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Carlyle circle information


In mathematics, a Carlyle circle is a certain circle in a coordinate plane associated with a quadratic equation; it is named after Thomas Carlyle. 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.

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Carlyle circle

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mathematics, a Carlyle circle is a certain circle in a coordinate plane associated with a quadratic equation; it is named after Thomas Carlyle. The circle has the...

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Thomas Carlyle

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Dumfriesshire, Scotland, Carlyle attended the University of Edinburgh where he excelled in mathematics, inventing the Carlyle circle. After finishing the...

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Pentagon

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) / 4 {\displaystyle \left({\sqrt {5}}-1\right)/4} as desired. The Carlyle circle was invented as a geometric method to find the roots of a quadratic...

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Quadratic equation

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solutions in the diagram are −AX1/SA and −AX2/SA. The Carlyle circle, named after Thomas Carlyle, has the property that the solutions of the quadratic...

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Circle

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of the circle and the centre is called the radius. The circle has been known since before the beginning of recorded history. Natural circles are common...

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Robert Carlyle

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Robert Carlyle OBE (born 14 April 1961) is a Scottish actor. His film work includes Trainspotting (1996), The Full Monty (1997), The World Is Not Enough...

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Constructible polygon

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285, 288, 291, 292, 296, ... (sequence A122254 in the OEIS) Polygon Carlyle circle Bold, Benjamin. Famous Problems of Geometry and How to Solve Them, Dover...

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List of circle topics

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Circle of antisimilitude Bankoff circle Brocard circle Carlyle circle Circumscribed circle (circumcircle) Midpoint-stretching polygon Coaxal circles Director...

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Heptadecagon

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William Richmond in 1893. The following method of construction uses Carlyle circles, as shown below. Based on the construction of the regular 17-gon, one...

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Regular polygon

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Platonic solid List of regular polytopes and compounds Equilateral polygon Carlyle circle Hwa, Young Lee (2017). Origami-Constructible Numbers (PDF) (MA thesis)...

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Straightedge and compass construction

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angle and becomes physically impractical after about 20 binary digits. Carlyle circle Geometric cryptography Geometrography List of interactive geometry software...

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Belinda Carlisle

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successful solo career with radio hits such as "Mad About You", "I Get Weak", "Circle in the Sand", "Leave a Light On", and "Heaven Is a Place on Earth". The...

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Geometrography

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A certain construction of the regular heptadecagon involving the Carlyle circles can be represented by the expression 8R1 + 4R2 + 22C1 + 11C3 and has...

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Alan Cumming

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album, recorded live at New York City's Café Carlyle, Alan Cumming Sings Sappy Songs: Live at the Cafe Carlyle. He toured an aptly styled, intimate, cabaret-like...

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Dandy

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dandyism" as defined by Victorian novelist George Meredith; whereas Thomas Carlyle, in his novel Sartor Resartus (1831), dismissed the dandy as "a clothes-wearing...

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Too Like the Lightning

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For instance, Carlyle is mostly referred to using she/her pronouns starting with Seven Surrenders, whereas in the first book Carlyle is referred to with...

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Sartor Resartus

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1831 novel by the Scottish essayist, historian and philosopher Thomas Carlyle, first published as a serial in Fraser's Magazine in November 1833 – August...

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Bin Laden family

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bin Ladin, is a wealthy family intimately connected with the innermost circles of the Saudi royal family. It is the namesake and controlling shareholder...

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Sutton Foster

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in while she was out. An Evening with Sutton Foster: Live at the Café Carlyle (2011) Wish (2009) Take Me to the World (2018) Tours An Evening with Sutton...

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Friedrich Nietzsche

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Enlightenment: A Brave New Era for Carlyle?". In Kerry, Paul E.; Hill, Marylu (eds.). Thomas Carlyle Resartus: Reappraising Carlyle's Contribution to the Philosophy...

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