The Blaschke-Santalo Inequality is a result of convex geometry concerning the Mahler volume, a dimensionless quantity associated with a centrally symmetric convex body that remains unchanged under linear transformations. The inequality establishes that, among all centrally symmetric convex bodies, the ball and the solid ellipsoids attain the largest possible Mahler volume, making them the extremal shapes for this quantity.
Facts
StatementAmong all centrally symmetric convex bodies, the ball and solid ellipsoids attain the largest possible Mahler volume. 2 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Wikipedia: Mahler volume
Sources
1. Wikipedia: Mahler volume
WikipediaLead section, statement-form reference
It is known that the shapes with the largest possible Mahler volume are the balls and solid ellipsoids; this is now known as the Blaschke-Santaló inequality.
In Branch: Discrete Geometry, Lead sentence
In convex geometry, the Mahler volume of a centrally symmetric convex body is a dimensionless quantity that is associated with the
View the Source 2. Blaschke-Santalo inequality, Wikipedia
Introduction
It is known that the shapes with the largest possible Mahler volume are the balls and solid ellipsoids; this is now known as the Blaschke-Santalo inequality.
Extreme shapes
the full result was proven much later by Luis Santalo (1949)
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