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), ... (A030452 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.
Five is the second Sierpinski number of the first kind, and can be written as S2=(2^2)+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 groupSn 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 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, as is the case with most primes, 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.
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.
The Saros number of the lunar eclipse series which began on -2581October 8 and ended on -1084March 24. The duration of Saros series 5 was 1496.5 years, and it contained 84 lunar eclipses.
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.
In Greek OrthodoxChristian 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 Discordianism, 5 is seen as a very important number as demonstrated in the Law of Fives and The Pentabarf, which contains five rules. Each page of the Principia Discordia, the primary religious document in Discordianism, is also labeled with 5 digits.
In music
The Five is the name of a 19th century Russian Group of nationalistic composers who included César Cui, Aleksandr Borodin, Mily Balakirev, Modest Mussorgsky, and Nikolay Rimsky-Korsakov
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, e.g. 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.
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.
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 majortriadchord when played in just intonation (most often the case in a cappella vocal ensemble singing), will contain such a pure major third.
In sports
In professional Wrestling, if a wrestler grabs the ropes when he is in a submission hold, the attacking wrestler has up to a 5 count to break the hold until a disqualification is made. This is also the case for choking, grabbing the referee, or standing to the top of the turnbuckle. Contrary to belief, it is not a four count, as emphasised in WWE.
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.
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).
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).
5 is the most common number of gears for automobiles with manual transmission.
Quintessence, meaning 'fifth element', refers to the elusive fifth element that completes the basic four elements (water, fire, air and earth). There is also a movie called The Fifth Element.
A popular Internet catch phrase commonly used on forums such as Something Awful. Posts are given a rating out of five. Posts which receive an average rating of five are referred to as 'top posts' or 'comedy gold'.
There are 5 digits in a United States zip code
An informal term for the British Security Service, MI5
In tarot, card No. 5 is "the Hierophant".
The typical number of members in a Super Sentai team.
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