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- Golden_ratio_base abstract "Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number (1+√5)/2 ≈ 1.61803399 symbolized by the Greek letter φ) as its base. It is sometimes referred to as base-φ, golden mean base, phi-base, or, colloquially, phinary. Any non-negative real number can be represented as a base-φ numeral using only the digits 0 and 1, and avoiding the digit sequence "11" – this is called a standard form. A base-φ numeral that includes the digit sequence "11" can always be rewritten in standard form, using the algebraic properties of the base φ — most notably that φ + 1 = φ2. For instance, 11φ = 100φ.Despite using an irrational number base, when using standard form, all non-negative integers have a unique representation as a terminating (finite) base-φ expansion. The set of numbers which possess a finite base-φ representation is the ring Z[1 + √5/2]; it plays the same role in this numeral systems as dyadic rationals play in binary numbers, providing a possibility to multiply.Other numbers have standard representations in base-φ, with rational numbers having recurring representations. These representations are unique, except that numbers (mentioned above) with a terminating expansion also have a non-terminating expansion, as they do in base-10; for example, 1=0.99999….".
- Golden_ratio_base wikiPageExternalLink phigits.html.
- Golden_ratio_base wikiPageID "61373".
- Golden_ratio_base wikiPageRevisionID "575139213".
- Golden_ratio_base hasPhotoCollection Golden_ratio_base.
- Golden_ratio_base subject Category:Golden_ratio.
- Golden_ratio_base subject Category:Non-standard_positional_numeral_systems.
- Golden_ratio_base type Artifact100021939.
- Golden_ratio_base type Instrumentality103575240.
- Golden_ratio_base type Non-standardPositionalNumeralSystems.
- Golden_ratio_base type Object100002684.
- Golden_ratio_base type PhysicalEntity100001930.
- Golden_ratio_base type System104377057.
- Golden_ratio_base type Whole100003553.
- Golden_ratio_base comment "Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number (1+√5)/2 ≈ 1.61803399 symbolized by the Greek letter φ) as its base. It is sometimes referred to as base-φ, golden mean base, phi-base, or, colloquially, phinary. Any non-negative real number can be represented as a base-φ numeral using only the digits 0 and 1, and avoiding the digit sequence "11" – this is called a standard form.".
- Golden_ratio_base label "Base d'or".
- Golden_ratio_base label "Golden ratio base".
- Golden_ratio_base label "Złoty system liczbowy".
- Golden_ratio_base label "黄金进制".
- Golden_ratio_base label "黄金進法".
- Golden_ratio_base sameAs Base_d'or.
- Golden_ratio_base sameAs 黄金進法.
- Golden_ratio_base sameAs Talstelsel_met_basis_gulden_snede.
- Golden_ratio_base sameAs Złoty_system_liczbowy.
- Golden_ratio_base sameAs m.0gmyl.
- Golden_ratio_base sameAs Q2886580.
- Golden_ratio_base sameAs Q2886580.
- Golden_ratio_base sameAs Golden_ratio_base.
- Golden_ratio_base wasDerivedFrom Golden_ratio_base?oldid=575139213.
- Golden_ratio_base isPrimaryTopicOf Golden_ratio_base.