Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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AREA OF TRIANGLES ASSOCIATED WITH A STRICTLY LOCALLY CONVEX CURVE

  • Kim, Dong-Soo (Department of Mathematics, Chonnam National University) ;
  • Kim, Dong Seo (Department of Mathematics, Chonnam National University) ;
  • Bae, Hyun Seon (Department of Mathematics, Chosun University) ;
  • Kim, Hye-Jung (Department of Mathematics, Chonnam National University)
  • Received : 2014.11.07
  • Accepted : 2014.12.11
  • Published : 2015.03.25
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Abstract

It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. Recently, it was proved that this property is a characteristic one of parabolas. That is, among strictly locally convex $C^{(3)}$ curves in the plane $\mathbb{R}^2$ parabolas are the only ones satisfying the above area property. In this article, we study strictly locally convex curves in the plane $\mathbb{R}^2$. As a result, generalizing the above mentioned characterization theorem for parabolas we present some conditions which are necessary and sufficient for a strictly locally convex $C^{(3)}$ curve in the plane to be an open part of a parabola.

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References

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