24

24
Name	24
Numeral	24
Divisors	1, 2, 3, 4, 6, 8, 12, 24
Prime factorization	2^3 × 3

24 is an integer following 23 and preceding 25. It appears frequently in numeration systems, calendrical reckoning, and diverse cultural artifacts, offering connections to notable figures, institutions, events, and mathematical structures. Its properties as a highly composite, abundant, and practical number have led to recurrence across architecture, philosophy, astronomy, and popular television.

Etymology and Symbolism

The English name derives from Old English numerals paralleled in Latin and Greek traditions associated with lists such as the Twelve Olympians doubled, echoing mythic pairings like the Twelve Apostles and seasonal cycles acknowledged by Julius Caesar and later codified by Pope Gregory I. In heraldry and iconography, groups of twenty-four appear in the decorative schemes of the Palace of Versailles, the mosaics of Hagia Sophia, and the statuary programs of the British Museum, where curatorial decisions reference canonical ensembles like the Canon of Medicine and the Encyclopédie's contributors. Philosophers from Plato to Kant have invoked numerical harmony; numerologists of the Victorian era connected twenty-four to systems promoted by figures such as Aleister Crowley and Madame Blavatsky.

Mathematics

As a composite number with prime factorization 2^3·3, it is a factorial divisor: 24 = 4!, which relates it to permutations studied by Évariste Galois and Augustin-Louis Cauchy through symmetric group S4. It is a highly composite integer examined by Ramanujan and appears in the classification of perfect numbers and abundant numbers discussed by Euclid and Leonhard Euler. Twenty-four surfaces in lattice theory—most famously the Leech lattice linked to the work of John Conway and Simon Norton—and underpins sporadic group constructions culminating in the discovery of the Monster group. In algebraic topology, twenty-four occurs in index theorems by Atiyah and Singer, and in modular form contexts developed by Srinivasa Ramanujan and Richard Borcherds.

Science and Technology

In astronomy, twenty-four marks the traditional division of the celestial sphere into right ascension hours employed since the reforms of Hipparchus and standardized in catalogs like those compiled by Tycho Brahe and Johannes Kepler. The element chromium, discovered by Louis Nicolas Vauquelin, has atomic number 24. Twenty-four-bit color depth in computer graphics is a standard promoted by companies such as IBM, Microsoft, and Apple and implemented in graphics APIs from OpenGL and DirectX. In genetics, chromosomal counts like the haploid number in some species have been cataloged in databases curated by institutions like the Human Genome Project and the National Center for Biotechnology Information. Engineering standards, including screw specifications and gear ratios, reference twenty-four in manuals from ISO and DIN.

Culture and Media

The number has titles and motifs in literature and film; authors such as William Shakespeare embedded ensembles resembling pairs of twelve in plays collected by editors like Samuel Johnson and Edmond Malone. In music, compositions by J.S. Bach and collections like the 24 Preludes have influenced pedagogues such as Franz Liszt and performers represented by labels like Deutsche Grammophon. Television series and films by creators affiliated with 20th Century Fox, BBC, or HBO have used the numeral as a structural conceit. Visual artists tied to movements in the Renaissance or Modernism, including exhibitions at the Museum of Modern Art and the Tate Modern, have incorporated grids or cycles of twenty-four panels.

Time and Calendrical Significance

Twenty-four hours form the conventional solar day codified by astronomers like Greenwich Observatory staff and formalized in treaties such as the adoption of the Prime Meridian at the International Meridian Conference. Timekeeping devices from ancient Egypt's sundials through medieval Islamic Golden Age astrolabes to mechanical clocks by Peter Henlein reflect division into twenty-four. The practice of dividing the day into two cycles of twelve inherits from systems promoted by Hipparchus and transmitted via Ptolemy to later navigators like Ferdinand Magellan.

Sports, Games, and Recreation

In team sports and games, the number appears as regulatory limits and scoring devices: shot clock durations influenced by leagues such as the National Basketball Association and play formats standardized by federations like Fédération Internationale de Football Association in scheduling matrices. Board games and role-playing rulebooks from publishers like Games Workshop and Hasbro employ twenty-four spaces or turns in classic configurations; tournament brackets in events organized by bodies such as the International Olympic Committee sometimes use pools of twenty-four competitors, as seen in historical editions of the FIFA World Cup and UEFA competitions.

Category:Integers