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right In geometry, the nine-point conic of a complete quadrilateral is a conic that passes through the three diagonal points and the six midpoints of sides of the complete quadrilateral. The nine-point conic was described by Maxime Bôcher in 1892. The celebrated nine-point circle is an instance of Bôcher's conic. The nine-point hyperbola is another instance. Bôcher used the four points of the complete quadrilateral as three vertices of a triangle with one independent point: :Given a triangle ''ABC'' and a point ''P'' in its plane, a conic can be drawn through the following nine points: :: the midpoints of the sides of ''ABC'', :: the midpoints of the lines joining ''P'' to the vertices, and :: the points where these last named lines cut the sides of the triangle. The conic is an ellipse if ''P'' lies in the interior of ''ABC'' or in one of the regions of the plane separated from the interior by two sides of the triangle, otherwise the conic is a hyperbola. Bôcher notes that when ''P'' is the orthocenter, one obtains the nine-point circle, and when ''P'' is on the circumcircle of ''ABC'', then the conic is an equilateral hyperbola. In 1912 Maud Minthorn showed that the nine-point conic is the locus of the center of a conic through four given points. ==References== * Maxime Bôcher (1892) (Nine-point Conic ), Annals of Mathematics, link from Jstor. * Fanny Gates (1894) (Some Considerations on the Nine-point Conic and its Reciprocal ), Annals of Mathematics 8(6):185–8, link from Jstor. * Maud A. Minthorn (1912) (The Nine Point Conic ), Master's dissertation at University of California, Berkeley, link from HathiTrust. * Eric W. Weisstein (Nine-point conic ) from MathWorld. * Michael DeVilliers (2006) (The nine-point conic: a rediscovery and proof by computer ) from ''International Journal of Mathematical Education in Science and Technology'', a Taylor & Francis publication. * Christopher Bradley (The Nine-point Conic and a Pair of Parallel Lines ) from University of Bath. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Nine-point conic」の詳細全文を読む スポンサード リンク
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