1. Points, Lines, and Planes
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We need three points to define a plane. Think of the floor as a plane and the end of the legs as points. A chair with three legs will remain in contact with the floor, even if the legs are not all the same length. This is because they all need to be on the ground to maintain the plane. This is why a three legged chair does not rock.
By the same line of thought, a four-legged chair can rock. Imagine that three of the legs are the same length and one is shorter. This is a common reason why chairs rock from side to side. As long as three legs are in contact with the floor, the chair is still standing on the plane.