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Note on a conjecture of L. A. Santaló
Published online by Cambridge University Press: 26 February 2010
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Let be a plane bounded convex set whose width in the direction φ is
. It has been shown by L. A. Santaló that
is invariant under unimodular affine transformations. Santaló [1] established a number of properties of this invariant and conjectured that if the area of is A(
) then
and that equality characterizes triangles. In this note Santaló's conjecture is shown to be true.
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