Undecimal

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). The idea of counting by elevens remains of interest for its relation to a traditional method of tally-counting practiced in Polynesia.

During the French Revolution, undecimal was briefly considered as a possible basis for the reformed system of measurement. Today, undecimal numerals have applications in computer science, technology, and the International Standard Book Number system. They also occasionally feature in works of popular fiction.

Any numerical system with a base greater than ten requires one or more new digits; "in an undenary system (base eleven) there should be a character for ten." To allow entry on typewriters, letters such as ⟨A⟩ (as in hexadecimal), ⟨T⟩ (the initial of "ten"), or ⟨X⟩ (the Roman numeral 10) are used for the number 10 in base 11. It is also possible to use the digit ↊ ("dek"), the so-called Pitman numeral for 10 proposed in 1947 by Isaac Pitman as one of the two transdecimal symbols needed to represent base 12 (duodecimal).

Alleged use by the Māori

Conant and Williams

For about a century, the idea that Māori counted by elevens was best known from its mention in the writing of the American mathematician Levi Leonard Conant. He identified it as a "mistake" originating with a 19th-century dictionary of the New Zealand language published by the Rev.