15 (number)

15 (fifteen) is the natural number following 14 and preceding 16.

Mathematics[edit]

M = 15

The 15 perfect matchings of K₆

15 is:

• A composite number, and the sixth semiprime; its proper divisors being 1, 3 and 5.
• A deficient number, a smooth number, a lucky number, a pernicious number, a bell number (i.e., the number of partitions for a set of size 4), ^[1] a pentatope number, ^[2] and a repdigit in binary (1111) and quaternary (33). In hexadecimal, and higher bases, it is represented as F.
• A triangular number, a hexagonal number,^[3] and a centered tetrahedral number.
• The number of partitions of 7.
• The smallest number that can be factorized using Shor's quantum algorithm.
• The magic constant of the unique order-3 normal magic square.
• The number of supersingular primes.

Furthermore,

• 15 is one of two numbers within the teen numerical range (13-19) not to use a single-digit number in the prefix of its name (the first syllable preceding the teen suffix); instead, it uses the adjective form of five (fifth) as the prefix. The other such number is 13.
• The first 15 superabundant numbers are the same as the first 15 colossally abundant numbers.
• 15 contains the decimal digits 1 and 5, and is the result of adding together the integers from 1 to 5 (1 + 2 + 3 + 4 + 5 = 15). The only other number with this property is 27.
• There are 15 truncatable primes which are both right-truncatable and left-truncatable:

2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397 (sequence A020994 in the OEIS)

• There are 15 perfect matchings of the complete graph K₆ and 15 rooted binary trees with four labeled leaves, both of these being among the types of objects counted by double factorials.
• With only two exceptions, all prime quadruplets enclose a multiple of 15, with 15 itself being enclosed by the quadruplet (11, 13, 17, 19).
• If a positive definite quadratic form with integer matrix represents all positive integers up to 15, then it represents all positive integers via the 15 and 290 theorems.
• 15 is the product of distinct Fermat primes, 3 and 5; hence a regular pentadecagon is constructible with compass and unmarked straightedge, and cos π/15 is expressible in terms of square roots.
• There are 15 monohedral convex pentagonal tilings, with 8 being edge-to-edge.
• There are 15 regular and semiregular tilings when infinite (improper) apeirogonal forms are counted: 3 are regular (with one self-dual), 8 are semiregular (with one chiral), and 4 are apeirogonal (from a total of 8, in-which 4 are duplicates).
• Full icosahedral symmetry contains 15 mirror planes (2-fold axes). Specifically, the symmetry order for both the regular icosahedron and regular dodecahedron (which is made of regular pentagons) is 120: equal to sum of the first 15 integers, and the factorial of 5, wherein the sum of the first 5 integers itself is 15. Expressed mathematically:

  ${\displaystyle \sum _{i=1}^{15}i=120}$, while ${\displaystyle \sum _{i=1}^{5}i=15}$, and ${\displaystyle 5!=120}$.

• There are 15 Archimedean solids and 15 Catalan solids when enantiomorphic forms are counted separately.
• There are 15 regular honeycombs in hyperbolic 3-space: 4 are compact and 11 are paracompact.^[4]

Science[edit]

Seashells from the mollusk Donax variabilis have 15 coloring pattern phenotypes.

• The atomic number of phosphorus.
• Group 15 of the periodic table are sometimes known as the pnictogens.
• 15 Eunomia is the largest Eunomian asteroid in the inner asteroid belt.

Religion[edit]

Sunnism[edit]

The Hanbali Sunni madhab states that the age of fifteen of a solar or lunar calendar is when one's taklif (obligation or responsibility) begins and is the stage whereby one has his deeds recorded.^[5]

Judaism[edit]

• In the Hebrew numbering system, the number 15 is not written according to the usual method, with the letters that represent "10" and "5" (י-ה, yodh and heh), because those spell out one of the Jewish names of God. Instead, the date is written with the letters representing "9" and "6" (ט-ו, teth and vav)
• Passover begins on the 15th day of the Hebrew month of Nisan
• Sukkot begins on the 15th day of the Hebrew month of Tishrei
• Tu Bishvat is a Jewish holiday occurring on the 15th of the Hebrew month of Shevat

Modern use[edit]

15 is designated as an emergency number in Pakistan, for mobile phones, similar to the international GSM emergency number 112;^[6] if 112 is used in Pakistan, then the call is routed to 15. 112 can be used in an emergency even if the phone is locked and does not have a SIM card in it.^{[citation needed]}

Sports[edit]

• In all four of the major Gaelic games—hurling, Gaelic football for men and women, and camogie—each team has 15 players on the field at any given time.
• In both major forms of gridiron football (American and Canadian), standard games are played in 15-minute quarters.
• In rugby union:
  • Each team has 15 players on the field at any given time, unless one or more players are removed for a serious rules infraction.
  • The jersey number 15 is worn by the starting fullback.
• In tennis, the number 15 represents the first point gained in a game.
• In NCAA Division I women's college basketball, teams are allowed to provide scholarships to no more than 15 players at any given time.
• In Australian rules football, games in the AFL Women's league consist of 15-minute quarters.
• The maximum number of players on an NBA team roster.
• On 17 December 2022, the Sydney Thunder were bowled out for just 15 runs in a loss to the Adelaide Strikers during the 2022–23 Big Bash League season. It is the lowest score ever recorded by any professional team in worldwide Twenty20 cricket history.^[7]

Age 15[edit]

• The age of a quinceañera, a Latina girl celebrating her 15th birthday. Thus, Spanish bingo callers might refer to the number 15 as la niña bonita (the beautiful girl).
• The age for obtaining a driver's (or learner's) permit in certain jurisdictions, including some, where the legal age for a driver's license is 16.
• The minimum age for driving a moped in some countries.^{[citation needed]}
• The age of criminal responsibility in various countries.
• In the UK, a minor can be sent to prison to await trial at the age of 15.
• In some countries, it is the legal age for sexual consent.^[8]
• In the UK, it is the legal age to watch a BBFC "15" rated film in a cinema or purchase a "15" rated film or video game.
• The drinking age in Ethiopia.
• The age of majority in Indonesia, Myanmar, Iran and Yemen.

Music[edit]

• "Fifteen" is a song composed by Taylor Swift on her album Fearless

In other fields[edit]

Fifteen is:

• The 15 puzzle.
• The number of minutes in one quarter of an hour; 15 minutes past or before an hour is often known as quarter past and quarter to, respectively.

See also[edit]

• List of highways numbered 15

References[edit]

Further reading[edit]

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 91–93

External links[edit]

Look up 15 in Wiktionary, the free dictionary.

• Clewett, James. "15: f in hexadecimal". Numberphile. Brady Haran. Archived from the original on 2013-05-16. Retrieved 2013-04-02. – discussing hexadecimals
• Bowley, Roger. "15: Bumfit". Numberphile. Brady Haran. Archived from the original on 2013-05-16. Retrieved 2013-04-01. – discussing the Celtic number as used in Lincolnshire