Luis Pedro Montejano
Abstract
We prove that if K is a convex body in En+1, n⩾2, and p0 is a point of K with the property that all n-sections of K through p0 are homothetic, then K is a Euclidean ball.
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We prove that if K is a convex body in En+1, n⩾2, and p0 is a point of K with the property that all n-sections of K through p0 are homothetic, then K is a Euclidean ball.
Key concepts: Homothetic transformation, Mathematics, Convex body, Regular polygon, Ball (mathematics), Euclidean geometry, Mixed volume, Combinatorics