5 (number)

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456
−1 0 1 2 3 4 5 6 7 8 9
Cardinalfive
Ordinal5th
(fifth)
Factorizationprime
Divisors1, 5
Roman numeralV
Roman numeral (unicode)Ⅴ, ⅴ
Greek prefixpenta-/pent-
Latin prefixquinque-/quinqu-/quint-
Binary1012
Ternary123
Quaternary114
Quinary105
Senary56
Octal58
Duodecimal512
Hexadecimal516
Vigesimal520
Base 36536
Greekε (or Ε)
Arabic٥,5
Persian۵
Urdu۵
Ge'ez
Bengali
Kannada
Punjabi
Chinese numeral五,伍
Korean다섯,오
Devanāgarī (panch)
Hebrewה (Hey)
Khmer
Telugu
Malayalam
Tamil
 
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456
−1 0 1 2 3 4 5 6 7 8 9
Cardinalfive
Ordinal5th
(fifth)
Factorizationprime
Divisors1, 5
Roman numeralV
Roman numeral (unicode)Ⅴ, ⅴ
Greek prefixpenta-/pent-
Latin prefixquinque-/quinqu-/quint-
Binary1012
Ternary123
Quaternary114
Quinary105
Senary56
Octal58
Duodecimal512
Hexadecimal516
Vigesimal520
Base 36536
Greekε (or Ε)
Arabic٥,5
Persian۵
Urdu۵
Ge'ez
Bengali
Kannada
Punjabi
Chinese numeral五,伍
Korean다섯,오
Devanāgarī (panch)
Hebrewה (Hey)
Khmer
Telugu
Malayalam
Tamil

5 (five /ˈfv/) is a number, numeral, and glyph. It is the natural number following 4 and preceding 6.

In mathematics[edit]

Five is the third prime number. Because it can be written as 221+1, five is classified as a Fermat prime; therefore a regular polygon with 5 sides (a regular pentagon) is constructible with compass and unmarked straightedge. 5 is the third Sophie Germain prime, the first safe prime, the third Catalan number, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. Five is the first good prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n - 1. It is also the only number that is part of more than one pair of twin primes. Five is a congruent number. Five is conjectured to be the only odd untouchable number and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree.

The number 5 is the fifth Fibonacci number, being 2 plus 3. 5 is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... (OEISA030452 lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers.

In bases 10 and 20, 5 is a 1-automorphic number.

5 and 6 form a Ruth–Aaron pair under either definition.

There are five solutions to Znám's problem of length 6.

Five is the second Sierpinski number of the first kind, and can be written as S2=(22)+1

While polynomial equations of degree 4 and below can be solved with radicals, equations of degree 5 and higher cannot generally be so solved. This is the Abel–Ruffini theorem. This is related to the fact that the symmetric group Sn is a solvable group for n ≤ 4 and not solvable for n ≥ 5.

While all graphs with 4 or fewer vertices are planar, there exists a graph with 5 vertices which is not planar: K5, the complete graph with 5 vertices.

Five is also the number of Platonic solids.[1]

A polygon with five sides is a pentagon. Figurate numbers representing pentagons (including five) are called pentagonal numbers. Five is also a square pyramidal number.

Five is the only prime number to end in the digit 5, because all other numbers written with a 5 in the ones-place under the decimal system are multiples of five. As a consequence of this, 5 is in base 10 a 1-automorphic number.

Vulgar fractions with 5 or 2 in the denominator do not yield infinite decimal expansions, unlike expansions with all other prime denominators, because they are prime factors of ten, the base. When written in the decimal system, all multiples of 5 will end in either 5 or 0.

There are five Exceptional Lie groups.

Evolution of the glyph[edit]

Evolution5glyph.png

The evolution of our modern glyph for five cannot be neatly traced back to the Indians quite the same way it can for 1 to 4. Later on the Indian Empires of Kushana and Gupta from India had among themselves several different glyphs which bear no resemblance to the modern glyph. The Nagari and Punjabi took these glyphs and all came up with glyphs that are similar to a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, producing glyphs that were more similar to the numbers 4 or 3 than to the number 5.[2] It was from those characters that the Europeans finally came up with the modern 5, though from purely graphical evidence, it would be much easier to conclude that our modern 5 came from the Khmer. The Khmer glyph develops from the Kushana/Ândhra/Gupta numeral, its shape looking like a modern day version with an extended swirled 'tail' [3]

While the shape of the 5 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in TextFigs256.png.

Science[edit]

Astronomy[edit]

Biology[edit]

Religion and culture[edit]

Christian
Jewish


Islamic
Sikh
Discordianism
Other

Music[edit]

Film and television[edit]

Literature[edit]

Sports[edit]

Technology[edit]

5 as a resin identification code, used in recycling.

Miscellaneous fields[edit]

St. Petersburg Metro, Line 5

Five can refer to:

The fives of all four suits in playing cards

See also[edit]

References[edit]

  1. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 61
  2. ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 394, Fig. 24.65
  3. ^ Ifrah, Georges (1998). The universal history of numbers : from prehistory to the invention of the computer (in translated from the French by David Bellos ... [et al.]). London: Harvill Press. ISBN 978-1-86046-324-2. 

External links[edit]