Area Properties of Strictly Convex Curves

Dong-Soo Kim, Young Ho Kim and Yoon-Tae Jung
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Dong-Soo Kim: Department of Mathematics, Chonnam National University, Gwangju 61186, Korea
Young Ho Kim: Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
Yoon-Tae Jung: Department of Mathematics, Chosun University, Gwangju 61452, Korea

Mathematics, 2019, vol. 7, issue 5, 1-14

Abstract: We study functions defined in the plane E 2 in which level curves are strictly convex, and investigate area properties of regions cut off by chords on the level curves. In this paper we give a partial answer to the question: Which function has level curves whose tangent lines cut off from a level curve segment of constant area? In the results, we give some characterization theorems regarding conic sections.

Keywords: Archimedes; level curve; chord; conic section; strictly convex plane curve; curvature; equiaffine transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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