• DOI:10.1023/A:1021287302603
• Corpus ID: 116027099

An Extremal Property of the Rellot Triangle

@article{Makeev2003AnEP,
  title={An Extremal Property of the Rellot Triangle},
  author={Vladimir V. Makeev},
  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.