The most surprising What-Comes-Next? or How did Fibonacci beat the Solitaire army?

2022-01-22

[public] 22.1K views, 6.16K likes, dislikes audio only

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

/youtube/video/FtNWzlfEQgY

/youtube/video/Or0uWM9bT5w

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

Today's music: I promise by Ian Post

Enjoy!

Burkard