Main Page | See live article | Alphabetical index 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. Table of contents 1 Flatness in mechanical engineering 2 External links 3 Flatness in cosmology 4 External links 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) External links A New Scientist article on Whitworth's method 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 External links http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/FlatnessProblem.html This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.