A book of puzzles collected by Ivan Moscovich includes the six circles theorem (first announced in 1974 by Evelyn, Money-Coutts, and Tyrell) as a remarkable fact, but no explanation is given. Diagrams and geometry software seem to confirm it, but no proof could be found in the accessible literature. It took months of thinking time and the pursuit of several ideas that led nowhere before the following proof materialised.
The Six Circles Theorem
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Ed, Paul and Erin will touch on our favourite Whetstones, and even some things that didn't make it to a Whetstone.