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Lie group of complex numbers of unit modulus; topologically a circle
mathematics, the circle group, denoted by T {\displaystyle \mathbb {T} } or S 1 {\displaystyle S^{1}} , is the multiplicative group of all complex numbers
Circle_group
Peer-to-peer payments technology company
Circle Internet Group, Inc. is a payments technology company. Founded by Jeremy Allaire and Sean Neville in 2013, it is currently headquartered in New
Circle_Internet_Group
British private healthcare provider
Circle Health Group is a private healthcare provider in the United Kingdom, and is the country's biggest private hospital provider. The company was founded
Circle_Health_Group
Simple curve of Euclidean geometry
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of
Circle
Group that is also a differentiable manifold with group operations that are smooth
into the circle group, an archetypal example of a Lie group. Lie groups are widely used in many parts of modern mathematics and physics. Lie groups were first
Lie_group
Circle with radius of one
mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1
Unit_circle
Two or more humans who interact with one another
Older people who were more active in social circles tended to be better off health-wise. Social groups tend to form based on certain principles of attraction
Social_group
British public company
Blue Circle Industries was a British public company manufacturing cement. It was listed on the London Stock Exchange, and a long time constituent of the
Blue_Circle_Industries
Topics referred to by the same term
Circle Sport – The Motorsports Group may refer to: Hillman–Circle Sport The Motorsports Group This disambiguation page lists articles associated with
Circle Sport – The Motorsports Group
Circle_Sport_–_The_Motorsports_Group
American punk band
Circle Jerks (stylized as Ciʀcle JƎʀᴋs) are an American hardcore punk band, formed in 1979 in Los Angeles, California. The group was founded by former
Circle_Jerks
Group male masturbation
A circle jerk, also sometimes spelled circlejerk, is a sexual practice in which a group of men form a circle and masturbate or touch each other's genitals
Circle_jerk
American parody group
The Inner Circle is an American musical parody group made up of seasoned reporters, bloggers, web journalists, and television and radio personalities from
Inner_Circle_(parody_group)
Duality for locally compact abelian groups
compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers
Pontryagin_duality
Number, approximately 3.14
mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics
Pi
Mathematical group that can be generated as the set of powers of a single element
around an axis, but instead rotoreflections. The group of all rotations of a circle (the circle group, also denoted S1) is not cyclic, because there is
Cyclic_group
Complex numbers with unit norm and both real and imaginary parts rational numbers
The set of rational points on the unit circle, shortened G in this article, forms an infinite abelian group under rotations. The identity element is
Group of rational points on the unit circle
Group_of_rational_points_on_the_unit_circle
Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
groups of spheres are not trivial in general. It also provides a basic example of a principal bundle, by identifying the fiber with the circle group.
Hopf_fibration
Topics referred to by the same term
Look up full circle in Wiktionary, the free dictionary. Full Circle may refer to: Full circle (unit), a unit of plane angle Full Circle, a 1962 novel by
Full_Circle
Group of unitary matrices
group U ( 1 ) {\displaystyle \operatorname {U} (1)} corresponds to the circle group, isomorphic to the set of all complex numbers that have absolute value
Unitary_group
South Korean girl group
Yourself: "Circle Album Chart – December 2024". Circle Chart (in Korean). Retrieved January 9, 2025. "Circle Album Chart – Week 1, 2025". Circle Chart (in
Kiss_of_Life_(group)
First part of Dante Alighieri's Divine Comedy
one circle for violence (Circle 7) and two circles for fraud (Circles 8 and 9). As a Christian, Dante adds Circle 1 (Limbo) to Upper Hell and Circle 6 (Heresy)
Inferno_(Dante)
Group that is a topological space with continuous group operations
space forms an (abelian) topological group. Some other examples of abelian topological groups are the circle group S 1 {\displaystyle S^{1}} , or the torus
Topological_group
Group of transformations under which the object is invariant
symmetry group of a circle and the continuous equivalent of Cn. There is no geometric figure that has as full symmetry group the circle group, but for
Symmetry_group
Symbol of anarchism
The circle-A or anarchist A, written as Ⓐ, is a graphic and political symbol representing the anarchist movement and ideology. Seeking a symbol that could
