Mathematically, the "envelope" of a family of planar straight lines (or curves) refers to a curve tangent to any of these straight lines (or curves). Assuming that this family of plane curves is denoted as F(t, x, y), where different t corresponds to different curves in the curve family, then each point on the envelope satisfies two equations at the lower right, and the implicit representation of the envelope can be obtained by eliminating t from these two equations.

Similarly, you can define the envelope of a family of planes (or surfaces) in space.

As shown in figure 1, straight lines form a circle, but in fact we have not "drawn" this circle, so we call this circle an envelope.

If you want to draw a similar envelope, first draw a big circle (for example, the diameter is 10cm), divide the circumference into 36 equal parts, and use a protractor to make a point every 10.

Connect the nth point with the n+ 10 point, and you can draw a circular envelope as shown in figure 1. If n+ 10 is greater than 36, 36 must be subtracted. For example, when n=29, n+ 10=39, and after subtracting 36, 3 is obtained, so the 29th point is connected with the 3rd point.