affine geometry
"Affine geometry" is a branch of geometry focusing on properties that remain invariant under affine transformations, such as parallelism and ratios of lengths.
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Definition
C1Mathematics
(technical, academic)A field of geometry that studies properties of shapes and figures that remain unchanged under transformations like translation, scaling, and shearing.
Example
- In affine geometry, parallel lines remain parallel after an affine transformation.
- Affine geometry simplifies many problems by ignoring distances and angles.
C1Geometry
(technical, academic)The study of geometric properties and relations that do not depend on distances and angles, focusing instead on parallelism and proportionality.
Example
- Affine geometry allows us to analyze shapes in a more abstract way than Euclidean geometry.
- Understanding affine transformations is crucial for mastering affine geometry.
Similar
Terms that have similar or relatively close meanings to "affine geometry":
finite geometryconformal geometryabsolute geometrycontact geometryhyperbolic geometrylinear algebracomplex geometrycombinatorial geometry