Vigesimal

Vigesimal refers to a numeral system that uses twenty as its base. In a vigesimal system, numbers are expressed with place values that progress by powers of twenty, and digits typically range from zero to nineteen in each position. Like decimal systems, it is a positional numeral system, but its base is twenty rather than ten.

Historically, the most well-documented vigesimal system is that of the Maya Civilization in Mesoamerica. The Maya used a mixed radix that is essentially vigesimal: the first two places follow powers of 20, but the third place uses 18×20 (360) to accommodate approximate solar years, producing place values of 1, 20, 360, 7200, and so on. Maya numerals were often drawn with dots and bars, with a separate symbol for zero.

Vigesimal features also appear in the nomenclature of some languages. In European contexts, vigesimal influence survives in certain numbers in French, where 80 is quatre-vingts (four twenties) and 90 can be expressed as quatre-vingt-dix (four twenty plus ten). Various other languages and dialects have historically used vigesimal counting patterns or mixed radix systems to describe larger quantities or to organize groups, even if daily speech has largely shifted to decimal.

Etymology and scope: The term vigesimal comes from Latin vigesimus, meaning “twentieth,” and is used in mathematics and linguistics to describe systems that are based on twenty. It contrasts with decimal (base-10) and sexagesimal (base-60). In linguistic and historical studies, vigesimal systems illuminate how cultures structured numbers and calendars.

Today, vigesimal is mainly of historical and descriptive interest, illustrating how human counting practices adapt to cultural needs and calendrical calculations.