Also, why do we say "four legged table" in reference to common, rectangular tables? The position of the fourth leg is determined from the other three, so it shouldn't count!
my grandfather was a custom cabinet builder, and for whatever reason 4 legged tables were his absolute nemesis. i have the last remaining 3 legged table of his. it's a round table, so i thought the 3 legs were a design choice. that notion was corrected when my dad started laughing at remembering his dad's sheer frustration when he realized 3 of 4 table legs were the same length...on multiple occasions.
(1) Diagonal legs that give the table a wide stance. Draw a triangle that the tabletop fits entirely inside of. The legs touch the ground at the vertices of the triangle.
(2) Make the table itself arbitrarily heavy. A downward force on the corner of the tabletop will create torque around an axis, and this torque wants to tip it over. But the table's center of mass is on the other side of this axis, and the table's weight creates torque too. If the table's mass is high enough, this torque is greater, and it won't tip.
(3) Screw the table to the floor. Is this a table? I think it's still a table. You often see tables attached to the floor.
(4) Make one leg really wide so that it stretches from one corner to the other. The other two legs can be traditional.
The table + load will tip over if the center of mass is vertically outside of the convex polygon formed by the tips of the legs (in this case a triangle); i.e. the base of the object.
