plane quadric
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Quadric (projective geometry) — In projective geometry a quadric is the set of points of a projective space where a certain quadratic form on the homogeneous coordinates becomes zero. It may also be defined as the set of all points that lie on their dual hyperplanes, under some … Wikipedia
Principal axes of a quadric — Principal Prin ci*pal, a. [F., from L. principalis. See {Prince}.] 1. Highest in rank, authority, character, importance, or degree; most considerable or important; chief; main; as, the principal officers of a Government; the principal men of a… … The Collaborative International Dictionary of English
Principal of a quadric — Principal Prin ci*pal, a. [F., from L. principalis. See {Prince}.] 1. Highest in rank, authority, character, importance, or degree; most considerable or important; chief; main; as, the principal officers of a Government; the principal men of a… … The Collaborative International Dictionary of English
Principal plane — Principal Prin ci*pal, a. [F., from L. principalis. See {Prince}.] 1. Highest in rank, authority, character, importance, or degree; most considerable or important; chief; main; as, the principal officers of a Government; the principal men of a… … The Collaborative International Dictionary of English
Complex projective plane — In mathematics, the complex projective plane, usually denoted CP2, is the two dimensional complex projective space. It is a complex manifold described by three complex coordinates where, however, the triples differing by an overall rescaling are… … Wikipedia
Fake projective plane — For Freedman s example of a non smoothable manifold with the same homotopy type as the complex projective plane, see 4 manifold. In mathematics, a fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have… … Wikipedia
diametral plane — noun 1. : a plane bisecting a system of parallel chords of a quadric surface; specifically : any plane through the center of a sphere 2. of a linear complex : a plane conjugate to a point at infinity … Useful english dictionary
Algebraic surface — In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface is therefore of complex dimension two (as a complex manifold, when it is non singular)… … Wikipedia
Lie sphere geometry — is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. It was introduced by Sophus Lie in the nineteenth century. [The definitive modern textbook on Lie sphere geometry is Harvnb|Cecil|1992 … Wikipedia
Plücker coordinates — In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogenous coordinates to each line in projective 3 space, P 3. Because they satisfy a quadratic constraint, they establish a one to one… … 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
