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Pseudosphere

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 surface is a surface piecewise smoothly immersed in R 3 {\displaystyle \mathbb {R} ^{3}} with constant negative Gaussian curvature. A "pseudospherical surface of radius R" is a surface in R 3…

Tractroid, Relation to solutions to the sine-Gordon equation & Universal covering space

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Overview

Tractroid

Line congruence

  • ODEs Ordinary differential equation

Universal covering space

Hyperboloid

Relation to solutions to the sine-Gordon equation

Advanced semantic analysis

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Map overview Semantic statistics

Pseudosphere

Nodes46
Edges45
Triples15
Avg. degree1.96
Density0.043478
Components1

How this topic connects Entity context

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Pseudosphere

Top relations

related to Tractroid · 5
Pseudosphere → As, By, Gaussian, It, The
related to Universal covering space · 5
Pseudosphere → In, Poincaré, The, Then, This
related to Hyperboloid · 3
Pseudosphere → In, Minkowski, This
is a · 2
Pseudosphere → important geometric precursor to mathematical fabric arts and pedagogy, surface in R 3

Important terminology Word statistics

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Important terminology

surface displaystyle curvature pseudospherical surfaces mathbb sine-gordon geometry sphere equation radius line tractroid two congruence point hyperbolic solutions hyperboloid focal

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Pseudosphereis asurface in R 30.90text
Pseudosphereis aimportant geometric precursor to mathematical fabric arts and pedagogy0.90text
Pseudosphererelated to HyperboloidIn0.60section
Pseudosphererelated to HyperboloidThis0.60section
Pseudosphererelated to HyperboloidMinkowski0.60section
Pseudosphererelated to TractroidBy0.60section
Pseudosphererelated to TractroidThe0.60section
Pseudosphererelated to TractroidAs0.60section
Pseudosphererelated to TractroidIt0.60section
Pseudosphererelated to TractroidGaussian0.60section
Pseudosphererelated to Universal covering spaceThe0.60section
Pseudosphererelated to Universal covering spaceIn0.60section

Related concept clusters Concept neighborhoods

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    Connections between topic areas Semantic bridges

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    Min side: 3
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