Cayley-Menger Determinant

The Cayley-Menger determinant is a mathematical tool used to calculate the volume of a simple geometric shape, like a triangle or tetrahedron, when only the distances between its points are known. It forms a matrix from these distances and computes its determinant to directly find the shape's volume. This method allows us to determine the size of a shape without needing the actual coordinates of the points, relying solely on how far apart they are. It's a powerful approach in geometry and distance-based shape analysis.