Flatness
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The intuitive idea of flatness is important in several fields.
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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 homological algebra and algebraic geometry means, of an object <math>A<math> in an abelian category, that <math>- \otimes A<math> is an exact functor. See flat module or, for more generality, flat morphism.
Flatness in cosmology
In cosmology, the concept of "curvature of space" is considered. A space without curvature is called a "flat space" or Euclidean space.
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
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 (http://journals.iranscience.net:800/www.newscientist.com/www.newscientist.com/lastword/article.jsp@id=lw801)