By turning a great many puzzles into mathematics accessible to keen amateurs, John Conway cast a new and wholly unexpected light on a wide variety of subjects. His inventive genius also found expression in geometry, where he not only conceived previously unsuspected results but also created innovative games and devices. He also put his own spin on the proofs of certain results.

The Conway circle of triangle ABC.

The Conway circle -------------------
We begin with nothing more than a triangle ABC and mark off, on the extensions of its sides, lengths equal to the lengths of the triangle's sides, thereby determining six new points. Conway had the idea that these six points were cocyclic—and he was right! The resulting circle naturally became known as the Conway circle of triangle ABC.