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Geometric surface
In geometry, a pseudosphere is a surface in R 3 {\displaystyle \mathbb {R} ^{3}} . It is the most famous example of a pseudospherical surface. A pseudospherical
Pseudosphere
Italian mathematician (1835–1900)
non-Euclidean geometry by modelling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein
Eugenio_Beltrami
Two geometries based on axioms closely related to those specifying Euclidean geometry
opposite each other are identified (considered to be the same). The pseudosphere has the appropriate curvature to model hyperbolic geometry. The simplest
Non-Euclidean_geometry
Surface of constant negative curvature
examples of generalized pseudospheres. There is a correspondence between embedded surfaces of constant curvature -1, known as pseudospheres, and solutions to
Breather_surface
Curve traced by a point on a rod as one end is dragged along a line
asymptote: the pseudosphere. Studied by Eugenio Beltrami in 1868, as a surface of constant negative Gaussian curvature, the pseudosphere is a local model
Tractrix
Set of points equidistant from a center
that lacks a boundary with constant, positive Gaussian curvature. The pseudosphere is an example of a surface with constant negative Gaussian curvature
Sphere
Geometric surface
surface with constant negative curvature that can be created by twisting a pseudosphere. It is named after Ulisse Dini and described by the following parametric
Dini's_surface
Product of the principal curvatures of a surface
surfaces of class C2 immersed in R3, but breaks down for C1-surfaces. The pseudosphere has constant negative Gaussian curvature except at its boundary circle
Gaussian_curvature
Type of non-Euclidean geometry
relative velocities of "nearby" points (velocities). There exist various pseudospheres in Euclidean space that have a finite area of constant negative Gaussian
Hyperbolic_geometry
Nonlinear partial differential equation
singular due to the Hilbert embedding theorem. In the simplest case, the pseudosphere, also known as the tractroid, corresponds to a static one-soliton, but
Sine-Gordon_equation
Museum exhibit about mathematics
Pseudosphere model
Mathematica: A World of Numbers... and Beyond
Mathematica:_A_World_of_Numbers..._and_Beyond
Hyperbolic 3-manifold proposed as a model for the shape of the universe
model for the shape of the universe in 2004. The term "horn" is due to pseudosphere models of hyperbolic space. A modern description, in terms of fundamental
Picard_horn
Nuclear reaction splitting an atom into multiple parts
uranium metal from the Ames process, meant the replacement of oxide pseudospheres with Frank Spedding's "eggs". Starting on 16 November 1942, Fermi had
Nuclear_fission
Maximally symmetric Lorentzian manifold with a negative cosmological constant
embedding in a flat space of one higher dimension (as the sphere and pseudosphere respectively), anti-de Sitter space can be visualized as the Lorentzian
Anti-de_Sitter_space
sheets Hyperbolic paraboloid (a ruled surface) Paraboloid Dini's surface Pseudosphere Cayley cubic Barth sextic Clebsch cubic Monkey saddle (saddle-like surface
List_of_surfaces
Type of three-dimensional shape
of revolution. Cylindrical symmetry Gabriel's Horn Guldinus theorem Pseudosphere Surface of revolution Ungula Sharma, A. K. (2005). Application Of Integral
Solid_of_revolution
German-Russian mathematician (1806–1885)
surfaces and surfaces of revolution and determined geodesics on the pseudosphere. Minding's results on the geometry of geodesic triangles on a surface
Ferdinand_Minding
Non-Euclidean geometry
3-manifold Ideal polyhedron Mostow rigidity theorem Murakami–Yano formula Pseudosphere Grigor'yan, Alexander; Noguchi, Masakazu (1998), "The heat kernel on
Hyperbolic_space
