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Conformal geometric algebra, the Glossary

Index Conformal geometric algebra

Conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a map from points in an -dimensional base space to null vectors in.[1]

Table of Contents

  1. 23 relations: Advances in Applied Clifford Algebras, Affine space, Blade (geometry), Chasles' theorem (kinematics), Conformal map, David Hestenes, Dilation (metric space), Exterior algebra, Flat (geometry), Geometric algebra, Inversion transformation, Inversive geometry, Liouville's theorem (conformal mappings), Minkowski space, N-sphere, Perpendicular distance, Point at infinity, Projective geometry, Pseudo-Euclidean space, Quasi-sphere, Quaternions and spatial rotation, Rigid transformation, Screw theory.

  2. Conformal geometry
  3. Geometric algebra
  4. Inversive geometry

Advances in Applied Clifford Algebras

Advances in Applied Clifford Algebras is a peer-reviewed scientific journal that publishes original research papers and also notes, expository and survey articles, book reviews, reproduces abstracts and also reports on conferences and workshops in the area of Clifford algebras and their applications to other branches of mathematics and physics, and in certain cognate areas.

See Conformal geometric algebra and Advances in Applied Clifford Algebras

Affine space

In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

See Conformal geometric algebra and Affine space

Blade (geometry)

In the study of geometric algebras, a -blade or a simple -vector is a generalization of the concept of scalars and vectors to include simple bivectors, trivectors, etc. Conformal geometric algebra and Blade (geometry) are geometric algebra.

See Conformal geometric algebra and Blade (geometry)

Chasles' theorem (kinematics)

In kinematics, Chasles' theorem, or Mozzi–Chasles' theorem, says that the most general rigid body displacement can be produced by a translation along a line (called its screw axis or Mozzi axis) followed (or preceded) by a rotation about an axis parallel to that line.

See Conformal geometric algebra and Chasles' theorem (kinematics)

Conformal map

In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths.

See Conformal geometric algebra and Conformal map

David Hestenes

David Orlin Hestenes (born May 21, 1933) is a theoretical physicist and science educator.

See Conformal geometric algebra and David Hestenes

Dilation (metric space)

In mathematics, a dilation is a function f from a metric space M into itself that satisfies the identity for all points x, y \in M, where d(x, y) is the distance from x to y and r is some positive real number.

See Conformal geometric algebra and Dilation (metric space)

Exterior algebra

In mathematics, the exterior algebra or Grassmann algebra of a vector space V is an associative algebra that contains V, which has a product, called exterior product or wedge product and denoted with \wedge, such that v\wedge v.

See Conformal geometric algebra and Exterior algebra

Flat (geometry)

In geometry, a flat or affine subspace is a subset of an affine space that is itself an affine space (of equal or lower dimension).

See Conformal geometric algebra and Flat (geometry)

Geometric algebra

In mathematics, a geometric algebra (also known as a Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors.

See Conformal geometric algebra and Geometric algebra

Inversion transformation

In mathematical physics, inversion transformations are a natural extension of Poincaré transformations to include all conformal, one-to-one transformations on coordinate space-time.

See Conformal geometric algebra and Inversion transformation

Inversive geometry

In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves.

See Conformal geometric algebra and Inversive geometry

Liouville's theorem (conformal mappings)

In mathematics, Liouville's theorem, proved by Joseph Liouville in 1850, is a rigidity theorem about conformal mappings in Euclidean space.

See Conformal geometric algebra and Liouville's theorem (conformal mappings)

Minkowski space

In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation.

See Conformal geometric algebra and Minkowski space

N-sphere

In mathematics, an -sphere or hypersphere is an -dimensional generalization of the -dimensional circle and -dimensional sphere to any non-negative integer.

See Conformal geometric algebra and N-sphere

Perpendicular distance

In geometry, the perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or both.

See Conformal geometric algebra and Perpendicular distance

Point at infinity

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

See Conformal geometric algebra and Point at infinity

Projective geometry

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.

See Conformal geometric algebra and Projective geometry

Pseudo-Euclidean space

In mathematics and theoretical physics, a pseudo-Euclidean space of signature is a finite-dimensional ''n''-space together with a non-degenerate quadratic form.

See Conformal geometric algebra and Pseudo-Euclidean space

Quasi-sphere

In mathematics and theoretical physics, a quasi-sphere is a generalization of the hypersphere and the hyperplane to the context of a pseudo-Euclidean space.

See Conformal geometric algebra and Quasi-sphere

Quaternions and spatial rotation

Unit quaternions, known as ''versors'', provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space.

See Conformal geometric algebra and Quaternions and spatial rotation

Rigid transformation

In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points.

See Conformal geometric algebra and Rigid transformation

Screw theory

Screw theory is the algebraic calculation of pairs of vectors, such as angular and linear velocity, or forces and moments, that arise in the kinematics and dynamics of rigid bodies.

See Conformal geometric algebra and Screw theory

See also

Conformal geometry

Geometric algebra

Inversive geometry

References

[1] https://en.wikipedia.org/wiki/Conformal_geometric_algebra