How did Fibonacci beat the Solitaire army?

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
https://www.qedcat.com/archive_cleaned/212.html

Marty and my new book "Putting two and two together"
https://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.
https://www.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 :)
https://www.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.
https://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
https://www.chiark.greenend.org.uk/~sgtatham/solarmy/

A page of very interesting solitaire-army puzzles by Luciano Gualà, Stefano Leucci, Emanuele Natale, and Roberto Tauraso
https://www.isnphard.com/g/solitaire-army/

Numberphile videos on "Conway's checkers" starring the mathematician Zvezdelina Stankova
https://youtu.be/FtNWzlfEQgY
https://youtu.be/Or0uWM9bT5w

Today's t-shirt: https://teeherivar.com/product/funny-math-fibonacchos/

Today's music: I promise by Ian Post

Enjoy!

Burkard

Next episode

S08E02 - Tesla’s 3-6-9 and Vortex Math: Is this really the key to the universe?