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Cartesian product of 3 circles
three-dimensional torus, or 3-torus, is defined as any topological space that is homeomorphic to the Cartesian product of three circles, T 3 = S 1 × S 1 ×
3-torus
Doughnut-shaped surface of revolution
is called a torus of revolution, also known as a ring torus. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis
Torus
Knot which lies on the surface of a torus in 3-dimensional space
In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies
Torus_knot
Mathematical space
Equivalently, the 3-torus is obtained from the 3-dimensional cube by gluing the opposite faces together. A 3-torus in this sense is an example of a 3-dimensional
3-manifold
3-dimensional object
torus. A solid torus is a torus plus the region inside the torus, with a non-zero volume. Real-world objects that approximate a solid torus include O-rings
Solid_torus
Local and global geometry of the universe
topological characteristics. For example; a multiply connected space like a 3 torus has everywhere zero curvature but is finite in extent, whereas a flat simply
Shape_of_the_universe
Non-trivial knot which cannot be written as the knot sum of two non-trivial knots
crossings. The trefoil is actually a (2, 3)-torus knot. The figure-eight knot, with four crossings, is the simplest non-torus knot. For any positive integer n
Prime_knot
Proposed NASA design for space habitat
proposed his Island One or Bernal sphere as an alternative to the torus). "Stanford torus" refers only to this particular version of the design, as the concept
Stanford_torus
Loss of one degree of freedom in a three-dimensional, three-gimbal mechanism
no covering map from the 3-torus to the 3-dimensional real projective space; the only (non-trivial) covering map is from the 3-sphere, as in the use of
Gimbal_lock
Smooth closed surface with g holes
In mathematics, a genus g surface (also known as a g-torus or g-holed torus) is a surface formed by the connected sum of g distinct tori: the interior
Genus_g_surface
Geometrical object in four-dimensional space
In differential geometry, the Clifford torus is the standard embedding of the 2-torus as a product of circles in Euclidean space R4 (equivalently C2).
Clifford_torus
Simplest non-trivial closed knot with three crossings
a (2,3)-torus knot lying on torus ( r − 2 ) 2 + z 2 = 1 {\displaystyle (r-2)^{2}+z^{2}=1} : x = ( 2 + cos 3 t ) cos 2 t y = ( 2 + cos 3 t ) sin
Trefoil_knot
Maximal compact connected Abelian Lie subgroup
Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups. A torus in a compact Lie group G is a compact, connected
Maximal_torus
In differential geometry, a Wente torus is an immersed torus in R 3 {\displaystyle \mathbb {R} ^{3}} of constant mean curvature, discovered by Henry C
Wente_torus
quartic (a genus 3 surface) Möbius strip Real projective plane, RP2 Sphere, S2 Surface of genus g Torus Double torus 3-sphere, S3 3-torus, T3 Poincaré homology
List_of_manifolds
Closed flat 3-manifold
that would arise if the universe is a closed flat manifold, such as the 3-torus. The HW manifold can be built from two cubes that share a face. One construction
Hantzsche–Wendt_manifold
geometry, a torus action on an algebraic variety is a group action of an algebraic torus on the variety. A variety equipped with an action of a torus T is called
Torus_action
Elevated mucous membrane in the nasopharynx
The torus tubarius (or torus of the auditory tube) is an elevation of the mucous membrane of the nasal part of the pharynx formed by the underlying base
Torus_tubarius
leaf theorem, every smooth foliation of the 3-sphere includes a compact torus leaf, bounding a solid torus foliated in the same way. Reeb, Georges (1952)
Reeb_foliation
Three dimensional analogue of uniformization conjecture
O(3, R), with 2 components. Examples are the 3-torus, and more generally the mapping torus of a finite-order automorphism of the 2-torus; see torus bundle
Geometrization_conjecture
Short story by Greg Egan
best possible universe. While the 3-torus ( T 3 = R 3 / Z 3 {\displaystyle T^{3}=\mathbb {R} ^{3}/\mathbb {Z} ^{3}} ), also one of the ten platycosms
Didicosm
Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
