An affine geometry is a geometry in which properties are preserved by parallel projection from one plane to another. In an affine geometry, the third and fourth of Euclid's postulates become meaningless. This type of geometry was first studied by Euler.

# Affine Geometry

## See also

Absolute Geometry, Affine Complex Plane, Affine Equation, Affine Group, Affine Hull, Affine Plane, Affine Space, Affine Transformation, Ordered Geometry## Explore with Wolfram|Alpha

## References

Birkhoff, G. and Mac Lane, S. "Affine Geometry." §9.13 in*A Survey of Modern Algebra, 5th ed.*New York: Macmillan, pp. 268-275, 1996.Graustein, W. C.

*Introduction to Higher Geometry.*New York: Macmillan, pp. 179-182, 1930.Leichtweiß, K.

*Affine Geometry of Convex Bodies.*Heidelberg, Germany: Barth Verlag, 1998.

## Referenced on Wolfram|Alpha

Affine Geometry## Cite this as:

Weisstein, Eric W. "Affine Geometry."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/AffineGeometry.html