Affinigeometria

Affinigeometria, also known as affine geometry, is a branch of geometry that studies properties of figures that are preserved under affine transformations. These transformations include translations, scalings, rotations, and shears, but not reflections or projections. Affinigeometria is a generalization of Euclidean geometry, which is a special case of affine geometry where the underlying field is the real numbers and the transformations are isometries.

In affine geometry, parallelism is preserved, but lengths and angles are not necessarily preserved. This makes affine geometry useful in studying shapes and figures that maintain parallelism but may be distorted in other ways. For example, affine transformations can be used to model the perspective of an image or the distortion of an object viewed through a lens.

One of the fundamental concepts in affinigeometria is the concept of an affine space. An affine space is a set of points equipped with a vector space structure, where each point can be associated with a vector. This allows for the definition of lines, planes, and other geometric objects in terms of vectors.

Another important concept is the concept of an affine transformation. An affine transformation is a function that maps an affine space to itself and preserves the affine structure. These transformations can be represented by matrices, and they are used in various applications, such as computer graphics, image processing, and robotics.

In summary, affinigeometria is a branch of geometry that studies properties of figures preserved under affine transformations. It is a generalization of Euclidean geometry and is useful in studying shapes and figures that maintain parallelism but may be distorted in other ways. The concepts of affine space and affine transformation are fundamental to affine geometry.