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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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Inequality $\frac{C}{d_{max}} \le \pi $ relating perimeter and diameter of planar convex body

Let $C$ is a perimeter of a convex hull (plane geometry) and $d_{max}$ is the largest distance of two arbitrary points in the convex hull. I am looking for a proof that: $$\frac{C}{d_{max}} \le \pi …
Đào Thanh Oai's user avatar