This reminds me about Numberphile has a video that proves you can get a 4 legged table to be stable with all 4 legs touching the ground by rotating it.
Yeah, I guess the assumption it takes is that there aren’t larger topographic changes for the other legs between their points, and that the legs are equal length. But I like it, it’s a fun one I’m trying next time
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.
This reminds me about Numberphile has a video that proves you can get a 4 legged table to be stable with all 4 legs touching the ground by rotating it.
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.
Yeah, I guess the assumption it takes is that there aren’t larger topographic changes for the other legs between their points, and that the legs are equal length. But I like it, it’s a fun one I’m trying next time
So we assume a perfect table on an imperfect floor?
Sounds like a theological allegory.
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.
https://m.youtube.com/watch?v=OuF-WB7mD6k