Channel: Mathologer

Category: Education

Description: Fibonacci and a super pretty piece of life-and-death mathematics. What can go wrong? 00:00 Intro 02:20 Solitaire 03:12 Survivor challenge 05:32 Invasion 11:41 The triangles of death 20:22 Final animation 21:43 Thank You! Here is an online version of Marty and my newspaper article about the possible positions of one remaining peg when playing peg solitaire on various boards qedcat.com/archive_cleaned/212.html Marty and my new book "Putting two and two together" bookstore.ams.org/mbk-141 Martin Aigner's paper "Moving into the desert with Fibonacci". Bit of a pain to access it for free, possible though via this site. jstor.org/stable/2691046 This paper contains the proof that I am focussing on in this video. It also has Conway's golden ratio based proof. An implementation of the solitaire army game by Mark Bensilum. Use it to play solitaire army general. Note that this implementation starts with all of the bottom squares occupied by pegs. Please read carefully how you are supposed to play the game using this app :) cleverlearning.co.uk/blogs/blogConwayInteractive.php The paper "The minimum size required of a solitaire army" by George I. Bell, Daniel S. Hirschberg, Pablo Guerrero-Garcia considers all sorts of variations of the basic solitaire army game. The animation and challenge at the end of the video is based on some of the findings in this paper. Highly recommended. arxiv.org/pdf/math/0612612.pdf Reaching row 5 in Solitaire Army using infinitely many pegs (featuring a pretty spectacular animation at the bottom of the page) by Simon Tatham and Gareth Taylor chiark.greenend.org.uk/~sgtatham/solarmy A page of very interesting solitaire-army puzzles by Luciano Gualà, Stefano Leucci, Emanuele Natale, and Roberto Tauraso isnphard.com/g/solitaire-army Numberphile videos on "Conway's checkers" starring the mathematician Zvezdelina Stankova youtu.be/FtNWzlfEQgY youtu.be/Or0uWM9bT5w Today's t-shirt: teeherivar.com/product/funny-math-fibonacchos Today's music: I promise by Ian Post Enjoy! Burkard