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A cool thing is, you can achieve the same effect by rotating the table in a circle (if possible) until you find a stable angle, since for 4 points on a circle there has to exist at least one rotation angle where they are on the same elevation.
I don't think that's exactly right. to create a plane you only need 3 points and 4th point can be on a different height than that plane. A different thing is when the ground itself is uneven and you manage to make both fit to the same shape.
There's no guarantee you can draw a circle through the bottom of the four legs of a table (opposite legs can be off in the same direction). Also, most floors are not perfectly flat, therefore you can't assume the floor is at one elevation.
This requires the legs to be all the same height and the floor to cause the wobble. That doesn’t happen often irl, but I’ve done it a few times and it always makes me happy when it works
Problem is, that you might have to move the table legs through the floor to archive the desired result
I've done this with my dinner table several times.
Is there mathematical proof for this? It sounds like it could be true, but also sounds like you could actively create a floor which it wasn't true for
Yes there is. The wobbly table theroem. https://people.math.harvard.edu/~knill/teaching/math1a_2011/exhibits/wobblytable/
I'm pretty sure this doesn't account for any floor that isn't a flat plane.
It doesn't require a flat plane ground, but it does require the table legs to be equal in length
This is one of those things that works in a simulated environment but not in practice in the real world.
It does work in the real world, as long as the floor is the problem, and the table is perfect.
Most of the time at a restaurant, it's the table that's been beaten up and is no longer even.