But the mathematical importance doesn’t end with an unexpected reveal of impossibility. Conway found that the secret to *why* it’s impossible depends on the Golden Ratio of 1.618, which has fascinated mathematicians since Pythagoras and Euclid. We see the Golden Ratio in aesthetically-pleasing magazine layouts, flower patterns, and pretty faces, but John Conway showed us that it’s at the heart of why we can’t reach the fifth row of a checker game.
Play the game yourself with the online simulator and check out Zvezdelina Stankova’s proof on Numberphile. It’ll make sense. John Conway may be gone now, but we’ll be playing his games and poring over his ideas for centuries.
Conway Checkers (proof), Numberphile2 | Zvezdelina Stankova: https://youtu.be/Or0uWM9bT5w
Conway’s Soldiers Interactive Game (Clever Learning): https://www.cleverlearning.co.uk/blogs/blogConwayInteractive.php
*** SOURCES ***
Berlekamp, E. R.; Conway, J. H; and Guy, R. K. “The Solitaire Army.” In Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, pp. 715-717 and 729, 1982.
Honsberger, Ross. “A Problem in Checker Jumping.” Ch. 3 in Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 23-28, 1976.
Tatham, Simon and Taylor, Gareth. “Reaching Row Five in Solitaire Army.” https://tartarus.org/gareth/maths/stuff/solarmy.pdf
plus magazine, “Mathematical Mysteries: The Solitaire Advance.” https://plus.maths.org/content/os/issue12/xfile/index
Bell, George. “The Peg Solitaire Army.” http://www.gibell.net/pegsolitaire/army/index.html
Bell, Hirschberg, Guerrero-Garcia. “The Minimum Size Required of a Solitaire Army.” https://arxiv.org/pdf/math/0612612.pdf
Taylor, Jasper. “Conway’s Soldiers.” https://sites.math.washington.edu/~morrow/336_10/papers/jasper.pdf
John Conway’s obituary, New York Times: https://www.nytimes.com/2020/04/15/technology/john-horton-conway-dead-coronavirus.html
Roberts, Siobhan. “Genius at Play: The Curious Mind of John Horton Conway” (2015). https://www.amazon.com/Genius-At-Play-Curious-Horton-ebook/dp/B00UX2UR44
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