The model seems to have nothing to do with mathematics, but it can be expressed in mathematical language and verified by mathematical tools. After analysis, the position of the chair can be expressed by a univariate variable, the distance between the four legs of the chair and the ground can be expressed by two functions, and then the model hypothesis and the conclusion that the legs of the chair touch the ground at the same time are expressed by simple and accurate mathematical language, which constitutes the mathematical model of this practical problem.

Model hypothesis

In order to clarify the problem, under the premise of daily life, we make the following assumptions about the related factors in the above phenomenon:

(1) The four legs of the chair are equal in length, the contact between the chair legs and the ground is regarded as a point, and the connecting lines of the four legs are rectangular.

(2) The height of the ground changes continuously, and there will be no discontinuity in any direction (there is no step), that is, from a mathematical point of view, the ground is a continuous surface. This assumption is equivalent to giving the necessary conditions for the stability of the chair.

(3) The chair should have at least three feet touching the ground at any position. In order to ensure this, in terms of the distance between legs and the length of legs, the ground is required to be relatively flat, because if there is a deep ditch or hump on the ground (even if it changes continuously), it is impossible for three feet to land at the same time.