Search results
Results from the WOW.Com Content Network
Kissing circles. Given three mutually tangent circles (black), there are, in general, two possible answers (red) as to what radius a fourth tangent circle can have. In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this ...
Tangent lines to circles; Circle packing theorem, the result that every planar graph may be realized by a system of tangent circles; Hexafoil, the shape formed by a ring of six tangent circles; Feuerbach's theorem on the tangency of the nine-point circle of a triangle with its incircle and excircles; Descartes' theorem; Ford circle; Bankoff circle
The same inversion transforms the third circle into another circle. The solution of the inverted problem must either be (1) a straight line parallel to the two given parallel lines and tangent to the transformed third given circle; or (2) a circle of constant radius that is tangent to the two given parallel lines and the transformed given circle.
The size of each new circle is determined by Descartes' theorem, which states that, for any four mutually tangent circles, the radii of the circles obeys the equation (+ + +) = (+ + +). This equation may have a solution with a negative radius; this means that one of the circles (the one with negative radius) surrounds the other three.
Pages in category "Theorems about circles" The following 21 pages are in this category, out of 21 total. ... Descartes' theorem; E. Eyeball theorem; F. Five circles ...
Seven circles theorem – A chain of six circles tangent to a seventh circle and each to its 2 neighbors; Six circles theorem – Relates to a chain of six circles together with a triangle; Smallest circle problem – Finding the smallest circle that contains all given points
A special case of Descartes' theorem on the sphere has three circles of radius 60° (''k'' = 1/√3, in blue) for which both circles touching all three (in green) have radius 30° (''k'' = √3). Items portrayed in this file
The purpose of including it was to (a) demonstrate how the generalization works in a specific case, and (b) show how the two "soddy circles" (related by the ± cases of the find-the-fourth-curvature version of Descartes' theorem) are strictly related to each-other as well as related to the other three circles, while (c) also showing how ...