Carlyle circle

noun

A certain circle in a coordinate plane associated with a quadratic equation, having the property that the solutions of the 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.”

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Meanings

nounCarlyle circle (plural Carlyle circles)

plural Carlyle circles

  1. mathematicsA certain circle in a coordinate plane associated with a quadratic equation, having the property that the solutions of the 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.

Origin

The idea of using such a circle to solve a quadratic equation is attributed to Thomas Carlyle (1795–1881).

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Cite this entry
APA

Carlyle circle. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Carlyle%20circle

MLA

“Carlyle circle.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Carlyle%20circle. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Carlyle circle,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Carlyle%20circle.

Source: Carlyle circle on Wiktionary, CC BY-SA 4.0.