The fix-the-wobbly-table theorem

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This video is about the absolutely wonderful wobbly table theorem. A special case of this theorem became well-known in 2014 when Numberphile dedicated a video to it: A wobbling square table can often be fixed by turning it on the spot.
Today I'll show you why and to what extent this trick works, not only for square tables but also general rectangular ones. I'll also let you in on the interesting history of this theorem and I'll tell you how a couple of friends and I turned the ingenious heuristic argument for why stabilising-by- turning should work into a proper mathematical theorem.
Here is a link to a preprint of the article by Bill Baritompa, Rainer Löwen, Marty Ross and me that I refer to in the video: arxiv.org/abs/math/0511490 . This preprint is pretty close to the printed article that appeared in the Mathematial Intelligencer and which lives behind a pay wall, Math. Intell. 29(2), 49-58 (2007). The argument that I show you in this video is somewhat different from the one Bill, Rainer, Marty and I used in our paper. It's a mix of what we do in our paper and the original argument by Miodrag Novacovic as presented by Martin Gardner in his Mathematical Games column.
Here is a link to the 2014 Numberphile video on table turning featuring the prominent German mathematician Matthias Kreck • Fix a Wobbly Table (wi...
And this is an article by Andre Martin that features an alternative proof for why stabilising-by-turning works for square tables on continuous grounds that are not too steep: arxiv.org/abs/math-ph/0510065
Thank you very much to Danil for his Russian subtitles and Marty for his help with getting the draft of the script for this video just right.
Enjoy!

[@d-fan]

The wobbling tables at work have always gotten the best of me.

[@borismezhibovskiy7607]

Hey that totally worked! Fixed my wobbly table that's been wobbling for years. Thanks Mathologer!

[@machineman8920]

two most important figures in math over centuries

[@mastheadmike]

This is my all time favorite Numberphile topic to bring up in daily small talk and now even better due to learning it is a 180 degree turn for recantular tables! Such a great video. From a guy that grasps only about 40% of what you discuss I still love it all. Solid editing and realistic enthusiasm with unpretentious delivery, Thanks!

[@Squossifrage]

In typography and computer graphics, a “hugging rectangle” is called a minimum bounding box.

[@ericvilas]

I once tried to apply the wobbly table theorem but didn't realize the floor had a slight kind of step to it. A discontinuity that wouldn't let me stabilize the table, so I had to find other means.

[@-_Nuke_-]

Turning the tables with DJ Mathologer

[@JustOneAsbesto]

Don't lie, that circle was rotating too!

[@rafaelmarques1773]

You don't know history ahead of its time. I may dare say, however, that you and 3brown are really together with Gardner in creating the next generation of mathematicians, physicists and so forth. I was just beginning college by the time I discovered this sort of education on YTB, however, I think it still had some profound impact on my interests and to deepen my studies, that's for sure.

[@2346Will]

Annoyed that it's not called the stable table theorem >:(

[@enzogiannotta]

THANK YOU MATHOLOGGER!!! I always wanted to watch a video about the wobbly table theorem!

[@Galdo145]

In regard to the question posed about other shapes where all hugging rectangles are squares:

[@ethanjensen661]

The proof at the end is AMAZING!!

[@danielinfinito6304]

Amazing, really amazing visual proof. Thank you very much.

[@tilek1983]

You simplify math. Amazing. Keep it up

[@legendhero-eu1lc]

Thank you for the video! All of you friends awesome!

[@vinceturner3863]

Brilliant video, Burkard; the Intermediate Value Theorem is beautiful!

[@marcusklaas4088]

Excellent video. Thanks!

[@bulwinkle]

Thank you once again BP.

[@sd4dfg2]

I loved Gardner, and Scientific American. I read every magazine my highschool library had, and then rescued my favorites when they were being thrown out.