# Flatness

The

**flatness** of a

surface is the degree to which it approximates a

mathematical plane. The term is generalized for higher-dimensional manifolds to describe the degree to which they approximate the

Euclidean space of the same dimensionality.

Joseph Whitworth invented the first practical method of making and polishing accurate flat surfaces in 1830. This used engineer's blue and polishing techniques using three trial surfaces. This led to an explosion of development of precision instruments using his flat surfaces as a basis for further construction of precise shapes.

References:

- Wayne R. Moore,
*Foundations of Mechanical Accuracy*, Moore Special Tool Company, Bridgeport, CT (1970)

## External links

In cosmology, a question often asked is "is the Universe flat"? According to the Theory of Relativity, it probably is curved and warped due to gravity.

See also:

## External links