Douze

Douze is the French word for the integer 12. It is the number that follows onze and precedes treize in the decimal system and is written as 12 in numerals. The word is used across mathematics, commerce, time, and everyday counting.

Etymology and related terms: Douze comes from Latin duodecim and entered Old French in forms such as doze or douze, evolving into the modern French spelling. In other languages, cognates include doce in Spanish and doce in Portuguese, reflecting the shared Indo-European root.

Mathematical properties: 12 is an even, composite number with prime factorization 2^2 × 3. Its divisors are 1, 2, 3, 4, 6, and 12. The sum of its proper divisors is 16, making 12 the smallest abundant number. It is also noted as the first highly composite number, having more divisors than any smaller positive integer.

Uses and cultural significance: A dozen, meaning 12 units, is a common counting unit in commerce and everyday life, giving rise to terms such as “dozen” (and the French “douzaine”). Related concepts include the gross (12 dozen = 144) and the great gross (12 gross = 1,728). The number 12 also appears in many systems of organization and measurement.

Time, calendar, and science: There are 12 months in a year and 12 signs of the zodiac. On a clock face, the circle is divided into 12 hours, and in Western music, the 12-tone equal temperament divides an octave into 12 semitones. The atomic number of magnesium is 12, tying the numeral to a chemical element.

Overall, douze plays a central role in numeration, measurement, and cultural conventions across various domains.