This is a tool to showcase and explore how circle inversion works. Through this unusual symmetry you can construct interesting and beautiful canvases. This tool will provide you with an empty canvas to place shapes upon and define the inversion(s) you would like to apply. It is inspired by the YouTube video "Epic Circles" from numberphile [1].
See it in action at http://epic-circles.torpedro.com/. Go to http://epic-circles.torpedro.com/#epic-circles for the example shown in the video from numberphile [1].
Circle inversion is a special type of geometric inversion. Points on a plane are inverted at a circle. In the case of this tool we are working in a two dimensional plane, but circle inversion is not constrained to two dimensions. A inverted point P' of a point P at a circle C is defined as:
|P' - C_center| * |P - C_center| = C_radius²
Based on this general formula, we can also invert complex shapes at a circle. As it turns out: A Circle will usually be inverted to another circle (in some cases to lines). Whereas lines will usually be inverted to circles and line segments will be converted to circle segments.