# An Extremal Property of the Rellot Triangle

@article{Makeev2003AnEP,
title={An Extremal Property of the Rellot Triangle},
journal={Journal of Mathematical Sciences},
year={2003},
volume={113},
pages={816-817}
}
• V. Makeev
• Published 1 March 2003
• Mathematics
• Journal of Mathematical Sciences
AbstractLet $$K \subset \mathbb{R}^2$$ be a planar set having unit constant width and piecewise $$C^2$$ -smooth boundary. Then the area of the set of the points belonging to at least three diameters of K is at most $$\sqrt 3 /4$$ , and the area of the set of the points belonging to a unique diameter of K is at least $$(2\pi - 3\sqrt 3 )/4$$ . In both cases, an equality is attained only if K is the Rellot triangle. Bibliography: 2 titles.

## References

A Kinematic Formula for Affine Diameters and Affine Medians of a Convex Set
AbstractFor a planar convex set K with C2-smooth boundary, the area of the set of the points lying on a given number of affine diameters of K is estimated. As a corollary, it is proved that the area