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# Affine geometry

## Definition of the noun affine geometry

What does affine geometry mean as a name of something?

noun

1. the geometry of affine transformations

## Explanation

Affine geometry: In mathematics, affine geometry is the study of parallel lines. Its use of Playfair's axiom is fundamental since comparative measures of angle size are foreign to affine geometry so that Euclid's parallel postulate is beyond the scope of pure affine geometry. In affine geometry, the relation of parallelism may be adapted so as to be an equivalence relation. Comparisons of figures in affine geometry are made with affinities, which are mappings comprising the affine group A. Since A lies between the Euclidean group E and the group of projectivities P, affine geometry is sometimes mentioned in connection with the Erlangen program, which is concerned with group inclusions such as E ⊂ A ⊂ P.

• also known as 仿射几何学

## Printed dictionaries and other books with definitions for Affine geometry

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### Subject Headings Used in the Dictionary Catalogs of the Library of Congress [from 1897 Through June 1964] (1966)

by Library of Congress. Subject Cataloging Division

Geometry, Affine x Affine geometry xx Geometry, Modern Geometry, Modern t sa Geometry, Affine Geomorphic geology See Geomorphology Geomorphology ( Indirect) sa Erosion Landforms x Geomorphic geology Physiography xx Erosion ...

### Encyclopaedia of Mathematics (2012)

by Michiel Hazewinkel

The group of affine transformations contains various subgroups; as a result, in addition to general affine geometry, subordinated geometries – equi-affine geometry, centro-affine geometry, etc. – arose, corresponding to these groups. Affine ...

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

See also AFFINE CONNECTION, AFFINE EQUATION, AFFINE GEOMETRY, AFFINE GROUP, AFFINE HULL, AFFINE PLANE, AFFINE SPACE, AFFINE TRANSFORMATION, AFFINITY, COMPLEX PLANE, COMPLEX PROJECTIVE PLANE ...

### Dictionary of Computer Vision and Image Processing (2013)

by Robert B. Fisher, Toby P. Breckon, Kenneth Dawson-Howe, Andrew Fitzgibbon, Craig Robertson, Emanuele Trucco, Christopher K. I. Williams

Affine geometry is a studyofproperties of geometric objects that remain invariant under affine transformations (mappings), ...

### The Concise Oxford Dictionary of Mathematics (2009)

by Christopher Clapham, James Nicholson

affine geometry A geometry in which some properties are preserved by *parallel projection from one plane to ...

### Encyclopedia of Distances (2016)

by Michel Marie Deza, Elena Deza

Affine Geometry ...

### Dictionary of Distances (2006)

by Michel-Marie Deza, Elena Deza

AFFINE GEOMETRY An n-dimensional affine space over a field F is a set An (the elements of which are called points of the affine space) ...

### Dictionary of Applied Math for Engineers and Scientists (2002)

by Emma Previato

affine geometry spaces. The geometry of affine affine map Let X and Y be vector spaces and C a convex subset of X. A map T : C → Y is called an affine map if T((1 − t)x + ty) = (1 − t)Tx + tTy for all x,y ∈ C, and all ...

### The Facts on File Dictionary of Mathematics (2009)

by John Daintith, Richard Rennie

affine geometry /ă-fÿn/ The study of properties left invariant under the group of affine transformations. See affine ...

### MCGRAW-HILL DICTIONARY OF MATHEMATICS, 2/E (2002)

by McGraw-Hill Education

{ o'fin ko'nek-shon } affine geometry The study ...

### Encyclopedia of Geographic Information Science (2007)

by Karen Kemp

a a Betweenness, Convexity, and Affine Geometry Affine geometry concerns properties that are definable from the relation of betweenness. This includes the notion of convexity, since a convex ...

## Online dictionaries and encyclopedias with entries for Affine geometry

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