Axioms

On a floor that is not perfectly flat we often have to put some­thing under a table's leg so that it is not unsteady.

It turn's out that than one should blame the axioms of stere­om­etry.

Let's before recall some facts of planimetry. Through a given point on a plane pass a whole, as it is some­times said in math­e­matics, pencil of lines. However, if we fix another point, there is a single line passing through both of them. Indeed, through any two distinct points in a space (partic­u­larly in a plane) we can always draw a line, in addi­tion a single one.

And what do three points in a space define? As one of the stere­om­etry axioms says, if three points are not collinear, there is a plane passing through them which is unique. As a conse­quence through a line and a point not that doesn't lie on it, passes a unique plane. You can check it your­self.

That is why a stool with three legs is always stable on any floor. But a stool (or a table) with four pivots is often unsteady. The length of it's three legs and the level of the floor in the pivots uniquely define a plane. While the end of the fourth leg be upper than the floor level.