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tangency theorem

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  • Circle packing theorem — Example of the circle packing theorem on K5, the complete graph on five vertices, minus one edge. The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane …   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

  • Hairy ball theorem — The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on the sphere. If f is a continuous function that assigns a vector in R3 to every point p on a sphere such that f ( p ) is always… …   Wikipedia

  • Bézout's theorem — is a statement in algebraic geometry concerning the number of common points, or intersection points, of two plane algebraic curves. The theorem claims that the number of common points of two such curves X and Y is equal to the product of their… …   Wikipedia

  • Marden's theorem — A triangle and its Steiner inellipse. The zeroes of p(z) are the black dots, and the zeroes of p (z) are the red dots). The center green dot is the zero of p (z). Marden s theorem states that the red dots are the foci of the ellipse. In… …   Wikipedia

  • Casey's theorem — In mathematics, Casey s theorem, also known as the generalized Ptolemy s theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey. Formulation of the theorem Let ,O be a circle of radius ,R. Let ,O 1, O 2, O 3, O …   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

  • Modern portfolio theory — Portfolio analysis redirects here. For theorems about the mean variance efficient frontier, see Mutual fund separation theorem. For non mean variance portfolio analysis, see Marginal conditional stochastic dominance. Modern portfolio theory (MPT) …   Wikipedia

  • Tangential quadrilateral — An example of a tangential quadrilateral In Euclidean geometry, a tangential quadrilateral or circumscribed quadrilateral is a convex quadrilateral whose sides all lie tangent to a single circle inscribed within the quadrilateral. This circle is… …   Wikipedia

  • Tangent lines to circles — In Euclidean plane geometry, tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is perpendicular to the radius to …   Wikipedia

  • Apollonius of Perga — Apollonius of Perga. Apollonius of Perga [Pergaeus] (Ancient Greek: Ἀπολλώνιος) (ca. 262 BC – ca. 190 BC) was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the… …   Wikipedia

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