Gyration: Difference between revisions
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{{Short description|A rotation in a discrete subgroup of symmetries of the Euclidean plane}} |
{{Short description|A rotation in a discrete subgroup of symmetries of the Euclidean plane}} |
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{{about|rotational symmetry in mathematics|the size measure in structural engineering|radius of gyration|the motion of a charged particle in an magnetic field|gyroradius|the tensor of second moments|gyration tensor}} |
{{about|rotational symmetry in mathematics|the size measure in structural engineering|radius of gyration|the motion of a charged particle in an magnetic field|gyroradius|the tensor of second moments|gyration tensor}} |
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In geometry, a '''gyration''' is a [[rotation]] in a [[discrete group|discrete]] [[symmetry group|subgroup of symmetries]] of the [[Euclidean plane]] such that the subgroup does not also contain a [[reflection symmetry]] whose axis passes through the center of [[rotational symmetry]]. In the [[orbifold]] corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a [[mirror]], called a '''gyration point'''.<ref name="Liebeck"/> |
In geometry, a '''gyration''' is a [[rotation]] in a [[discrete group|discrete]] [[symmetry group|subgroup of symmetries]] of the [[Euclidean plane]] such that the subgroup does not also contain a [[reflection symmetry]] whose axis passes through the center of [[rotational symmetry]]. In the [[orbifold]] corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a [[mirror]], called a '''gyration point'''.<ref name="Liebeck"/> |
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<ref name="Liebeck">{{cite book |authorlink1=Martin Liebeck |author-first1=Martin W. |author-last1=Liebeck |author-first2=Jan |author-last2=Saxl |author-first3=N. J. |author-last3=Hitchin |author-first4=A. A. |author-last4=Ivanov |title=Groups, Combinatorics & Geometry |url=https://books.google.com/books?id=5h84AAAAIAAJ&pg=PA439 |location=Symposium, London Mathematical Society: Symposium on Groups and Combinatorics (1990), Durham |date=1992-09-10 |orig-year=1990 |edition=illustrated |publisher=[[Cambridge University Press]] |access-date=2010-04-07 |series=Lecture note series |volume=165 |issn=0076-0552 |isbn=0-52140685-4 }} (489 pages)</ref> |
<ref name="Liebeck">{{cite book |authorlink1=Martin Liebeck |author-first1=Martin W. |author-last1=Liebeck |author-first2=Jan |author-last2=Saxl |author-first3=N. J. |author-last3=Hitchin |author-first4=A. A. |author-last4=Ivanov |title=Groups, Combinatorics & Geometry |url=https://books.google.com/books?id=5h84AAAAIAAJ&pg=PA439 |location=Symposium, London Mathematical Society: Symposium on Groups and Combinatorics (1990), Durham |date=1992-09-10 |orig-year=1990 |edition=illustrated |publisher=[[Cambridge University Press]] |access-date=2010-04-07 |series=Lecture note series |volume=165 |issn=0076-0552 |isbn=0-52140685-4 }} (489 pages)</ref> |
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==External links== |
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[[Category:Euclidean geometry]] |
[[Category:Euclidean geometry]] |
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{{geometry-stub}} |
{{geometry-stub}} |
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Revision as of 21:31, 12 May 2024
 | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (May 2024) |
In geometry, a gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection symmetry whose axis passes through the center of rotational symmetry. In the orbifold corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a mirror, called a gyration point.[1]
For example, having a sphere rotating about any point that is not the center of the sphere, the sphere is gyrating. If it was rotating about its center, the rotation would be symmetrical and it would not be considered gyration.
References
- ^ Liebeck, Martin W.; Saxl, Jan; Hitchin, N. J.; Ivanov, A. A. (1992-09-10) [1990]. Groups, Combinatorics & Geometry. Lecture note series. Vol. 165 (illustrated ed.). Symposium, London Mathematical Society: Symposium on Groups and Combinatorics (1990), Durham: Cambridge University Press. ISBN 0-52140685-4. ISSN 0076-0552. Retrieved 2010-04-07.
{{cite book}}: CS1 maint: location (link) (489 pages)
External links
The dictionary definition of gyration at Wiktionary
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