Metric (idea)

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 R³, it is given by ds²=dx²+dy²+dz²- essentially a differential statement of Pythagoras' Theorem.
• In a more general context, ds is given by ds²=M_ijdx_idx_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