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Undecimal (also known as unodecimal, undenary, and the base 11 numeral system) is a positional numeral system that uses eleven as its base. While no known society counts by elevens, two are purported to have done so: the Māori (one of the two Polynesian peoples of New Zealand ) and the Pañgwa (a Bantu -speaking people of Tanzania ).
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
For example, "11" represents the number eleven in the decimal or base-10 numeral system (today, the most common system globally), the number three in the binary or base-2 numeral system (used in modern computers), and the number two in the unary numeral system (used in tallying scores). The number the numeral represents is called its value.
The unary numeral system is the simplest numeral system to represent natural numbers: [1] to represent a number N, a symbol representing 1 is repeated N times. [ 2 ] In the unary system, the number 0 (zero) is represented by the empty string , that is, the absence of a symbol.
The base can also be used to show the relationship between the side of a square to its diagonal as a square with a side length of 1 √ 2 will have a diagonal of 10 √ 2 and a square with a side length of 10 √ 2 will have a diagonal of 100 √ 2. Another use of the base is to show the silver ratio as its representation in base √ 2 is ...
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Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number + ≈ 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 .
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