The cross ratio is a projective invariant used in geometry, particularly in projective geometry, to describe the ratio of the distances between four collinear points. It remains unchanged under projective transformations, making it a powerful tool for analyzing geometric properties that are invariant under perspective changes.

Cross Ratio

cross ratio

projective invariant

Geometry is a branch of mathematics concerned with the properties and relationships of points, lines, surfaces, and shapes in space. It encompasses various subfields that explore dimensions, transformations, and theorems to understand and solve spatial problems.

geometry

Projective geometry is a branch of mathematics that studies the properties of geometric figures that remain invariant under projection, focusing on the relationships between points, lines, and planes. It extends the concepts of geometry by adding 'points at infinity' to account for parallel lines intersecting, offering a more unified and generalized framework for understanding geometric transformations and perspectives.

projective geometry

distances between four collinear points

projective transformations

Geometric properties are characteristics that define the shape, size, and relative position of figures in space, often used to determine congruence, similarity, and symmetry. These properties play a crucial role in various fields such as mathematics, physics, engineering, and computer graphics, where they help in modeling and analyzing physical structures and phenomena.

Relevant Degrees

Your Lessons