infinity"). Each torus is the stereographic projection of the inverse image of a circle of latitude of the 2-sphere. (Topologically, a torus is the product
Hopf_fibration
Search quality measure in information retrieval
could calculate the mean reciprocal rank as ( 1 / 3 + 1 / 2 + 1 ) / 3 = 11 / 18 {\displaystyle (1/3+1/2+1)/3=11/18} , or approximately 0.61. If none of the
Mean_reciprocal_rank
Medical condition
A torus palatinus (pl.: tori palatini), or palatal torus (pl.: palatal tori), is a bony protrusion on the palate. Palatal tori are usually present on the
Torus_palatinus
by Radars and UAS of Supercells Project, often shorted to the TORUS Project or just TORUS, is a United States federal government funded meteorological
TORUS_Project
Concept in physics
space itself is closed, with the Brillouin zone having the topology of a 3-torus in three dimensions, the requirements of integrating over a closed loop
Berry connection and curvature
Berry_connection_and_curvature
Three-dimensional shape
forms define a surface – the umbilic torus. Christopher Zeeman named this set the umbilic bracelet in 1976. The torus is defined by the following set of
Umbilic_torus
Defunct Australian video game developer
business. Torus has developed over 145 titles. The company is most known for family action/adventure games, based on well-known licenses. Torus began developing
Torus_Games
Type of geometry for connecting computer nodes
A torus interconnect is a switch-less network topology for connecting processing nodes in a parallel computer system. In geometry, a torus is created by
Torus_interconnect
known as dynamical systems theory, a linear flow on the torus is a flow on the n-dimensional torus T n = S 1 × S 1 × ⋯ × S 1 ⏟ n , {\displaystyle \mathbb
Linear_flow_on_the_torus
Type of mathematical knot
an incompressible, non boundary-parallel torus in its complement. Every knot is either hyperbolic, a torus, or a satellite knot. The class of satellite
Satellite_knot
In differential geometry, the Angenent torus is a smooth embedding of the torus into three-dimensional Euclidean space, with the property that it remains
Angenent_torus
because S 3 {\displaystyle S^{3}} is not aspherical. Nevertheless, the Borel conjecture for the 3-torus T 3 = S 1 × S 1 × S 1 {\displaystyle T^{3}=S^{1}\times
Borel_conjecture
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
the torus, the radii of these circles become inverted, and one is left with a new torus which is "fatter" or "skinnier" than the original. This torus is
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Topological space
fiber has a tubular neighborhood that forms a standard fibered torus. A standard fibered torus corresponding to a pair of coprime integers ( a , b ) {\displaystyle
Seifert_fiber_space
Theorem that the Clifford torus is the only minimally embedded torus in the 3-sphere
geometry, Lawson's conjecture states that the Clifford torus is the only minimally embedded torus in the 3-sphere S3. The conjecture was featured by the Australian
Hsiang–Lawson's_conjecture
List of concrete topologies and topological spaces
projective line Torus 3-torus Solid torus Unknot Whitehead manifold − An open 3-manifold that is contractible, but not homeomorphic to R 3 . {\displaystyle
List_of_topologies
Intersection of a torus and a plane
circles produced by cutting a torus obliquely through its center at a special angle. Given an arbitrary point on a torus, four circles can be drawn through
Villarceau_circles
Differentiable function whose derivative is everywhere injective
S 3 {\displaystyle \mathbb {S} ^{3}} and the 3-torus T 3 {\displaystyle \mathbb {T} ^{3}} are both parallelizable, there is no immersion T 3 →
Immersion_(mathematics)
Common type of fracture in children
itself is orthogonal to that axis. The word "torus" originates from the Latin word "protuberance." Torus fractures are low risk and may cause acute pain
Torus_fracture
Type of lens
ring torus is produced. If R = r, a horn torus is produced, where the opening is contracted into a single point. R < r results in a spindle torus, where
Toric_lens
Japanese mythological creatures
of Asian America. Temole University Press. p. 242. ISBN 978-0-87722-935-3. Toru Yagi [in Japanese] (12 May 2023). 「鬼」という概念はどのようにして生まれたのか？ (in Japanese)
Oni
