👉 Envelope math, also known as envelope calculus or differential geometry of curves and surfaces, is a branch of mathematics that studies the properties of geometric objects by analyzing their behavior along curves and surfaces through the lens of calculus. It involves the concept of an "envelope" or "boundary" of a curve or surface, which is essentially the limiting case where the object approaches its minimal or maximal extent. This approach allows mathematicians to define derivatives and integrals in a way that is consistent with the intrinsic geometry of the object, rather than relying on external coordinate systems. By focusing on these boundaries, envelope math provides a powerful framework for understanding the local and global properties of geometric shapes, such as curvature, torsion, and geodesics, which are crucial in fields like physics, engineering, and computer graphics.
