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 4 vertices, and another version states that a simple convex curve in the affine plane has at least 6 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
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