Mathematical descriptions of a rotation group
example, the Euler angles appear to give a variable in the 3-torus, and the unit quaternions in a 3-sphere. The uniqueness of the representation by Euler angles
Charts_on_SO(3)
2-sphere has Yamabe invariant equal to 8 π {\displaystyle 8\pi } , and the 2-torus has Yamabe invariant equal to zero. In the late 1990s, the Yamabe invariant
Yamabe_invariant
2024 film directed by Jeff Fowler
Group, Jeff Fowler returned as director while Neal H. Moritz, Toby Ascher, Toru Nakahara, and Hitoshi Okuno returned as producers. Haruki Satomi, Shuji Utsumi
Sonic_the_Hedgehog_3_(film)
Game Boy Advance, Microsoft Windows, PlayStation, PlayStation 2, PlayStation 3, PlayStation 4, PlayStation 5, PlayStation Portable, Xbox 360, Wii, and mobile
List of DreamWorks Animation video games
List_of_DreamWorks_Animation_video_games
Type of continuous map in topology
in three dimensions. Topologically this corresponds to a map from the 3-torus T3 of three angles to the real projective space RP3 of rotations, and the
Covering_space
compactly and therefore transmitting fewer bits. Torus Rubin, Karl; Silverberg, Alice (2003). "Torus-Based Cryptography". In Boneh, Dan (ed.). Advances
Torus-based_cryptography
Specific algebraic group
In mathematics, an algebraic torus, where a one dimensional torus is typically denoted by G m {\displaystyle \mathbf {G} _{\mathbf {m} }} , G m {\displaystyle
Algebraic_torus
Magnetic confinement device used to produce thermonuclear fusion power
magnetic field inside the torus; a pulsed magnetic field through the hole in the torus induces the axial current in the torus which has a poloidal magnetic
Tokamak
corresponds to a map from the 3-torus T3 of three angles to the real projective space RP3 of rotations, but this map does not have rank 3 at all points (formally
Rank_(differential_topology)
Describes the line bundles on a complex torus or complex abelian variety
group with the real torus given above. In fact, this torus can be equipped with a complex structure, giving the dual complex torus. Explicitly, a line
Appell–Humbert_theorem
Manifold that "locally looks like" Euclidean space
metric on the 2-dimensional torus is not the metric induced by its usual embedding into R 3 {\displaystyle \mathbb {R} ^{3}} ). Every one-dimensional Riemannian
Flat_manifold
Symmetric bipartite cubic graph with 16 vertices and 24 edges
embedding into a triple torus (genus 3 torus) that is a regular map having four 12-gonal faces, and is the Petrie dual of the double torus embedding described
Möbius–Kantor_graph
Loewner's torus inequality is an inequality due to Charles Loewner. It relates the systole and the area of an arbitrary Riemannian metric on the 2-torus. In
Loewner's_torus_inequality
1992 film by Jon Turteltaub
Rocky's crush Joel Swetow as Mr. Nigel Brown, Snyder's consigliere Professor Toru Tanaka as Rushmore, Snyder's enforcer Patrick Labyorteaux as Fester, Brown's
3_Ninjas_(film)
Equivalence of two physical theories
manifold is a torus (a surface shaped like a donut). Such a surface can be viewed as the product of two circles. This means that the torus can be viewed
T-duality
In mathematics, specifically in topology, the mapping torus of a homeomorphism f of some topological space X to itself is a particular geometric construction
Mapping_torus
three-manifolds. To obtain a torus bundle: let f {\displaystyle f} be an orientation-preserving homeomorphism of the two-dimensional torus T {\displaystyle T}
Torus_bundle
Disorder of the jaw
An oral torus - also known as: dental torus - is an oral condition in which bony growth occurs in the mouth; there are three locations in which oral tori
Oral_torus
In mathematics, on the region between two well-behaved spheres
(1924), in dimension 3 by Moise (1952), in dimension 4 by Quinn (1982), and in dimensions at least 5 by Kirby (1969). Robion Kirby's torus trick is a proof
Annulus_theorem
Argentine-born American mathematician
tightly fasten those 7-cycles in Γ'. This yields an embedding of Γ' into a 3-torus T3 which forms the Klein map of Coxeter notation (7,3)8. The dual graph
Italo_Jose_Dejter
Mathematical object
structure of compact groups, de Gruyter Studies in Mathematics, vol. 25 (2nd ed.), Berlin: Walter de Gruyter & Co., ISBN 978-3-11-019006-9, MR 2261490 v t e
