sábado, 18 de abril de 2015

Carlyle Circles

Carlyle circles
Thomas Carlyle was a Scottish philosopher and teacher, and discovered a geometric interpretation for solving quadratic equations. If you start with the equation x2 – sx = 0, and construct the circle with the line joining (0, 1) and (sp) as a diameter, then the abscissas of the points where the circle intersects the x-axis are exactly the roots of the polynomial.
For instance, consider x2 – 4+ 3 = 0. Its Carlyle circle intersects the x-axis in 1 and 3, which are indeed the solutions of the quadratic equation!

Carlyle circles can be used for developing explicit ruler-and-compass constructions of regular polygons. 

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