Mukhopadhyaya theorem

Short description: One of several closely related theorems about the number of vertices of a curve

In geometry Mukhopadhyaya's theorem may refer to one of several closely related theorems about the number of vertices of a curve due to Mukhopadhyaya (1909). One version, called the four-vertex theorem, states that a simple convex curve in the plane has at least four vertices, and another version states that a simple convex curve in the affine plane has at least six affine vertices.

References

• Mukhopadhyaya, Syamadas (1909), "New Methods in the Geometry of a Plane Arc.-I Cyclic and Sextactic Points", Bulletin of Calcutta Mathematical Society 1 (1): 31–37, http://bulletin.calmathsoc.org/article.php?ID=B.1909.1.2