It is shown that the classical John ellipsoid, the Petty ellipsoid and a recently discovered ‘dual’ of the Legendre ellipsoid are all special cases (p = ∞, p = 1 and p = 2) of a family of Lp ellipsoids which can be associated with a fixed convex body. This insight allows for a unified view of, alternative approaches to, and extensions of some basic results in convex geometry. 2000 Mathematics Subject Classification 52A40.

Author notes

Research supported, in part, by NSF Grants DMS–9803261 and DMS–0104363.