Any two points determine a line segment, which is contained on a line. Any three points determine a triangle, which can be used to define only one plane. In the case of a table with 3 legs, let us consider the 3 points corresponding to the feet of the table. Since there is only one plane in 3-dimensional space that contains the feet of the table, the table can't wobble (unless the floor wobbles, which means that either your neighbors are rearranging furniture or there's an earthquake). The complication comes in when you have four legs. When you add in a fourth leg, you have no guarantee that the new foot lies in the plane determined by the other 3 feet. If the fourth foot isn't in this plane, it is impossible for all four feet to be on the floor at the same time. In other words, your table has suddenly become a Weeble that wobbles, but doesn't fall down. |