There are a few other uses of the word metric in mathematics, that all revolve around the concept described above:

- A metric can also be a scalar differential, say ds, which is something you integrate along a curve to find its length. In
**R**^{3}, it is given by ds^{2}=dx^{2}+dy^{2}+dz^{2}- essentially a differential statement of Pythagoras' Theorem. - In a more general context, ds is given by ds
^{2}=M_{ij}dx_{i}dx_{j}(using abstract index notation), where (M_{ij}) is a real symmetrix matrix, which is also called a metric tensor. In General Relativity, it is denoted g_{αβ}