Envelope

An envelope in mathematics is a concept used to describe the boundary that "tangents" a family of curves or functions from above or below. Think of it as the "covering line" that just touches each member of the family at some point without crossing them, forming a boundary. Envelopes are useful for understanding maximum or minimum limits of a system of curves, such as in physics or engineering, where they define the outermost limits of a set of moving or changing curves, capturing the overall behavior of the system.