Spirals

Ever wonder about the mathematics behind spirals?

Number spirals are very simple. To make one, we just write the non-negative integers on a ribbon and roll it up with zero at the center.

The trick is to arrange the spiral so all the perfect squares (1, 4, 9, 16, etc.) line up in a row on the right side:

...we saw that primes tend to line up in curves on the number spiral. In fact, the whole spiral is made of curves of this kind, and every integer belongs to an infinite number of them.

The simplest curve of this type (the one with least curvature) is the line of perfect squares which extends from the center toward the east, shown here in blue: