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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

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