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.
- Reflexive Graph
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