inversive points

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• Inversive geometry — Not to be confused with Inversive ring geometry. In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion. These… …   Wikipedia

• Inversive plane — An inversive plane is a class of incidence structure in mathematics.It may be axiomatised by taking two classes, points and circles (or blocks ) with the properties * any three points lie on exactly one circle; * if P and Q are points and c a… …   Wikipedia

• Inversive ring geometry — In mathematics, inversive ring geometry is the extension to the context of associative rings, of the concepts of projective line, homogeneous coordinates, projective transformations, and cross ratio, concepts usually built upon rings that happen… …   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

• Möbius plane — A Möbius plane or inversive plane is a particular kind of plane geometry, built upon some affine planes by adding one point, called the ideal point or point at infinity. In a Möbius plane straight lines are a special case of circles; they are the …   Wikipedia

• Generalised circle — A generalized circle, also referred to as a cline or circline , is a straight line or a circle. The concept is mainly used in inversive geometry, because straight lines and circles have very similar properties in that geometry and are best… …   Wikipedia

• Möbius transformation — Not to be confused with Möbius transform or Möbius function. In geometry, a Möbius transformation of the plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − …   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

• Apollonian circles — Some Apollonian circles. Every blue circle intersects every red circle at a right angle. Every red circle passes through the two points, C and D, and every blue circle separates the two points. This article discusses a family of circles sharing a …   Wikipedia

• HEBREW GRAMMAR — The following entry is divided into two sections: an Introduction for the non specialist and (II) a detailed survey. [i] HEBREW GRAMMAR: AN INTRODUCTION There are four main phases in the history of the Hebrew language: the biblical or classical,… …   Encyclopedia of Judaism

• Peaucellier-Lipkin linkage — The Peaucellier Lipkin linkage (or Peaucellier Lipkin cell), invented in 1864, was the first linkage capable of transforming rotary motion into perfect straight line motion, and vice versa. It is named after Charles Nicolas Peaucellier (1832… …   Wikipedia