Protorus
Feature of plant cell walls
In other vascular plants, the torus is rare. The pit membrane is separated into two parts: a thick impermeable torus at the center of the pit membrane
Pit_(botany)
Type of motion that is approximately periodic
motion on a torus that never comes back to the same point. This behavior can also be called quasiperiodic evolution, dynamics, or flow. The torus may be a
Quasiperiodic_motion
Process in mathematics of decomposing a topological space
the mapping torus of an Anosov map of a torus has a finite volume sol structure, but its JSJ decomposition cuts it open along one torus to produce a
JSJ_decomposition
Mathematical knot with crossing number 7
septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number seven. It is the simplest torus knot after the trefoil and cinquefoil
71_knot
Kind of complex manifold
In mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian
Complex_torus
Open 3-manifold that is contractible but not homeomorphic to R3
sphere. Now find a compact unknotted solid torus T 1 {\displaystyle T_{1}} inside the sphere. (A solid torus is the topological space S 1 × D 2 {\displaystyle
Whitehead_manifold
Non-orientable mathematical surface
image of the other, yield a fundamental region of the torus. The universal cover of both the torus and the Klein bottle is the plane R2. The fundamental
Klein_bottle
Concept in algebraic topology
spaces, CPn, a point, spheres Sn( n ≥ 1 {\displaystyle n\geq 1} ), and a 3-torus T3 with integer coefficients. As an example of how to compute homology
Singular_homology
Japanese voice actor
Tōru Furusawa (古澤 融(real name/old stage name,古澤 徹), Furusawa Tōru; born August 3, 1962) is a Japanese voice actor. Anime Ganbare Goemon (Mr. Protein) Cardcaptor
Tōru_Furusawa
Knot invariant
sufficiently large crossing numbers, non-alternating torus knots will have a lower ropelength than alternating torus knots. This is seen empirically even at low
Ropelength
4-dimensional object
is the boundary between the two bounding (solid) torus cells. It is in the shape of a Clifford torus, which is the Cartesian product of two circles. Intuitively
Duocylinder
Array containing every possible matrix of size m × n
smallest possible binary "square" de Bruijn torus, depicted above right, denoted as (4,4;2,2)2 de Bruijn torus (or simply as B2), contains all 2×2 binary
De_Bruijn_torus
Below is a sortable list of compositions by Tōru Takemitsu. The works are categorized by genre, date of composition, titles and scoring. Scores by Takemitsu
List of compositions by Tōru Takemitsu
List_of_compositions_by_Tōru_Takemitsu
2013 studio album by Sub Focus
Focus on Torus". XFM. "Exclusive: Sub Focus reveals 'Torus' tracklist". Mixmag. 19 August 2013. Retrieved 20 August 2013. "iTunes - Music - Torus (Deluxe
Torus_(album)
2022 video game
Splatoon 3 is a 2022 third-person shooter game developed and published by Nintendo for the Nintendo Switch. It is the third game in the Splatoon series
Splatoon_3
2021 edition of the G1 Climax
in Hamamatsu, Shizuoka. The fifth night of A Block took place on October 3, 2021, at Aichi Prefectural Gymnasium in Naka-ku, Nagoya. The fifth night
G1_Climax_31
Bony ridge located above the eye sockets of all primates
paleoanthropologists distinguish between frontal torus and supraorbital ridge. In anatomy, a torus is a projecting shelf of bone that unlike a ridge
Brow_ridge
Restricts the possible topology of a negatively curved compact Riemannian manifold
abelian. As an example, Preissmann's theorem implies that the n-dimensional torus admits no Riemannian metric of strictly negative sectional curvature. More
Preissmann's_theorem
Fusion power device
cored apple. The spherical tokamak is sometimes referred to as a spherical torus and often shortened to ST. The spherical tokamak is an offshoot of the conventional
Spherical_tokamak
Graph able to be embedded on a torus
is a graph that can be embedded on a torus. In other words, the graph's vertices and edges can be placed on a torus such that no edges intersect except
Toroidal_graph
Japanese voice actor
– Mikazuki Subaru Radiant – Diabal Star-Myu: High School Star Musical 3 – Toru Nayuki Vinland Saga – Canute 2020 Bofuri – Payne IDOLiSH7 Second Beat!