Circle-A
Number with an integer power equal to 1
cyclic group. It is worth remarking that the term of cyclic group originated from the fact that this group is a subgroup of the circle group. Let Q (
Root_of_unity
Geometric representation of the complex numbers
multiplication by a complex number of modulus 1 acts as a rotation (the circle group). The complex plane is sometimes called the Argand plane or Gauss plane
Complex_plane
Group of unitary complex matrices with determinant of 1
where × denotes the direct product and U(1), known as the circle group, is the multiplicative group of all complex numbers with absolute value 1. For completeness
Special_unitary_group
Property of a planar object which maps onto itself after rotation by any angle
symmetry is isomorphic with the circle group in the complex plane, or the special orthogonal group SO(2), and unitary group U(1). Reflective circular symmetry
Circular_symmetry
Relationship among tones of the chromatic scale
In music theory, the circle of fifths (sometimes also cycle of fifths) organizes the twelve pitch classes of the chromatic scale in a cycle of ascending
Circle_of_fifths
South Korean girl group
2023, the group released their first extended play Expérgo and its single "Love Me Like This", which peaked at number 11 on South Korea's Circle Digital
Nmixx
Topological group structure arising in Fourier analysis
or the real numbers or the circle (both with their usual topology) are locally compact abelian groups. A topological group is called locally compact if
Locally_compact_abelian_group
Rotation of a circle by an angle of π times an irrational number
2πθ radians). Since θ is irrational, the rotation has infinite order in the circle group and the map Tθ has no periodic orbits. Alternatively, we can use multiplicative
Irrational_rotation
South Korean girl group
streaming in Japan. The group's first English single "Perfect Night" (2023) became their first number-one song on the Circle Digital Chart, topping the
Le_Sserafim
Topics referred to by the same term
and the Circle, a 2014 music group The Circle (Wipers album), 1988 The Circle (B'z album), 2005 The Circle (Bon Jovi album), 2009 The Circle, a 2008 album
The_Circle
American metal band
media related to Circle II Circle. Circle II Circle discography at MusicBrainz Circle II Circle discography at Discogs Circle II Circle at Encyclopaedia
Circle_II_Circle
Group of German anti-Nazi dissidents
The Kreisau Circle (German: Kreisauer Kreis, pronounced [ˈkʁaɪ̯.zaʊ̯.ɐ kʁaɪ̯s] ) (1940–1944) was a group of about twenty-five German dissidents in Nazi
Kreisau_Circle
Canadian chain of convenience stores
Circle K Stores, Inc. is a convenience store chain owned by the Canadian multinational operator Alimentation Couche-Tard, Inc., based in Laval, Quebec
Circle_K
Topics referred to by the same term
Circle theorem may refer to: Any of many theorems related to the circle; often taught as a group in GCSE mathematics. These include: Inscribed angle theorem
Circle_theorem
Mathematical object
There is an interesting action of the circle group T on S3 giving the 3-sphere the structure of a principal circle bundle known as the Hopf bundle. If one
3-sphere
Canadian hip hop collective
together with all the Halal Gang members to form the hip hop supergroup "Full Circle". Jay Whiss released his debut studio album Peace of Mind on March 3, 2020
Prime_Boys
School group activity
Circle time, also called group time, refers to any time that a group of people, usually young children, are sitting together for an activity involving
Circle_time
South Korean girl group
at number one on the Circle Digital Chart, earning the group their second number-one song in South Korea and became the group's first song to achieve
Ive_(group)
1924–1936 group of philosophers and scientists
The Vienna Circle (German: Wiener Kreis) of logical empiricism was a group of philosophers and scientists drawn from the natural and social sciences,
Vienna_Circle
Type of group in mathematics
The symmetry group of a circle is O(2). The orientation-preserving subgroup SO(2) is isomorphic (as a real Lie group) to the circle group, also known as
Orthogonal_group
1975 studio album by Chick Corea
recorded between 1968 and 1970, including the first recordings by the group Circle, which was first released on the Blue Note label in 1975. It contains
Circling_In
Mathematical term in group theory
mathematician of the early 20th century. The Prüfer p-group may be identified with the subgroup of the circle group, U ( 1 ) {\displaystyle \operatorname {U}
Prüfer_group
American reality television series
platform called "The Circle", as they compete to be deemed the most popular in the group. As they communicate through "The Circle", players can portray
The Circle (American TV series)
The_Circle_(American_TV_series)
South Korean girl group
