euclidean plane wikipedia - EAS
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See all on Wikipediahttps://en.wikipedia.org/wiki/Euclidean_plane_isometryIn geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections, and glide reflections (see below under
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See moreInformally, a Euclidean plane isometry is any way of transforming the plane without "deforming" it. For example, suppose that the Euclidean plane is represented by a sheet of transparent plastic sitting on a desk. Examples of
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See moreAn isometry of the Euclidean plane is a distance-preserving transformation of the plane. That is, it is a map
such that for any points p...
See moreReflections, or mirror isometries, can be combined to produce any isometry. Thus isometries are an example of a reflection group.
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See more• Beckman–Quarles theorem, a characterization of isometries as the transformations that preserve unit distances
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It can be shown that there are four types of Euclidean plane isometries. (Note: the notations for the types of isometries listed below are not completely standardised.)
Reflections...
See moreIn terms of complex numbers, the isometries of the plane are either of the form
or of the form
for some complex...
See moreWikipedia text under CC-BY-SA license- https://en.wikipedia.org/wiki/Euclidean_geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first t…
Wikipedia · Text under CC-BY-SA license - https://en.wikipedia.org/wiki/Euclidean_space
- Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension, including the three-dimensional space and the Euclidean plane (dimens...
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- https://topospaces.subwiki.org/wiki/Euclidean_plane
- The Euclidean plane, denoted , is defined as the product , i.e., the set of ordered pairs of real numbers. It is equipped with the product topology from the Euclidean topology on the real line. In addition to a topological structure, the Euclidean plane also has a natural metric structure, group structure, and other structures, all of them giving r...
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