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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 wikiPageLength "14894".
- Golden_ratio_base wikiPageOutDegree "50".
- Golden_ratio_base wikiPageRevisionID "700188967".
- Golden_ratio_base wikiPageWikiLink 0.999....
- Golden_ratio_base wikiPageWikiLink Addition.
- Golden_ratio_base wikiPageWikiLink Base_(exponentiation).
- Golden_ratio_base wikiPageWikiLink Beta_encoder.
- Golden_ratio_base wikiPageWikiLink Binary_number.
- Golden_ratio_base wikiPageWikiLink Category:Golden_ratio.
- Golden_ratio_base wikiPageWikiLink Category:Non-standard_positional_numeral_systems.
- Golden_ratio_base wikiPageWikiLink Decimal.
- Golden_ratio_base wikiPageWikiLink Dyadic_rational.
- Golden_ratio_base wikiPageWikiLink E_(mathematical_constant).
- Golden_ratio_base wikiPageWikiLink Error_message.
- Golden_ratio_base wikiPageWikiLink Exponentiation.
- Golden_ratio_base wikiPageWikiLink Fibonacci_coding.
- Golden_ratio_base wikiPageWikiLink Fibonacci_number.
- Golden_ratio_base wikiPageWikiLink Field_(mathematics).
- Golden_ratio_base wikiPageWikiLink Finite_set.
- Golden_ratio_base wikiPageWikiLink Generalizations_of_Fibonacci_numbers.
- Golden_ratio_base wikiPageWikiLink Geometric_series.
- Golden_ratio_base wikiPageWikiLink Golden_ratio.
- Golden_ratio_base wikiPageWikiLink Greek_alphabet.
- Golden_ratio_base wikiPageWikiLink Integer.
- Golden_ratio_base wikiPageWikiLink Irrational_number.
- Golden_ratio_base wikiPageWikiLink Long_division.
- Golden_ratio_base wikiPageWikiLink Multiplication.
- Golden_ratio_base wikiPageWikiLink Negation_(disambiguation).
- Golden_ratio_base wikiPageWikiLink Negative_number.
- Golden_ratio_base wikiPageWikiLink Non-integer_representation.
- Golden_ratio_base wikiPageWikiLink Ostrowski_numeration.
- Golden_ratio_base wikiPageWikiLink Phi.
- Golden_ratio_base wikiPageWikiLink Pi.
- Golden_ratio_base wikiPageWikiLink Plus_and_minus_signs.
- Golden_ratio_base wikiPageWikiLink Quadratic_field.
- Golden_ratio_base wikiPageWikiLink Quadratic_integer.
- Golden_ratio_base wikiPageWikiLink Rational_number.
- Golden_ratio_base wikiPageWikiLink Real_number.
- Golden_ratio_base wikiPageWikiLink Recurrence_relation.
- Golden_ratio_base wikiPageWikiLink Ring_(mathematics).
- Golden_ratio_base wikiPageWikiLink Sign_(mathematics).
- Golden_ratio_base wikiPageWikiLink Square_(algebra).
- Golden_ratio_base wikiPageWikiLink Square_root_of_2.
- Golden_ratio_base wikiPageWikiLink Square_root_of_5.
- Golden_ratio_base wikiPageWikiLink Subtraction.
- Golden_ratio_base wikiPageWikiLink Uniqueness_quantification.
- Golden_ratio_base wikiPageWikiLinkText "Golden ratio base".
- Golden_ratio_base wikiPageWikiLinkText "golden ratio base".
- Golden_ratio_base wikiPageUsesTemplate Template:Cite_journal.
- Golden_ratio_base wikiPageUsesTemplate Template:Main.
- Golden_ratio_base wikiPageUsesTemplate Template:Metallic_ratios.
- Golden_ratio_base wikiPageUsesTemplate Template:Numeral_systems.
- Golden_ratio_base wikiPageUsesTemplate Template:OEIS.
- Golden_ratio_base wikiPageUsesTemplate Template:Sqrt.
- Golden_ratio_base subject Category:Golden_ratio.
- Golden_ratio_base subject Category:Non-standard_positional_numeral_systems.
- Golden_ratio_base hypernym System.
- Golden_ratio_base type Diacritic.
- Golden_ratio_base type Ratio.
- Golden_ratio_base type Redirect.
- 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 "Golden ratio base".
- Golden_ratio_base sameAs Q2886580.
- Golden_ratio_base sameAs Base_dor.
- 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 黄金进制.
- Golden_ratio_base wasDerivedFrom Golden_ratio_base?oldid=700188967.
- Golden_ratio_base isPrimaryTopicOf Golden_ratio_base.