Kensho_Ono
Mohyal Brahmin clan from Punjab
Titles. Anthropological Survey of India. p. 1591. ISBN 978-0-19-563357-3. Toru Takahashi (13 March 2014). "'Rajput', local deities and discrimination:
Datt
Result in dynamical systems
invariant d {\displaystyle d} -torus T d {\displaystyle {\mathcal {T}}^{d}} ( d ≥ 2 {\displaystyle d\geq 2} ) is called a KAM torus. The d = 1 {\displaystyle
Kolmogorov–Arnold–Moser theorem
Kolmogorov–Arnold–Moser_theorem
A toric section is an intersection of a plane with a torus, just as a conic section is the intersection of a plane with a cone. Special cases have been
Toric_section
1992 American film franchise
after attempting to flee from Mori. Rushmore — portrayed by Professor Toru Tanaka (3 Ninjas) Not much is known about Rushmore, except he is a personal strongman
3_Ninjas
American mathematician (born 1989)
stretch factor. He showed that on the contrary, the stretch factor of certain torus knots could be arbitrarily large. His proof was published in the Annals
John_Pardon
Japanese voice actor, singer and narrator
Chiaki Yoshino Stardust wink, So Nagase Nyanpire, Vampire 2012 Bakuman. 3, Toru Nanamine Ginga e Kickoff!!, Ryuuji Furuya Mobile Suit Gundam AGE, Gren
Shinnosuke_Tachibana
longitude for each boundary torus, i.e. simple closed curves that are generators for the fundamental group of the torus. Let M ( u 1 , u 2 , … , u n
Hyperbolic_Dehn_surgery
2001 film by Matt Codd
natives, who call it the Torus and consider it a gift from the gods with extraordinary healing properties. The US team enters the Torus, but an air strike by
Epoch_(film)
Country in Southeast Asia
Takahashi, Toru (27 November 2014). "Thailand's love affair with the pickup truck". Nikkei Asian Review. Archived from the original on 3 January 2015
Thailand
Innermost Galilean moon of Jupiter
occasionally provides sodium ions in the plasma torus with an electron, removing those new "fast" neutrals from the torus. These particles retain their velocity
Io_(moon)
Mathematical object
is from σπειρα meaning "torus" in ancient Greek. A spiric section is sometimes defined as the curve of intersection of a torus and a plane parallel to
Spiric_section
Association football tournament in Russia
21:00 MSK (UTC+3) Rostov Arena, Rostov-on-Don Attendance: 41,466 Referee: Malang Diedhiou (Senegal) 3 July 2018 (2018-07-03) 17:00 MSK (UTC+3) Krestovsky
2018_FIFA_World_Cup
atoroidal 3-manifold is one that does not contain an essential torus. There are two major variations in this terminology: an essential torus may be defined
Atoroidal
Professional wrestling tag team championship
Retrieved February 10, 2021. Dark Angelita (June 3, 2021). "Freedoms: "F☆Spirit" 2021″ Violento Jack tras Toru Sugiura". superluchas.com (in Spanish). Retrieved
King of Freedom World Tag Team Championship
King_of_Freedom_World_Tag_Team_Championship
Theorem in geometric topology
ball (which is known in mathematics as the two-dimensional sphere) or of a torus, are two-dimensional. The surface of a ball has trivial fundamental group
Poincaré_conjecture
Football match
Bando FW 9 Magno Alves Substitutes: GK 22 Yosuke Fujigaya DF 2 Sidiclei DF 3 Toru Irie MF 20 Shinichi Terada MF 27 Hideo Hashimoto FW 16 Masafumi Maeda FW
2006_Emperor's_Cup_final
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