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Golden field

In mathematics, ⁠ Q ( 5 ) {\displaystyle \mathbb {Q} {\bigl (}{\sqrt {5}}~\!{\bigr )}} ⁠, sometimes called the golden field, is a number system consisting of the set of all numbers ⁠ a + b 5 {\displaystyle a+b{\sqrt {5}}} ⁠, where ⁠ a {\displaystyle a} ⁠ and ⁠ b {\displaystyle b} ⁠ are both rational numbers and ⁠ 5 {\displaystyle {\sqrt {5}}} ⁠ is the…

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Overview

Basic arithmetic

Conjugation and norm

Golden integers

Matrix representation

Other properties

Fibonacci numbers

Relation to fivefold symmetry

Quasiperiodicity

Other applications

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Map overview Semantic statistics

Golden field

Nodes158
Edges157
Triples24
Avg. degree1.99
Density0.012658
Components1

How this topic connects Entity context

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Golden field

Top relations

has application · 7
Golden field → Adrien-Marie Legendre, Fermat's Last Theorem, Gustav Lejeune Dirichlet, In, The, The Clebsch, They
related to Golden integers · 4
Golden field → Alternately, Like, The, These
related to Other properties · 4
Golden field → Any, Delta, It, The
related to Basic arithmetic · 3
Golden field → Converting, Elements, It
related to Higher dimensions · 3
Golden field → E8, Each, The
is a · 1
Golden field → real quadratic field with the smallest discriminant
related to Relation to fivefold symmetry · 1
Golden field → The

Important terminology Word statistics

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Important terminology

displaystyle sqrt varphi mathbb bigl bigr numbers golden number doi textstyle field alpha overline fibonacci 10 begin end aligned integers

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Golden fieldis areal quadratic field with the smallest discriminant0.90text
ifinstance ofdivisibility properties0.80text
Golden fieldhas applicationThe0.60section
Golden fieldhas applicationFermat's Last Theorem0.60section
Golden fieldhas applicationGustav Lejeune Dirichlet0.60section
Golden fieldhas applicationAdrien-Marie Legendre0.60section
Golden fieldhas applicationIn0.60section
Golden fieldhas applicationThe Clebsch0.60section
Golden fieldhas applicationThey0.60section
Golden fieldrelated to Basic arithmeticElements0.60section
Golden fieldrelated to Basic arithmeticIt0.60section
Golden fieldrelated to Basic arithmeticConverting0.60section

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    Min side: 3
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