A Directional Curvature Formula for Convex Bodies in R^n

TL;DR

This paper introduces a new, easier-to-apply formula for computing the curvature at boundary points of convex bodies in R^n, applicable in any tangent direction.

Contribution

It provides a simplified and equivalent curvature formula for convex bodies, enhancing computational ease over existing methods.

Findings

The formula is mathematically equivalent to existing curvature formulas.

It simplifies the process of curvature computation for convex bodies.

Applicable in any tangent direction at boundary points.

Abstract

For a compact convex set F in R^n, with the origin in its interior, we present a formula to compute the curvature at a fixed point on its boundary, in the direction of any tangent vector. This formula is equivalent to the existing ones, but it is easier to apply.