Cross Ratio

The cross ratio is a mathematical concept used in geometry to measure the relative positions of four points on a line or in a projective space. It is calculated using a specific formula involving ratios of distances between these points. The cross ratio remains unchanged under projective transformations, making it a key invariant in geometry. In practical terms, it helps in understanding properties of shapes and maps, ensuring that certain proportions stay consistent even when the figure is viewed from different perspectives. It’s fundamental in areas like computer graphics, photography, and complex analysis.