South Korea's Circle Digital Chart, and eight days after its release it entered four U.S. Billboard charts. Illit became the first K-pop group to enter the
Illit
German writer and scholar (1911–2010)
German American lawyer and participant in the anti-Nazi opposition group, the Kreisau Circle, with her husband, Helmuth James von Moltke. During World War
Freya_von_Moltke
Roundabout in Accra, Ghana
template Use Ghanaian English is being considered for deletion.› Danquah Circle is a roundabout and traffic interchange in Osu, Accra, Ghana. It is a key
Danquah_Circle
South Korean girl group
Say My Name (Korean: 세이마이네임) is a South Korean girl group formed and managed by Inkode. The group currently consists of eight members: Hitomi, Shuie,
Say_My_Name_(group)
Geometry concept
orthogonal group SO(2), including SO(2) itself. That group is isomorphic to R/Z and the first unitary group, U(1), a group also known as the circle group. The
Point groups in two dimensions
Point_groups_in_two_dimensions
The following is a list of episodes from The Circle (sometimes called The Circle US to differentiate from other international versions), an American reality
List of The Circle (American TV series) episodes
List_of_The_Circle_(American_TV_series)_episodes
American rock supergroup
A Perfect Circle is an American rock supergroup formed in Los Angeles, California, in 1999 by guitarist Billy Howerdel and Tool vocalist Maynard James
A_Perfect_Circle
Topics referred to by the same term
Magic circle (games), a concept used in sociology and psychology Magic Circle (law firms), a group of leading London law firms Offshore magic circle, a group
Magic_circle_(disambiguation)
British housing association
in 2016 as a merger of Affinity Sutton and Circle Housing Group. Clarion Housing Group comprises the Group's housing association and sole landlord, Clarion
Clarion_Housing_Group
Style of dance done in a circle with rhythm instruments and singing
gentle to energetic, the dance can be an uplifting group experience or part of a meditation. Circle dancing, probably the oldest known dance formation
Circle_dance
South Korean girl group
July, 2025". Circle Chart. Retrieved August 7, 2025. "Circle Album Chart – Week 24, 2025". Circle Chart. Retrieved June 19, 2025. "Circle Album Chart –
Fifty_Fifty_(group)
Support group of like-minded writers
A writing circle is a group of like-minded writers needing support for their work, either through writing peer critiques, workshops or classes, or just
Writing_circle
Group obtained by aggregating similar elements of a larger group
equal to 1. The quotient group R / Z {\displaystyle \mathbb {R} \,/\,\mathbb {Z} } is isomorphic to the circle group, the group of complex numbers of absolute
Quotient_group
Dutch private banker
Excellence. Retrieved 3 December 2025. "Banking Circle Group to appoint Ralph Hamers as Chairman". Banking Circle Group. 13 April 2026. Retrieved 13 June 2026
Ralph_Hamers
Locally compact topological group with an invariant averaging operation
Borel measure on G which gives the whole group weight 1. As an example for compact groups, consider the circle group. The graph of a typical function f ≥
Amenable_group
The Wilton Circle were an influential group of 16th-century English poets, led by Mary Sidney. They were based at Wilton House, Wiltshire, which was run
Wilton_Circle
Type of topological group in mathematics
locally compact abelian groups is described by Pontryagin duality. Any compact group is locally compact. In particular the circle group S1 of complex numbers
Locally_compact_group
Pattern in a crop field
A crop circle, crop formation, or corn circle is a pattern created by flattening a crop, usually a cereal. The term was coined in the early 1980s. Crop
Crop_circle
South Korean boy band
sales of No Tragedy: "Circle Album Chart – April 2026". Circle Chart. Retrieved June 11, 2026. "Circle Album Chart – May 2026". Circle Chart. Retrieved June
TWS_(group)
Group of students who discuss literature
A literary circle or coterie, according to The Oxford Dictionary of Literary Terms, is a "small group of writers (and others) bound together more by friendship
Literary_circle
Set of points at distance less than one from a given point
Unlike the notationally similar circle group T {\displaystyle \mathbb {T} } , the (open) unit disk is not a multiplicative group. The function f ( z ) = z 1
Unit_disk
2015 American film by Aaron Hann and Mario Miscione
Circle is a 2015 American science fiction psychological thriller film written and directed by Aaron Hann and Mario Miscione. The ensemble cast includes
Circle_(2015_film)
metaphors like "inner circle" or "circular reasoning" in which the word does not refer literally to the geometric shape. Circle Circle anatomy Annulus (mathematics) –
List_of_circle_topics
White supremacist, neo-Nazi prison gang in the United States
