Golden Ratio

The golden ratio, also known as the golden number, golden proportion, or the divine proportion, is a ratio between two numbers that equals approximately 1.618. Usually written as the Greek letter φ ('phi'), it is strongly related with the Fibonacci sequence, a series of numbers in which each number is the sum of the previous two. (The process is generally started with 0 and 1 as the first two numbers.) The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on, with the ratio of each number and the previous number gradually approaching 1.618, or φ.

Calculate either h or w:

See the explanation and diagram below. Only positive numbers are allowed.

Given h: , w =
Given w: , h =

The golden ratio was originally derived to solve this problem: what does the ratio of w (width) to h (height) need to be such that the sides of the big rectangle have the same ratio as those of the small pink rectangle: