Descartes Circle Theorem relates the curvatures, meaning the reciprocals of the radii, of four mutually tangent circles by a single algebraic equation. First stated by Rene Descartes, it allows the radius of a fourth circle tangent to three given mutually tangent circles to be computed algebraically rather than found by geometric construction.
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StatementFor four mutually tangent circles, the equation relating the four curvatures, meaning the signed reciprocals of the radii, is quadratic: given the curvatures of any three mutually tangent circles, this equation determines the curvature of a fourth circle tangent to all three. 1 Proof YearYear Rene Descartes stated the theorem; restated in verse by Frederick Soddy in his 1936 poem The Kiss Precise. Classification
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1. Descartes Circle Theorem (Wikipedia)
Wikimedia FoundationLead section
The theorem is named after René Descartes, who stated it in 1643.
Lead section
In geometry, Descartes's theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic equation.
Lead section, third sentence
The theorem is named after René Descartes, who stated it in 1643.
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