Right. Somehow I was thinking only of the floor being uneven, not the table legs. Surely it’s trivial to have table legs sufficiently different to not fit on any arbitrary shape of floor?
Haha yes :) I was somehow thinking for this type of problem, the usual case is the legs are uneven… because if the floor is uneven or not level the table will be uneven or not level regardless of whether it has 0, 1, or n legs. But I guess the problem is about “wobbling” not about being level.
Does it require any arbitrary constraints on the topography of the floor?
Yes, the floor has to be bigger than the chair.
Oh dear. Usually the chair is so big it stands way above the floor.
Also what about the table? Should that still be larger than the chair?
Sorta. The function height(angle) needs to be continuous. From there it’s pretty clear why it works if you know the mean value theorem.
This can’t actually work if the floor is a level plane right?
Right. Somehow I was thinking only of the floor being uneven, not the table legs. Surely it’s trivial to have table legs sufficiently different to not fit on any arbitrary shape of floor?
Haha yes :) I was somehow thinking for this type of problem, the usual case is the legs are uneven… because if the floor is uneven or not level the table will be uneven or not level regardless of whether it has 0, 1, or n legs. But I guess the problem is about “wobbling” not about being level.
If the table has three legs it will be stable on any floor no matter how uneven (up to some limit!). Won’t be perfectly flat, but won’t wobble.