isepiphanic inequality

The classical isepiphanic inequality


concerns the volume V and the area A of any solid in 3.  It asserts that the ball has the greatest volume among the solids having a given area.

For a ball with radius r, we have

V=43πr3,A= 4πr2,

whence it follows the equality


Cf. the isoperimetric inequalityMathworldPlanetmath and the isoperimetric problemMathworldPlanetmath.


  • 1 Patrik Nordbeck: Isoperimetriska problemet eller Varför ser man så  få  fyrkantiga träd?  Examensarbete.  Lund University (1995).
Title isepiphanic inequality
Canonical name IsepiphanicInequality
Date of creation 2013-03-22 19:19:08
Last modified on 2013-03-22 19:19:08
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 6
Author pahio (2872)
Entry type Theorem
Classification msc 51M25
Classification msc 51M16