# Affine geometry

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## Definition of the noun affine geometry

What does affine geometry mean as a name of something?

**noun**

- the geometry of affine transformations
- domain: math / mathematics / maths
- lexical domain: Cognitive Processes - nouns denoting cognitive processes and contents
- more generic word: geometry = the pure mathematics of points and lines and curves and surfaces

## 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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### 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 ...

### Encyclopedia of Distances (2014)

by Michel Marie Deza, Elena Deza

**Affine Geometry** 121 6.3 Affine
Geometry.

### Dictionary of Distances (2006)

by Michel-Marie Deza, Elena Deza

* AFFINE GEOMETRY An n*-dimensional affine space over a field F ...

### 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 ...

### 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 ...

### 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),
...

### Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (2002)

by Ivor Grattan-Guinness

nineteenth century saw diverse developments in geometry that fundamentally
altered its conception since the time of Euclid two thousand years before:
projective geometry, **affine geometry**, nonEuclidean geometry and differential
geometry, ...

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

by Christopher Clapham, James Nicholson, James R. Nicholson

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

## Online dictionaries and encyclopedias with entries for Affine geometry

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## Video about Affine geometry

**Affine geometry Meaning**

Video shows what affine geometry means. The branch of geometry dealing with affine transformations.. Affine geometry Meaning. How to pronounce, definition ...

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