Descartes' theorem
Teorema de los círculos de Descartes
- Date
- 1643 · confidence high
- Place
- Egmond, Netherlands
- Credited to
- René Descartes
- Field
- Knowledge & symbols
What was discovered
A quadratic relation between the curvatures of four mutually tangent ('kissing') circles, which allows a fourth circle tangent to three given ones to be constructed. It generalises to tangent spheres in higher dimensions and to spherical and hyperbolic geometry.
Stated by Descartes in 1643 in a letter to Princess Elisabeth of Bohemia; later summarised in Frederick Soddy's poem 'The Kiss Precise' (1936).
What it led to
- geometric constructions of tangent circles
- generalisation to spheres and higher dimensions
- applications in Apollonian circle packing