Five

From Wikinfo

Five (5) is the natural number following four and preceding six.

5
Cardinal	Five
Ordinal	Fifth
Numeral system	quinary
Factorization	(prime number)
Roman numeral	V
Binary	0101
Hexadecimal	05

Mathematics

Five is the third smallest prime number, and the only one divisible by 5, the next smallest prime is seven. Because it can be written as 2^(2^1)+1, five is classified as a Fermat prime. 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.

The number 5 is a Fibonacci number, being 2 plus 3. The next Fibonacci number is 8.

Five is a factor of 10, so 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.

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.

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.)

Five 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 octal, decimal and hexadecimal) five is 5.
The Roman numeral for five is V, which comes from a representation of an outstretched hand.
In Greek alphabet, ε (epsilon) has numerical value of 5.
In Cyrillic alphabet, Е has numerical value of 5.
In Glagolitic alphabet, File:GlagolitsaDobro.gif (dobro) has numerical value of 5.
The kanji for five is 五.

Five in various cultures

There are five basic "pillars" of Islam.
Islamic people pray to Allah five times a day (Mohammed was said to have bargained it down with Allah from fifty).
According to the Maya mythology, we are now living in the Fifth World.
In the Oriental 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, rather than from the planets.
In Cantonese, five sounds like the word "not" (symbol 唔). So when five appears in front of a lucky number, e.g. 58, the result is considered unlucky.

Music

Using the Latin root, five musicians are called a quintet. One such group whose name celebrates their fiveness are the Jackson Five.
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 is a British boy band called 5ive.
Other bands with "five" in their name include We Five and the Five Stairsteps.
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.

Other fields

Five is:

The number of cents in a nickel, a coin with Thomas Jefferson's portrait.
The denomination of the U.S. dollar with Abraham Lincoln's portrait.
The designation of an Interstate Highway that runs from San Diego, California to Blaine, Washington.
The number of appendages on a starfish.
The number of players on a basketball team.
The number of permanent members with veto power on the UN Security Council.
The number necessary to make a majority decision in the U.S. Supreme Court.
The five senses are sight, smell, hearing, touch and taste.
The five basic tastes are sweet, salty, sour, bitter and umame.
Five babies born at one time are quintuplets. The most famous set of quintuplets were the Dionne Quintuplets born in the 1930s.
The word "quintessential" came from that elusive fifth element that completes the basic four elements (water, fire, air and earth). There is also a movie called Fifth Element. (The fifth element on the modern periodic table is boron).
The number of dots in a quincunx.
The number of points in a pentagram.
There are five sides in a pentagon.
Pentameter is verse with five repeating feet per line; iambic pentameter was the most popular form in Shakespeare.
Almost all amphibians, reptiles, birds and mammals which have fingers or toes have five of them on each extremity. The expression "five-finger discount" refers to shoplifting.
The five stages of grief are said to be shock, denial, anger, bargaining and acceptance.
The Garden of Cyrus is a Pythagorean Discourse based upon the number 5.
Giving five refers to slapping hands with someone as a sign of approbation.
The word "punch" comes from the Hindustani for five. Being true to the designation of punch, the drink Five Alive is named for its five ingredients.
Something that tries to bring an operation down or screw with the system can be called a "fifth wheel".
Aside from Hawaiian punch, the 50th state of the United states gives us the quinary TV show title Hawaii Five-O.
The Olympics 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).
Five Tiger Generals
Five spice powder
Five Principles of Peaceful Coexistence
Five Dynasties and Ten Kingdoms Period
For the UK TV channel Five, see Five (TV).
The year AD 5.