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单词 Carlyle Circle
释义

Carlyle Circle

Consider a Quadratic Equation where and denote signed lengths. The Circlewhich has the points and as a Diameter is then called the Carlyle circle of the equation. The Center of is then at the Midpoint of , , which is also the Midpoint of and . Call the points at which crosses the x-Axis and (with ). Then






so and are the Roots of the quadratic equation.

See also 257-gon, 65537-gon, Heptadecagon, Pentagon


References

De Temple, D. W. ``Carlyle Circles and the Lemoine Simplicity of Polygonal Constructions.'' Amer. Math. Monthly 98, 97-108, 1991.

Eves, H. An Introduction to the History of Mathematics, 6th ed. Philadelphia, PA: Saunders, 1990.

Leslie, J. Elements of Geometry and Plane Trigonometry with an Appendix and Very Copious Notes and Illustrations, 4th ed., improved and exp. Edinburgh: W. & G. Tait, 1820.


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更新时间:2025/4/5 9:05:58