you know?

A regular 10-gon that has side length 55, has two parallel diagonals with length 144 and 178.

This is however not exactly true.

Just almost. 55 and 144 are Fibonacci numbers and therefore their ratio is very close to the golden ratio. Also, 178=144+34, a sum of two Fibonacci numbers (or one Fibonacci number twice, namely, 89+89). For these reasons the diagonals are very close to integers if the side is a Fibonacci number.