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mutually tangent

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  • Tangent circles — In geometry, tangent circles (also known as kissing circles) are circles that intersect in a single point. There are two types of tangency: internal and external. Many problems and constructions in geometry are related to tangent circles; such… …   Wikipedia

  • Coxeter's loxodromic sequence of tangent circles — Blue circle 0 is tangent to circles 1, 2 and 3, as well as to preceding circles −1, −2 and −3. In geometry, Coxeter s loxodromic sequence of tangent circles is an infinite sequence of circles arranged such that any four consecutive circles in the …   Wikipedia

  • Problem of Apollonius — In Euclidean plane geometry, Apollonius problem is to construct circles that are tangent to three given circles in a plane (Figure 1); two circles are tangent if they touch at a single point. Apollonius of Perga (ca. 262 BC ndash; ca. 190 BC)… …   Wikipedia

  • Descartes' theorem — For other uses, see Descartes theorem (disambiguation). In geometry, Descartes theorem, named after René Descartes, establishes a relationship between four kissing, or mutually tangent, circles. The theorem can be used to construct a fourth… …   Wikipedia

  • Soddy's hexlet — [ ellipse.] In geometry, Soddy s hexlet is a chain of six spheres (shown in grey in Figure 1), each of which is tangent to both of its neighbors and also to three mutually tangent given spheres. In Figure 1, these three spheres are shown as an… …   Wikipedia

  • Malfatti circles — In geometry, the Malfatti circles are three circles inside a given triangle such that each circle is tangent to the other two and to two sides of the triangle. They are named after Gian Francesco Malfatti, who made early studies of the problem of …   Wikipedia

  • Apollonian gasket — In mathematics, an Apollonian gasket or Apollonian net is a fractal generated from triples of circles, where any circle is tangent to two others. It is named after Greek mathematician Apollonius of Perga.ConstructionAn Apollonian gasket can be… …   Wikipedia

  • Pedal curve — Geometric construction of the pedal of C with respect to P In the differential geometry of curves, a pedal curve is a curve derived by construction from a given curve (as is, for example, the involute). Let C be a given curve and P a fixed point… …   Wikipedia

  • Pseudotriangle — In Euclidean plane geometry, a pseudotriangle is the simply connected subset of the plane that lies between any three mutually tangent convex sets. A pseudotriangulation is a partition of a region of the plane into pseudotriangles, and a pointed… …   Wikipedia

  • Circles of Apollonius — Apollonian circle redirects here. For a subdivision of this subject, see Apollonian circles. The term circle of Apollonius is used to describe several types of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these… …   Wikipedia

  • Osculating circle — Kissing circles redirects here. For Descartes theorem on mutually tangent (kissing) circles, see Descartes theorem. An osculating circle In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given… …   Wikipedia

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