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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2016.1
- 수록면
- 583 - 595 (13page)
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초록· 키워드
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Archimedes showed that for a point P on a parabola X and a chord AB of Xparallel to the tangent of X at P, the area S of the region bounded by the parabola X andchord AB is four thirds of the area T of triangle △ABP. It is well known that the areaU formed by three tangents to a parabola is half of the area T of the triangle formed byjoining their points of contact. Recently, the first and third authors of the present paperand others proved that among strictly locally convex curves in the plane R2, these twoproperties are characteristic ones of parabolas.
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참고문헌 (25)
참고문헌 신청
J. -S. Baek / 2003 / A characterization of the unit sphere / Amer. Math. Monthly 110(9):830~833
A. Benyi / 2000 / Archimedean properties of parabolas / Amer. Math. Monthly 107:945~949
A. Benyi / 2003 / A generalized Archimedean property / Real Anal. Exchange 29:881~889
B.-Y. Chen / 2006 / New characterizations of W-curves / Publ. Math. Debrecen. 69(4):457~472
W. A. Day / 1991 / Inequalities for areas associated with conics / Amer. Math. Monthly 98(1):36~39
A. Benyi / 2000 / Archimedean properties of parabolas / Amer. Math. Monthly 107:945~949
A. Benyi / 2003 / A generalized Archimedean property / Real Anal. Exchange 29:881~889
B.-Y. Chen / 2006 / New characterizations of W-curves / Publ. Math. Debrecen. 69(4):457~472
W. A. Day / 1991 / Inequalities for areas associated with conics / Amer. Math. Monthly 98(1):36~39
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