Discovered by the
mathematician Bernhard Riemann c.1854, the metric tensor is way to describe the curvature of a surface given its points. Specifically, a collection of 10 numbers at every point on a 4-dimensional surface can fully describe that surface, no matter how many folds (
dimensions) the surface contains.
If one were to view 2-dimensional space, you would need a collection of 3 numbers at every point. To view
N-dimensional space, the metric tensor would look like a collection of
N x
N numbers, as on a
chessboard. Thusly, unfolding the surface and flattening it out reduces it to 2-dimensions and you get
Pythagoras famous formula.
The metric tensor, a mathematical breakthrough, later gave
Albert Einstein one of the keys to unlocking his theory of
general relativity.