Definition:Vigesimal System

Definition

A vigesimal system is a number system in which the base is $20$.

In conventional base $20$ notation, every number $x \in \R$ is expressed in the form:

$\ds x = \sum_{j \mathop \in \Z} r_j 20^j$

where:

$\forall j \in \Z: r_j \in \set {0, 1, \ldots, 19}$

Examples

Welsh

The Welsh language shows the remnants of a vigesimal system in its names for certain numbers:

\(\ds \)

\(20\)

\(\ds \)

ugain

\(\ds \)

\(30\)

\(\ds \)

deg ar ugain

\(\quad\) literally: ten and twenty

\(\ds \)

\(40\)

\(\ds \)

deugain

\(\quad\) literally: two twenties

and so on.

Also see

• Results about vigesimal systems can be found here.

Historical Note

The vigesimal system was used by the Maya civilization of Mesoamerica until the $18$th century.

The system used a zero and was a fully positional system.

Linguistic Note

The word vigesimal derives from the Latin vīgintī, meaning twenty, and vicesimus, meaning twentieth.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $20$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $20$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): number system
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): vigesimal system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): number system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): vigesimal system