Affine geometry is a branch of mathematics that deals with the study of geometric objects and their properties that are preserved under affine transformations. This can include translations, rotations, and scaling. Synonyms for affine geometry include Euclidean geometry, which focuses on properties that are preserved under rigid transformations, and projective geometry, which studies properties that are preserved under projective transformations. Other related terms and concepts include vector spaces, linear mappings, matrix algebra, and differential geometry. The study of affine geometry is useful in a variety of fields, including physics, engineering, computer graphics, and robotics. By understanding the properties of affine transformations, researchers and practitioners can design better algorithms, models, and systems that rely on geometric principles.