The last digit of the numbers in the Fibonacci Sequence are cyclic, they form a pattern that repeats after every 60th number: 0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3, 0, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1.

Fix a starting point on a circle and give it label 0. Move around the circle in steps of golden arcs (approx. 222.497 degrees), labeling the points 1, 2, 3, 4, 5 and so on… Then, at any time, the difference between the labels of every two adjacent points on the circle is a Fibonacci number.

The golden arc plays a significant role in the theory of phyllotaxis.