The Art of Inversion

Inversion is the great magic trick of geometry - and this book teaches you to work it.A single rule turns the inside of a circle into its outside, bends straight lines into circles, and collapses crowded, impossible-looking figures into calm, familiar ones. The theorem you could not see was there all along, wearing a disguise. The Art of Inversion shows you how to remove the disguise.This is not a formula sheet with problems attached. It is a discovery-driven course in the geometry of circles, built the way mathematics is actually found: every chapter opens with a problem you cannot yet solve, and the theory is built only once you have felt the need for it. You predict before you calculate, and you earn each theorem instead of being handed it.Written for ambitious students of competition and olympiad mathematics - and for the teachers who coach them - the book carries the reader from the very definition of inversion to the frontier of non-Euclidean geometry, one well-chosen mirror at a time.Inside you will find:Roughly one hundred clean, purpose-built diagrams make every construction visible, and hundreds of Review and Challenge problems - each with a one-line nudge rather than a spoiler - turn reading into doing.Discover inversion not as a trick, but as a way of seeing.The Art of Inversion is a volume in The Art of Creative Math, a series that develops one powerful mathematical idea at a time through intuition, elegant reasoning, and problems worth exploring.