Two opposite games involving golden ratio (ft. Tom Rocks Maths)

Thanks Tom for the little cameo in the beginning of the video! Dr. Tom Crawford, who got his PhD in Cambridge, is currently at the University of Oxford teaching undergraduates in St. Edmund Hall (nicknamed Teddy Hall, hence the name of the competition), St. Hugh's College and St. John's College. You might recognise him that he appeared on Numberphile talking about the Navier-Stokes equation.

Tom Rocks Maths: https://www.youtube.com/channel/UCRfo-DAifrP3lzcxUHtGm_A
Teddy Rocks Maths competition: https://tomrocksmaths.com/oxford-university/seh/teddy-rocks-maths/
The essay I submitted to the Teddy Rocks Maths competition: https://tomrocksmaths.files.wordpress.com/2020/05/trevor-cheung.pdf

(The essay was written in kind of a hurry, so there were a lot of typos there, and hopefully this video is a kind of "enhanced" version of the essay.)

The golden ratio appears unexpectedly in a game of removing stones, similar in style to NIM. It is a game played in the ancient Chinese, and there is also a variant called the Wythoff's game. The proof of the winning strategy is related to the Beatty's theorem and is shown in detail in this video.

There are two points of fascination during this video: the fact that two seemingly opposite games very similar winning strategy, and that the golden ratio is involved in all of this.

For people who might complain in the comments, phi should properly be pronounced as "fee" - that's the pronunciation in Greek. I adopted this pronunciation right from the Fibonacci video.

Sources:
(1) Wythoff's game: https://en.wikipedia.org/wiki/Wythoff%27s_game
(2) Beatty sequences and theorem: https://en.wikipedia.org/wiki/Beatty_sequence

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Видео Two opposite games involving golden ratio (ft. Tom Rocks Maths) канала Mathemaniac