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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:
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PLANE GEOMETRY, THEOREMSShowing 1 featured edition. View all 1 editions?
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An optimal control formulation of the Blaschke-Lebesgue theorem
1988, Naval Postgraduate School, Available from National Technical Information Service
in English
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Edition Notes
Cover title.
"NPS-55-88-008."
"August 1988."
AD A200 939.
Includes bibliographical references (p. 15-16).
aq/aq cc:9116 07/18/97
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