Wallachian and Romanian mathematician, physicist and chemist
participant in the 1848 Wallachian revolution. He is known for the "Bacaloglu pseudosphere". This is a surface of revolution for which the "Bacaloglu curvature"
Emanoil_Bacaloglu
Geometric figure which has infinite surface area but finite volume
Hyperbolic 3-manifold proposed as a model for the shape of the universe Pseudosphere – Geometric surface Shape of the universe – Local and global geometry
Gabriel's_horn
plane can be placed onto a pseudosphere and maintain angles and hyperbolic distances, as well as be bent around the pseudosphere and still keep its properties
Constructions in hyperbolic geometry
Constructions_in_hyperbolic_geometry
Laboratory, Los Alamos, New Mexico, United States Accidental criticality A pseudosphere of 35.4 kg of highly enriched uranium (enriched to an average of 79.2%
List of military nuclear accidents
List_of_military_nuclear_accidents
Hungarian mathematician (1802–1860)
in Budapest, Cluj-Napoca, and Timișoara are named after Bolyai. The Pseudosphere monument in Târgu Mureș Bust of János Bolyai in Cluj-Napoca Bust of János
János_Bolyai
2009 book by Daina Taimina
specific geometric objects with negatively-curved surfaces, including the pseudosphere, helicoid, and catenoid, investigate mathematical toys, and use these
Crocheting Adventures with Hyperbolic Planes
Crocheting_Adventures_with_Hyperbolic_Planes
Upper-half plane model of hyperbolic non-Euclidean geometry
model Hyperbolic motion Kleinian model Models of the hyperbolic plane Pseudosphere Schwarz–Ahlfors–Pick theorem Ultraparallel theorem Notes "Distance formula
Poincaré_half-plane_model
Model of hyperbolic geometry
world geometry, and also uses the Poincaré disk model. Poincaré metric Pseudosphere Inversive geometry Uniform tilings in hyperbolic plane Penrose, Roger
Poincaré_disk_model
Device for controlled nuclear reactions
name) of graphite blocks, embedded in which was natural uranium oxide 'pseudospheres' or 'briquettes'. Soon after the Chicago Pile, the Metallurgical Laboratory
Nuclear_reactor
Hyperbolic Plane: Beltrami Pseudosphere" Transliteration: "Sōkyoku Heimen no Arutairu" (Japanese: 双曲平面のアルタイル Beltrami Pseudosphere) August 9, 2018 (2018-08-09)
List of Steins;Gate 0 episodes
List_of_Steins;Gate_0_episodes
Mathematics of smooth surfaces
Gaussian curvature 0. A unit pseudosphere has constant Gaussian curvature -1 (apart from its equator, that is singular). Pseudosphere can be obtained by rotating
Differential geometry of surfaces
Differential_geometry_of_surfaces
Local and global geometry of the universe
informally called "horn topologies", so called because of the shape of the pseudosphere, a canonical model of hyperbolic geometry. An example is the Picard horn
Shape_of_the_universe
Space where every point locally resembles a hyperbolic space
The Pseudosphere. Each half of this shape is a hyperbolic 2-manifold (i.e. surface) with boundary.
Hyperbolic_manifold
Abstraction of ordered linear algebra
matroid has a realization as an arrangement of pseudospheres. A d {\displaystyle d} -dimensional pseudosphere is an embedding of e : S d ↪ S d + 1 {\displaystyle
Oriented_matroid
Crocheted hyperbolic pseudosphere from the IFF Collection
Institute_For_Figuring
Greek σφαῖρα (sphaîra) aspheric, hemisphere, hypersphere, mesosphere, pseudosphere, sphere, spherics, spheroid, spherometer, spherulite, stratosphere, trimetasphere
List of Greek and Latin roots in English/P–Z
List_of_Greek_and_Latin_roots_in_English/P–Z
Overview of and topical guide to geometry
geometry Non-Euclidean plane geometry Angle excess Hyperbolic geometry Pseudosphere Tractricoid Elliptic geometry Spherical geometry Minkowski space Thurston's
Outline_of_geometry
Bäcklund transforms originated as transformations of pseudospheres in the 1880s.
