Question

Consider a square table with four legs whose lengths are equal. Suppose that the ground is not a smooth flat surface but a wavy, humpy one (not too much relative to the length of the table’s legs). Show that a position always exists where the table could stand so that each leg rests on the ground (i.e., the table has no wobble although it may be tilted).

Answer 1

well i'd model the ground with sin(x)

then x=c where c is any constant

as a cross section c will intercept sin x twice that means that they touch

Answer 2

=|
Without more information, I actually feel pretty confident that you cannot show this.

Answer 3

It totally depends on the length of the legs and the actual shape of the surface.

Answer 4

Hmm..... okay thanks.

Answer 5

Now, reduce it to 3 legs and it's simple. Through any 3 points, there is a plane.