Meusnier's theorem
Encyclopedia
In differential geometry, Meusnier's theorem states that all curves on a surface
passing through a given point p and having the same tangent line at p also have the same normal curvature at p and their osculating circle
s form a sphere. The theorem was first announced by Jean Baptiste Meusnier
in 1776.
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
passing through a given point p and having the same tangent line at p also have the same normal curvature at p and their osculating circle
Osculating circle
In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally close to p...
s form a sphere. The theorem was first announced by Jean Baptiste Meusnier
Jean Baptiste Meusnier
Jean Baptiste Marie Charles Meusnier de la Place was a French mathematician, engineer and Revolutionary general. He is best known for Meusnier's theorem on the curvature of surfaces, which he formulated while he was at the École Royale du Génie . He also discovered the helicoid...
in 1776.