Bäcklund_transform
Journal of the Iranian Mathematical Society
Vanishing Hachtroudi< curvature and local equivalence to the Heisenberg pseudosphere. Bull. Iran. Math. Soc. 47, No. 6, 1775-1792 (2021). Javad Mashreghi
Bulletin of the Iranian Mathematical Society
Bulletin_of_the_Iranian_Mathematical_Society
rabies-infected nerve cells. Emanoil Bacaloglu: he is known for the "Bacaloglu pseudosphere". This is a surface of revolution for which the "Bacaloglu curvature"
List of Romanian inventors and discoverers
List_of_Romanian_inventors_and_discoverers
German mathematician (1868–1950)
und die nichteuklidische Geometrie, 2 vols., Teubner 1931, 1935 (See pseudosphere.) Pseudosphärische, hyperbolisch-sphärische und elliptisch-sphärische
Friedrich_Schilling
paraboloid (a ruled surface) Paraboloid Sphericon Oloid Dini's surface Pseudosphere See the list of algebraic surfaces. Cayley cubic Barth sextic Clebsch
List_of_mathematical_shapes
World's first human-made nuclear reactor
uranium. A hydraulic press was used to shape the uranium oxide into "pseudospheres", cylinders with rounded ends. Drill bits had to be sharpened after
Chicago_Pile-1
Study of mathematics and culture
Press. Luitel, Bal Chandra and Taylor, Peter. (2007). The shanai, the pseudosphere and other imaginings: Envisioning culturally contextualised mathematics
Ethnomathematics
Greek σφαῖρα (sphaîra) aspheric, hemisphere, hypersphere, mesosphere, pseudosphere, sphere, spherics, spheroid, spherometer, spherulite, stratosphere, trimetasphere
List of Greek and Latin roots in English/S
List_of_Greek_and_Latin_roots_in_English/S
torus (for curvature 0 {\displaystyle 0} ) and the hyperbolic plane and pseudosphere (for curvature − 1 {\displaystyle -1} ). For this reason these metrics
Non-positive_curvature
Chaotic dynamical system, a type of "billiards"
Balazs(Saclay), N.L.; Voros(Saclay), A. (Jun 1986). "Chaos on the pseudosphere". Phys. Rep. 143 (143): 109–240. Bibcode:1986PhR...143..109B. doi:10
Hadamard's_dynamical_system
Lie algebra classification
first and fourth quadrants of the a = 0 plane V 1 0 0 0 B has a hyper-pseudosphere as a special case the interval (0,1] along the axis a VI0 0 1 -1 0 A
Bianchi_classification
American historian of mathematics
1827 to 1887, concerned the history of non-Euclidean geometry and the pseudosphere,[b] also including material on a paper of Albert Victor Bäcklund on hyperbolic
Emily_Coddington_Williams
indicatrix in cartography. Emanoil Bacaloglu develops the "Bacaloglu pseudosphere". Arthur Cayley produces the first Cayley–Klein metric. Bernhard Riemann
1859_in_science
Italian physicist (1930–2018)
S2CID 4337125. Bertotti, B.; Catenacci, R.; Dappiaggi, C. (2005). "Pseudospheres in geometry and physics: from Beltrami to De Sitter and beyond". arXiv:math
Bruno_Bertotti
PSEUDOSPHERE
PSEUDOSPHERE
PSEUDOSPHERE
PSEUDOSPHERE
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Bengali, Hindu, Indian
Who Wears Politeness as an Ornament
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Australian, Danish, Swedish
God is Gracious; God has Shown Favor
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Hindu
Lord Murugan
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Tamil
Lord Krishna
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Indian, Sanskrit
Highest God; The First God for Prayer; The Lord Ganesha
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Hungarian
Hungarian form of French Jeannette, ZSANETT means "God is gracious."
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Tamil
Mercury planet
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Safeguarded, Well-protected
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English Teutonic
Rules with elf-wisdom. Introduced into Britain from France by Aubrey de Vere, a friend of William...
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African, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Name of Cupid or Kamadeva
PSEUDOSPHERE
PSEUDOSPHERE
PSEUDOSPHERE
PSEUDOSPHERE
PSEUDOSPHERE
n.
The surface of constant negative curvature generated by the revolution of a tractrix. This surface corresponds in non-Euclidian space to the sphere in ordinary space. An important property of the surface is that any figure drawn upon it can be displaced in any way without tearing it or altering in size any of its elements.