splinter group of the Aryan Brotherhood of Texas (ABT). During the 1980s the ABT had shifted focus away from overt crime towards religion. The Aryan Circle split
Aryan_Circle
Los Angeles-based girl group
"Circle Album Chart – Week 33 of 2024". Circle Chart. Archived from the original on August 22, 2024. "Circle Album Chart – Week 37 of 2024". Circle Chart
Katseye
Concept in topological group theory
simply connected Lie group G having the same Lie algebra as H. The universal covering group of the circle group T is the additive group of real numbers (R
Covering_group
Mathematics concept
The circle group inside this group of matrices is the unitary group U(1). Hodge structures arising in geometry, for example on the cohomology groups of
Mumford–Tate_group
Quaternion of norm 1 (unit quaternion)
subgroup that is isomorphic to the circle group. Next consider the finite subgroups, beyond the quaternion group Q8: As noted by Hurwitz, the 16 quaternions
Versor
Jamaican reggae band
Inner Circle, also known as The Inner Circle Band or The Bad Boys of Reggae, are a Jamaican reggae band formed in Kingston in 1968. The band first backed
Inner_Circle_(band)
Political party in Russia
The Petrashevsky Circle was a Russian literary discussion group of progressive-minded intellectuals in St. Petersburg in the 1840s. It was organized by
Petrashevsky_Circle
Country music streaming television
Circle Country, previously known as Circle, is a free ad-supported streaming television (FAST) service owned by Gray Media as part of its PowerNation Studios
Circle_Country
Type of complex number
length (or norm) unchanged. As a set, the possible phase factors form the circle group U ( 1 ) {\displaystyle U(1)} , but the term often refers to a scalar
Phase_factor
Correspondence between topics in Lie theory
(see real coordinate space and the circle group respectively) which are non-isomorphic to each other as Lie groups but their Lie algebras are isomorphic
Lie group–Lie algebra correspondence
Lie_group–Lie_algebra_correspondence
American hip hop group
WC and the Maad Circle was an American hip hop group from Los Angeles, California that consisted of WC, Big Gee, Coolio and DJ Crazy Toones. Following
WC_and_the_Maad_Circle
Japanese plastics manufacturer
touch screens between August 2018 and January 2019 to Chaozhou Three-Circle (Group), a producer of communications equipment parts based in China's Guangdong
Sekisui_Chemical
"nilsystem"; and nilsystems are "characteristic for multiple correlations". The circle group arises as the special case of the real line and its subgroup of the integers
Nilsequence
Topics referred to by the same term
Look up circle, circles, circled, or circling in Wiktionary, the free dictionary. A circle is a simple geometric shape. Circle or circles may also refer
Circle_(disambiguation)
the space of absolutely convergent Fourier series. Here T denotes the circle group. The norm of a function f ∈ A(T) is given by ‖ f ‖ = ∑ n = − ∞ ∞ | f
Wiener_algebra
Branch of mathematics that studies abstract algebraic structures
been solved for many particular groups, such as SL(2,R) and the Lorentz group. The duality between the circle group S1 and the integers Z, or more generally
Representation_theory
Chinese materials company
Chaozhou Three-Circle (CCTC; Chinese: 潮州三环; pinyin: Cháozhōu Sānhuán) is a publicly listed Chinese electronic components and advanced materials company
Chaozhou_Three-Circle
Topological group with compact topology
include the circle group T and the torus groups Tn, the orthogonal group O(n), the special orthogonal group SO(n) and its covering spin group Spin(n), the
Compact_group
Music group covering Disney songs
Disney Channel Circle of Stars are a music group created by Disney Channel/The Walt Disney Company, that makes cover versions of Disney's songs. They
Disney Channel Circle of Stars
Disney_Channel_Circle_of_Stars
Subgroup of the group of invertible n×n matrices
is not split, because its group of real points T(R) is the circle group, which is not isomorphic even as an abstract group to Gm(R) = R*. Every point
Linear_algebraic_group
Mathematical concept
subgroups. Let C× be the group of nonzero complex numbers under multiplication. Then C× is the internal direct product of the circle group T of unit complex
Direct_product_of_groups
Lie groups and their associated Lie algebras
table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness;
Table_of_Lie_groups
Continuous surjection satisfying a local triviality condition
SU(2)} . The abelian subgroup of diagonal matrices is isomorphic to the circle group U ( 1 ) {\displaystyle U(1)} , and the quotient S U ( 2 ) / U ( 1 ) {\displaystyle
Fiber_bundle
1984 studio album by the Pat Metheny Group
First Circle is the fourth studio album by the Pat Metheny Group. It was recorded over four days in February 1984 and released on ECM later that year.
