Every curve in the plane curve family is tangent to a curve C that is not in the family, and any point on the curve C is the tangent point of a curve in the family, and the curve C is called the envelope of the family.

Envelope is a kind of figure interwoven by many elliptic curves, which looks like a package. Envelope has its own unique significance in mathematics, signal processing, literature, economics, traditional Chinese medicine and other fields.

Here mainly refers to the envelope theorem, a theoretical tool used to analyze the long-term production cost function of manufacturers in western economics. Its content is to consider the unconditional extreme value problem of a function with parameter A, where X is an endogenous variable and A is an exogenous variable. Obviously, in general, its optimal solution v is a function of parameter a, that is.