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Golden ratio base - Wikipedia

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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 φn + φn − 1 = φn + 1. 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

Golden ratio base - Wikipedia Jump to content From Wikipedia, the free encyclopedia Positional numeral system This article includes a list of references , related reading , or external links , but its sources remain unclear because it lacks inline citations . Please help improve this article by introducing more precise citations. ( August 2018 ) ( Learn how and when to remove this message ) Part of a series on Numeral systems Place-value notation Hindu–Arabic numerals Western Arabic Eastern Arabic Bengali Devanagari Gujarati Gurmukhi Odia Sinhala Tamil Malayalam Telugu Kannada Dzongkha Tibetan

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