First_Circle_(album)
Group with a cyclic order respected by the group operation
Some of the most important cyclically ordered groups fall into neither previous category: the circle group T and its subgroups, such as the subgroup of
Cyclically_ordered_group
South Korean boy band
Did It: "Circle Album Chart – 2025". Circle Chart (in Korean). Archived from the original on January 9, 2026. Retrieved January 9, 2026. "Circle Album Chart
Idid_(group)
Neo-völkisch occult circle
and Rudolf J. Mund (1920–1985). The circle has also been referred to as the Landig Circle (Landig Kreis), Vienna Group (Wien Konzern) and Vienna Lodge (Wien
Landig_Group
The learning circle is a mechanism for organizing and honoring the collective wisdom of a group. Learning circles are present in many indigenous cultures
Learning_circle
Topics referred to by the same term
inner group Inner–outer directions, a method of labeling direction of travel for geographic loops Inner Circle (addiction recovery), inner-most circle of
Inner_circle
British journalist and publisher (1791–1844)
member of a group of Nonconformist Liberals, meeting in the Manchester home of John Potter, termed the Little Circle. Other members of the group included:
John_Edward_Taylor
CIRCLE GROUP
CIRCLE GROUP
Male
Celtic
, sea circle.
Surname or Lastname
English
English : variant spelling of Cordell.Possibly an Americanized spelling of German Kördel, a pet form of an old German personal name, formed with kuoni ‘daring’. Compare Conrad.
Female
Slovene
Feminine form of Slovene Ciril, CIRILA means "lord."
Boy/Male
Christian, Hindu, Indian
Bright Circle
Female
English
English name derived from the vocabulary word, from Latin miraculum, MIRACLE means "marvel, wonder."
Female
French
French form of Latin Carola, CAROLE means "man."
Girl/Female
British, English
Botanical Name; The Myrtle is a Dark Green Shrub with Pink or White Blossoms
Girl/Female
Bengali, Indian
Circle; Normal
Female
Yiddish
(מִירל) Yiddish form of Hebrew Miryam, MIRELE means "obstinacy, rebelliousness" or "their rebellion."Â
Girl/Female
Japanese
Ball; circle.
Girl/Female
French American
The french form of the English Carol, a dimunitive of Charles meaning strong.
Girl/Female
Latin
Circle of light.
Boy/Male
Spanish Greek
noble.
Boy/Male
English
From the bird hill.
Boy/Male
English
Birch.
Boy/Male
French Israeli
The circle.
Girl/Female
Greek Latin
A witch.
Girl/Female
Latin
Circle of light.
Girl/Female
Latin
Circle of light.
Male
Slovene
Slovene form of Greek Kyrillos, CIRIL means "lord."
CIRCLE GROUP
CIRCLE GROUP
Girl/Female
Tamil
Avanija | அவாநீஜா
Goddess Parvati
Boy/Male
English
Abbreviation of Elizabeth.
Boy/Male
Arabic, Muslim
Seal of the Prophets
Surname or Lastname
English
English : variant of Raison.Probably also an Americanized spelling of German Riesen.
Girl/Female
Australian, German, Greek, Italian
Form of Alice; Noble; Nobility; From the Blessed Isles
Boy/Male
Hindu, Indian, Kannada, Traditional
Brave One with a Bell Around his Neck
Male
English
 English pet form of Hebrew David, DAW means "beloved." Compare with another form of Daw.
Girl/Female
Muslim/Islamic
Poetess
Girl/Female
Australian
Kind
Girl/Female
Arabic, Indian, Japanese, Muslim
Limit; Border; Fence
CIRCLE GROUP
CIRCLE GROUP
CIRCLE GROUP
CIRCLE GROUP
CIRCLE GROUP
n.
To encompass, as by a circle; to surround; to inclose; to encircle.
n.
One entire round in a circle or a spire; as, a cycle or set of leaves.
n.
An imaginary circle or orbit in the heavens; one of the celestial spheres.
n.
An instrument of observation, the graduated limb of which consists of an entire circle.
n.
Alt. of Corcule
v. t.
To girdle; to encircle.
a.
Having the form of a circle; round.
a.
Having the nature, properties, or qualities, of an adult man; characteristic of developed manhood; hence, masterful; forceful; specifically, capable of begetting; -- opposed to womanly, feminine, and puerile; as, virile age, virile power, virile organs.
v. t.
See Encircle.
n.
A circular group of persons; a ring.
n.
A circlet.
v. i.
To move circularly; to form a circle; to circulate.
n.
A little circle; esp., an ornament for the person, having the form of a circle; that which encircles, as a ring, a bracelet, or a headband.
n.
A miracle play.
n.
A circle.
imp. & p. p.
of Circle
v. i.
To change into curd; to coagulate; as, rennet causes milk to curdle.
n.
An amphitheatrical circle for sports; a circus.
n.
A circle; a circus; a circular erection or arrangement of objects.
v. t.
To form a circle about; to inclose within a circle or ring; to surround; as, to encircle one in the arms; the army encircled the city.