5 (number)

Encyclopedia : 5 : 5N : 5NU : 5 (number)

This article discusses the number five. For the year 5 AD, see 5. For other uses of 5, including the UK television channel, see 5 (disambiguation)


Cardinal	5 five
Ordinal	5th fifth
Numeral system	quinary
Factorization	prime
Divisors	1, 5
Roman numeral	V
Unicode representation of Roman numeral	Ⅴ, ⅴ
prefixes	/ (from Greek) // (from Latin)
Binary	101
Octal	5
Duodecimal	5
Hexadecimal	5
Vigesimal	5
Hebrew	ה (He)

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

The SI prefix for 1000⁵ is peta (P), and for its reciprocal femto (f).

Contents

1 In mathematics

1.1 In numbering systems

2 The Arabic glyph
3 In science

3.1 Astronomy

4 In religion and culture
5 In music
6 In sports
7 In technology
8 In other fields
9 Historical years

In mathematics

Five is the second Sierpinski number of the first kind, and can be written as S2=(2^2)+1

Five is the third smallest prime number, after 2 and 3, and before 7. Because it can be written as 2^(2^1)+1, five is classified as a Fermat prime. 5 is the third Sophie Germain prime, the first safe prime, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. 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 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.

Five is a factor of 10, so vulgar fractions with 5 in the denominator do not yield infinite decimal expansions, unlike most other primes. When written in the decimal system, all multiples of 5 will end in either 5 or 0.

The number 5 is the 5th 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), ... ( lists Markov numbers that appear in solutions where one of the other two terms is 5).

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

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 S_n 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.

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 answer to the question asked at the very end of the mathematics quiz show in the movie Little Man Tate. (Our young protagonist blurts out the answer, but the host mishears it as being the answer from the contestant to whom the question is posed, and declares him the winner.)

In numbering systems

In binary code five is 101
In ternary code five is 12
In quaternary numeral system code five is 11
In quinary five is 10; in senary code and all codes above (such as decimal, duodecimal and vigesimal) five is 5.
The Roman numeral for five is V, which comes from a representation of an outstretched hand.
In the Greek alphabet, ε (epsilon) has numerical value of 5.
In the Hebrew alphabet, ה (heh) has numerical value of 5.
In the Cyrillic alphabet, Е has numerical value of 5.
In the Glagolitic alphabet, (dobro) has numerical value of 5.
The kanji and Chinese character for five are both 五, and its formal writing in Chinese is 伍 (pinyin wǔ).

The Arabic glyph

The evolution of our modern glyph for five cannot be neatly traced back to the Brahmin Indians quite the same way it can for 1 to 4. Later on the Kushana and Gupta Indians 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 look like a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, coming up with glyphs that look more like 4s or 3s than 5s. 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.

In fonts with text figures, 5 usually has a descender, for example, .

In science

The number of appendages on most starfish, which exhibit pentamerism.
Almost all amphibians, reptiles, birds and mammals which have fingers or toes have five of them on each extremity.
The most destructive known tornadoes rate an F-5 on the Fujita scale.
The atomic number of boron.
The lightest atomic mass (the sum of protons and neutrons) for which no stable isotopes exist for any element.

Astronomy

Messier object M5, a magnitude 7.0 globular cluster in the constellation Serpens.
The New General Catalogue [object] NGC 5, a magnitude 13 spiral galaxy in the constellation Andromeda
The Saros [number] of the solar eclipse series which began on April 4, 2720 BC and ended on May 24, 1422 BC. The duration of Saros series 5 was 1298.1 years, and it contained 73 solar eclipses.
The Saros [number] of the lunar eclipse series which began on -2581 October 8 and ended on -1084 March 24. The duration of Saros series 5 was 1496.5 years, and it contained 84 lunar eclipses.

