Fix a Wobbly Table (with Math)
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it as the standard, accessible demonstration of the wobbly table theorem and as a worked example of the intermediate value theorem in action.
Recommended by 2 people across 2 different months, 2015 to 2019.
What it is
A Numberphile video in which Matthias Kreck of the University of Bonn explains why a wobbly four-legged square table on uneven but continuous ground can be steadied by rotating it up to 90 degrees. The argument rests on the intermediate value theorem, with animation by Knut Johannes Haland and a link to a technical paper.
What people said
Recommends Alfe · 2019-10 · Mathematics Stack Exchange · on “What are the applications of the Mean Value Theorem?”
The MVT is one of the things where the first approach to it makes you think, "Where's the point?" because it seems so obvious that it can be hard to understand that this is worth a proof. You notice its value when you apply it to a problem where it isn't really obvious that it can be applied. A nice example was shown on Numberphile [this video] : Given is a round table with four legs on uneven (but continuous!) ground which is wobbly because not all of its four legs reach the ground. Then you can turn this table, and before you have turned it by 90 degrees you must have found a place where all its legs touch the ground at the same time, so that it isn't wobbly anymore. This application of the MVT
Recommends bobsburger · 2019-12 · Mathematics Stack Exchange · on “Extension to the wobbly table theorem”
I recently learned of the wobbly table theorem, I won't explain it here but Numberphile has a great video [this video] on it. But if one were to expand it could it be possible to have a stable table with n number of legs after just rotating it? I believe at some point you couldn't because the number of legs would be so large it would just form a hollow cube without one face and regard less of how you rotate it, it would remain unstable.
Cites vadim123 · 2015-04 · Mathematics Stack Exchange · on “How can we prove that a three legged chair will never be wobbly?”
In fact, even a four-legged chair [this video] can always be rotated to be stable on any smooth floor. The proof involves the intermediate value theorem.
Cites M. Winter · 2017-09 · Mathematics Stack Exchange · on “Fixing a wobbly table - Revisited”
There is this video [this video] on the Youtube channel Numberphile in which it is argued that each wobbly four legged square table can be made stable by just minor adjustments in position, namely an at most $90^°$ turn around its center. Too long to read : I doubt the completeness of the presented solution. Hence I am not sure if every table can be stabelized in the demonstrated way. Of course Numberphile is a popular math channel and cannot go into much detail, but I think there might be much more than just some simple gap filling and formalization work to complete the proof. Question : Is the problem indeed harder than demonstrated in the video? Or is the solution complete and I can just not s