why do chairs wobble explain in geometric terms?

Answer 1

Yeah, what Tycha said. My answer would have been that 3 points lie in one plane, but 4 points can lie in multiple planes.

Answer 2

On any surface, even crooked ones, chairs with 3 legs will not wobble no matter where they're placed. To see why this is so, first place 2 legs on the surface anywhere, and then bring down the 3rd leg to contact with the surface. There's nothing to rock. But precisely because the chair is now in a fixed position, any 4th leg is not likely to be in perfect contact with the surface, and so the chair will wobble, rocking from one firm 3-point contact to another. The only time this is not a problem is where the surface is flat, and all 4 points of the bottom of the chair is also flat. Then anywhere the chair is placed, the chair will not rock.

Answer 3

Think of the four feet of a chair as the four corners of a quadrilateral, maybe a rectangle or a trapezoid. If all four legs are the same length, then the feet will lie in the same plane, and the chair will not wobble. But let's say that one leg is shorter than the others. The the feet of that leg and the two legs nearest it will form a triangle, and the opposite foot will form a separate triangle. These two triangles lie on two different planes, and one or the other of those planes will be in contact with the floor depending on where weight is placed on the chair.

Answer 4

Not all chairs wobble. Only those with more than 3 legs. This is why many barstools have 3 legs, so they can take abuse. If there are more than 3 legs, it's possible that the endpoints of those legs do not lie in the same plane, and you get a wobble.