In religion and culture

There are five basic "pillars" of Islam.
Muslims pray to Allah five times a day (Muhammad was said to have bargained it down with Allah from 50).
The Torah contains five books—Genesis, Exodus, Leviticus, Numbers, and Deuteronomy—which are collectively called the Five Books of Moses, the Pentateuch (Greek for "five containers," referring to the scroll cases in which the books were kept), or Chumash (חומש, Hebrew for "fifth")
King David, author of Psalms, arranged the 150 Psalms into five books, paralleling the Five Books of Moses
The Khamsa, an ancient symbol shaped like a hand with five fingers, is used as a protective amulet by Jews and Muslims
According to some traditions of Maya mythology, we are now living in the Fifth World.
In East Asian tradition, there are five elements: (water, fire, earth, wood and metal). The Japanese names for the days of the week, Tuesday through Saturday, come from these elements via the identification of the elements with the five planets visible with the naked eye. Also, the traditional Japanese calendar has a five-day weekly cycle that can be still observed in printed mixed calendars combining Western, Chinese-Buddhist and Japanese names for each weekday.
In some cultures there are five cardinal directions, including the center.
In Cantonese, "five" sounds like the word "not" (symbol: 唔). When five appears in front of a lucky number, e.g. "58", the result is considered unlucky.
According to various mythologies, the universe is comprised of five classical elements: water, earth, air, fire and ether.
In Greek Orthodox Christian mysticism, the number 5 symbolizes the Holy Spirit as the bearer of all life. In the monastic tradition of Mount Athos there exists a "hymn" to the Holy Spirit composed entirely and solely of repetitions of the word "pente" (Greek for "five")

In music

A Perfect fifth is the most consonant harmony, and is the basis for most western tuning systems.
Modern musical notation uses a musical staff made of five horizontal lines.
Using the Latin root, five musicians are called a quintet. One such group whose name celebrates their fiveness are the Jackson Five. (In an episode of Will & Grace guest-starring Janet Jackson, she declared that 5 is a mystical number and for that reason she must have precisely 5 backup dancers).
The name of the band The Fifth Dimension implies that they are transcending beyond even the fourth dimension (time) into a new inner dimension.
There was a British boy band called 5ive.
Other bands with "five" in their name include We Five, Five For Fighting and the Five Man Electrical Band.
The Dave Clark Five and the Ben Folds Five both named themselves after their lead singers, with an implied four others.
The Vogues song "Five-o'clock World" came in reference to the hours 9 to 5 (ending at 5 p.m.), which are the hours of a standard work day. There are also five working days (non-week-ends) in a week.
5 is an album by Lenny Kravitz.
"Take Five" is a famous jazz standard composed by Paul Desmond. It counts five beats per bar.
The number of completed, numbered piano concertos of Ludwig van Beethoven and Camille Saint-Saëns.
Jurassic 5 is a hip hop crew whose second full length album was titled "Power In Numbers."
Maroon 5 is a pop/rock band from Los Angeles, California, that has become popular thanks to songs such as "Harder To Breathe" and "This Love." The band won the Grammy Award for Best New Artist in 2005.
In harmonics - The fifth partial (or 4th overtone) of a fundamental has a frequency ratio of 5/1 to the frequency of that fundamental. This ratio corresponds to the interval of 2 octaves + a pure major third. Thus, the interval of 5/4 is the interval of the pure third. A major triad chord when played in just intonation (most often the case in a capella vocal ensemble singing), will contain such a pure major third.

In sports

The number of players of a basketball team on the court at a given time.
Also used in basketball to represent the position of center.
In chess, the number of first titled grandmasters.
In chess, the fewest number of moves a pawn makes to a queening square.
The Olympic Games have five interlocked rings as their symbol, representing the number of inhabited continents represented by the Olympians (counting North America and South America as one continent).
The number of kyu (pupil) grades in judo
In rugby union, the number of the lock forward who usually jumps at number 4 in the line-out. It is also the number of points awarded for a try.
In rugby league, the number of the left wing.
In baseball, five represents the third baseman's position.
Retired number of former baseball players Joe DiMaggio, Hank Greenberg, Brooks Robinson, Johnny Bench, and George Brett
Retired Number of NHL Hall of Famer Bernie Geoffrion (March 11, 2006)
In 2005, University of Southern California football player Reggie Bush, while wearing number five, won the Heisman Trophy.
5 was the number of Terry Labonte's Chevy when he won the 1996 NASCAR Nextel Cup championship. Kyle Busch now has this number.
In 2005, St. Louis Cardinals first baseman Albert Pujols won the National League Most Valuable Player award wearing the number five.

In technology

Close up on the 5 key on a computer keybard's numeric keypad. Note the raised bar on the lower portion of the key.

The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.
On most telephones, the 5 key is associated with the letters J, K, and L, but on the BlackBerry it is the key for G and H.
On almost all devices with a numeric keypad such as telephones, computers, etc., the 5 key has a raised dot or raised bar to make dialing easier. Persons who are blind or have low vision find it useful to be able to feel the keys of a telephone. All other numbers can be found with their relative position around the 5 button. (On computer keyboards, the 5 key of the numpad has the raised dot or bar, but the 5 key that shifts with % does not).

In other fields

Historical years

5 A.D., 5 B.C., 1905, 2005, etc.

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