Part (1) shows you how to draw golden rectangles and find the golden ratio. Younger explorers should ignore the other parts of this problem.

Part (2) This is for older explorers. You need to know about Pythagoras Theorem. Here you will calculate the EXACT value of the golden ratio f.

Part (3) In this part you prove that
f = 1 + 1
f

.

Part (4) In this part you draw graphs to find the value of the golden ratio f.

Part (5) In this part you solve a quadratic equation to find the value of the golden ratio f.