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Constructible number

In geometry and algebra, a real number r {\displaystyle r} is constructible if and only if, given a line segment of unit length, a line segment of length | r | {\displaystyle |r|} can be constructed with compass and straightedge in a finite number of steps. Equivalently, r {\displaystyle r} is constructible if and only if there is a closed-form…

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Overview

Geometric definitions

Algebraic definitions

Equivalence of algebraic and geometric definitions

Algebraic properties

Trigonometric numbers

Impossible constructions

History

Advanced semantic analysis

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Map overview Semantic statistics

Constructible number

Nodes92
Edges91
Triples71
Avg. degree1.98
Density0.021739
Components1

How this topic connects Entity context

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Constructible number

Top relations

related to history · 37
Constructible number → According, Alhazen, Alhazen's, Although, Angle, Archimedes, Archytas, Ascalon, BCE, Carl Friedrich Gauss, Delian, Disquisitiones Arithmeticae, Elis, Eratosthenes, Eudemus, Eudoxus, Eutocius, Felix Klein, Gauss, Gauss's
related to Algebraic properties · 8
Constructible number → Euclidean, Examining, If, It, More, The, Thus, Using
related to Impossible constructions · 7
Constructible number → Angle, Archimedes' Neusis, Greeks, However, In, One, The
related to Geometrically constructible numbers · 6
Constructible number → Cartesian, Equivalent, For, In, It, The
related to Algebraically constructible numbers · 5
Constructible number → Alternatively, Analogously, Even, For, The
related to Equivalence of algebraic and geometric definitions · 4
Constructible number → If, In, It, The
related to External links · 4
Constructible number → Cut-the-knot, Eric, MathWorldConstructible Numbers, Weisstein

Important terminology Word statistics

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Important terminology

constructible numbers displaystyle number field compass points two straightedge real construction using algebraically constructed point segment geometric algebraic problems complex

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Constructible numberrelated to Algebraic propertiesThe0.60section
Constructible numberrelated to Algebraic propertiesThus0.60section
Constructible numberrelated to Algebraic propertiesMore0.60section
Constructible numberrelated to Algebraic propertiesEuclidean0.60section
Constructible numberrelated to Algebraic propertiesExamining0.60section
Constructible numberrelated to Algebraic propertiesIt0.60section
Constructible numberrelated to Algebraic propertiesIf0.60section
Constructible numberrelated to Algebraic propertiesUsing0.60section
Constructible numberrelated to Algebraically constructible numbersThe0.60section
Constructible numberrelated to Algebraically constructible numbersEven0.60section
Constructible numberrelated to Algebraically constructible numbersFor0.60section
Constructible numberrelated to Algebraically constructible numbersAnalogously0.60section

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