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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제59권 제2호
- 발행연도
- 2022.3
- 수록면
- 407 - 417 (11page)
- DOI
- 10.4134/BKMS.b210311
이용수
초록· 키워드
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Archimedes proved that for a point $P$ on a parabola $X$ and a chord $AB$ of $X$ parallel to the tangent of $X$ at $P$, the area of the region bounded by the parabola $X$ and the chord $AB$ is four thirds of the area of the triangle $\bigtriangleup ABP$. This property was proved to be a characteristic of parabolas, so called the Archimedean characterization of parabolas. In this article, we study strictly convex curves in the plane ${\mathbb R}^{2}$. As a result, first using a functional equation we establish a characterization theorem for quadrics. With the help of this characterization we give another proof of the Archimedean characterization of parabolas. Finally, we present two related conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open arc of a parabola.
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