High Quality Content by WIKIPEDIA articles! In convex geometry, the Mahler volume of a centrally symmetric convex body is a dimensionless quantity that is associated with the body and is invariant under affine transformations. It is named after German-English mathematician Kurt Mahler. It is known that the shapes with the largest possible Mahler volume are the spheres and ellipsoids; this is now known as the Blashke–Santalo inequality. The still-unsolved Mahler conjecture states that the minimum possible Mahler volume is attained by a hypercube.

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