Table of contents

1 Flatness in mathematics 2 Flatness in cosmology 3 External links 4 Flatness in mechanical engineering 5 External links

Flatness in mathematics

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. See curvature.

Flatness in cosmology

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:

• Curvature
• Flatness criterion

• http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/FlatnessProblem.html

Flatness in mechanical engineering

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)