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Carlyle circle : ウィキペディア英語版 | Carlyle circle In mathematics, a Carlyle circle (after Thomas Carlyle (1795–1881)) is a certain circle in a coordinate plane associated with a quadratic equation. The circle has the property that the solutions of the quadratic equation are the horizontal coordinates of the intersections of the circle with the horizontal axis. Carlyle circles have been used to develop ruler-and-compass constructions of regular polygons. ==Definition==
Given the quadratic equation :''x''2 − ''sx'' + ''p'' = 0 the circle in the coordinate plane having the line segment joining the points ''A''(0, 1) and ''B''(''s'', ''p'') as a diameter is called the Carlyle circle of the quadratic equation. 〔E. John Hornsby, Jr.: (''Geometrical and Graphical Solutions of Quadratic Equations'' ). The College Mathematics Journal, Vol. 21, No. 5 (Nov., 1990), pp. 362-369 ((JSTOR ))〕
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