In one of Numberphile's more in-depth videos (41 minutes), they have a full video proof of this, including the derivation of where the golden ratio comes from:

In one of Numberphile's more in-depth videos (41 minutes), they have a full video proof of this, including the derivation of where the golden ratio comes from: https://www.youtube.com/watch?v=Or0uWM9bT5w&t=10s https://www.youtube.com/watch?v=Or0uWM9bT5w&t=10s