15 (number)

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

14 15 16
Cardinalfifteen
Ordinal15th
(fifteenth)
Numeral systempentadecimal
Factorization3 × 5
Divisors1, 3, 5, 15
Greek numeralΙΕ´
Roman numeralXV
Binary11112
Ternary1203
Senary236
Octal178
Duodecimal1312
HexadecimalF16
Hebrew numeralט"ו / י"ה
Babylonian numeral𒌋𒐙

Mathematics

M = 15
The 15 perfect matchings of K6
15 as the difference of two positive squares (in orange).

15 is:

Furthermore,

  • 15's prime factors, (3 and 5), form the first twin-prime pair.
  • The first 15 superabundant numbers are the same as the first 15 colossally abundant numbers.
  • In decimal, 15 contains the 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 (in decimal) is 27.
  • There are 15 truncatable primes that 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 a compass and unmarked straightedge, and is expressible in terms of square roots.
  • There are 15 monohedral convex pentagonal tilings, with eight being edge-to-edge.
  • There are 15 regular and semiregular tilings when infinite (improper) apeirogonal forms are counted: three are regular (with one self-dual), eight are semiregular (with one chiral), and four 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:
    , while , and .
  • There are 15 Archimedean solids and 15 Catalan solids when enantiomorphic forms are counted separately.
  • There are 15 regular honeycombs in hyperbolic 3-space: four are compact, and 11 are paracompact.[8]
  • It is the smallest non-trivial Surprise Number. When 15 is partitioned into 2 parts of digits- smaller part 1 and larger part 5, adding numbers from smaller 1 to larger 5 = 1 + 2 + 3 + 4 + 5 = 15 = Original Number.

Science

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

Religion

Sunnism

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.[9]

Judaism

References

Further reading

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