Circle theorems are properties that are true for all circles, regardless of their size. There are six theorems to learn and recognise.

The theorem involves concentric circles that touch the sides of a triangle, and as the triangle changes shape, it generates the special crop-circle patterns.

In earlier work, the authors proved the Discrete Schwarz-Pick Lemma for circle packings. Here we establish a notion of spherical, parabolic, and hyperbolic "type" for circle packing configurations, ...