The circle constant is the ratio of circumference to radius; in a Euclidean space the length of the circumference is identical to tau*radius. This makes for a natural unit of angular measure, the radian. Tau radians is a full turn, an identity function. Any shape rotated by tau radians brings it to its original orientation.
Many interesting patterns are symmetric after a half-tau radian rotation. This one is a black and white inverse after a half-turn about an axis through the center point: