Bonnesen's inequality
From Wikipedia, the free encyclopedia
Bonnesen's inequality is an inequality relating the length, the area, the radius of the incircle and the radius of the circumcircle of a curve.
More precisely, consider a planar simple closed curve of length L bounding a domain of area F. Let r and R denote the radii of the incircle and the circumcircle. Then Bonnesen's inequality states that
[edit] References
- Bonnesen, "Sur une amélioration de l'inégalite isopérimétrique du cercle et la démonstration d'une inégalité Minkowski," C. R. Acad. Sci. Paris 172 (1921), 1087–1089.
- Yu. D. Burago and V. A. Zalgaller, Geometric inequalities. Translated from the Russian by A. B. Sosinskiĭ. Springer-Verlag, Berlin, 1988. ISBN 3-540-13615-0.
