Approximation to Golden Rectangle using Fibonacci Squares/Proof 2

Theorem

An approximation to a golden rectangle can be obtained by placing adjacent to one another squares with side lengths corresponding to consecutive Fibonacci numbers in the following manner:

It can also be noted, as from Sequence of Golden Rectangles, that an equiangular spiral can be approximated by constructing quarter circles as indicated.

Proof

From Sum of Sequence of Squares of Fibonacci Numbers:

$\forall n \ge 1: \ds \sum_{j \mathop = 1}^n {F_j}^2 = F_n F_{n + 1}$

Hence the result.

$\blacksquare$