Affine geometry

Affine geometry studies the properties of shapes and figures that are preserved under affine transformations, such as translations, scaling, shearing, and combinations of these. Unlike Euclidean geometry, affine geometry does not consider distances and angles, but focuses on parallelism and ratios of lengths along parallel lines.

Important properties

• Parallel lines remain parallel after an affine transformation.

• Midpoints of line segments may not be preserved, but the ratio of lengths along a line is preserved.

• Collinearity (points lying on the same line) is preserved.

• The concept of area can change, but the ratio of areas of two regions is preserved under affine transformations.