The Golden Ratio and Fibonacci Sequence are related because the further the Fibonacci Sequence continues, the closer the ratio of the latest two numbers becomes to the Golden Ratio.
The Golden Mean is a sequence of Fibonacci numbers. These numbers go in a sequence, 1,1,2,3,5,8,13, etc. (each new number being the sum of the previous two). Below is the Fibonacci sequence put into a sketch, using the Golden Rectangle and the Golden Mean.
During the Middle Ages, a mathematician developed the theory of the Fibonacci Sequence by looking at seashells.