||It has been suggested that this article be merged into Ternary numeral system. (Discuss) Proposed since July 2013.|
|Positional systems by base|
|List of numeral systems|
The first few numbers in decimal and nonary are:
The multiplication table in nonary is:
Except for three, no primes in nonary end in 0, 3 or 6, since any nonary number ending in 0, 3 or 6 is divisible by three.
Nonary is useful for determining the sum of the sum of all numbers in a sequence's digits until a single digit is obtained. For example if one was to determine the sum of all digits in the number 382, the result would be found by 3+8+2=13 however this number has more than one digit, so the process continues, 1+3=4 therefore the number 382 would solve to be 4. This answer may be found more easily with Nonary by simply converting 382 into the base 9, which gives 464, the last digit of which will always be the result found by adding each digit up until a single digit is achieved, where 0 reflects the answer of 9.[Watkins 1]
In popular culture
Although the term "Nonary" is used in describing the written form of the language used by the fictional civilization, The Culture, found in Iain M. Banks' books, the description on page 119 of Excession reads more like it is based on a binary system with a 9-bit 'byte'.
- It can be derived naturally from the definition of triangular number, that if we assume is triangular number, then: ; We then obtain: which means is triangular number.
- Watkins, Thayer. "Digit Sums Arithmetic". Digit Sums. Thayer Watkins. Retrieved 29 November 2012.