Matpic
mathematics, in pictures
Ladder

Inversion — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. Inversion in a circle of radius 1. Three points and their images under inversion in a circle: each image lies on the same ray from the centre, at the distance whose product with the original is the squared radius. Beside it, the tangent construction that finds the image with compass and straightedge.

    The map that trades circles for lines

    Send every point to the one on the same ray whose distance multiplies with it to a fixed number, and circles become lines, lines become circles, angles survive untouched, and a ring of tangent circles falls out of a ring of equal ones.

    rung 1 · geometry

All ladders