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An optimal control formulation of the Blaschke-Lebesgue theorem

by: Ghandehari, Mostafa.

Publication date: 1988-08

Topics: THEOREMS., PLANE GEOMETRY.

Publisher: Monterey, California : Naval Postgraduate School

Collection: navalpostgraduateschoollibrary; fedlink; americana

Contributor: Naval Postgraduate School, Dudley Knox Library

Language: en_US

Cover title

"NPS-55-88-008."

"August 1988."

AD A200 939

Includes bibliographical references (p. 15-16)

The Blaschke-Lebesgue theorem states that of all plane sets of given constant width the Reuleaux triangle has least area. The area to be minimized is a functional involving the support function and the radius of curvature of the set. The support function satisfies a second order ordinary differential equation where the radius of curvature is the control parameter. The radius of curvature of a plane set of constant width is non-negative and bounded above. Thus we can formulate and analyze the Blaschke-Lebesgue theorem as an optimal control problem. Keywords: Calculus of variation and optimal control. (KR) Limitation Statement:

aq/aq cc:9116 07/18/97