This article is about about the number. For the year, see 3
. For other uses, see 3 (disambiguation)
||This article may contain excessive, poor, or irrelevant examples. (July 2012)
3 (three; pron.: /ˈθriː/) is a number, numeral, and glyph. It is the natural number following 2 and preceding 4.
In mathematics 
- Three is the first odd prime number, and the second smallest prime. It is both the first Fermat prime (22n + 1) and the first Mersenne prime (2n − 1), the only number that is both, as well as the first lucky prime. However, it is the second Sophie Germain prime, the second Mersenne prime exponent, the second factorial prime (2! + 1), the second Lucas prime, the second Stern prime.
- Three is the first unique prime due to the properties of its reciprocal.
- Three is the aliquot sum of 4.
- Three is the third Heegner number.
- Three is the second triangular number and it is the only prime triangular number. Three is the only prime which is one less than a perfect square. Any other number which is n2 − 1 for some integer n is not prime, since it is (n − 1)(n + 1). This is true for 3 as well, but in its case one of the factors is 1.
- Three non-collinear points determine a plane and a circle.
- Three is the fourth Fibonacci number. In the Perrin sequence, however, 3 is both the zeroth and third Perrin numbers.
- Three is the fourth open meandric number.
- Vulgar fractions with 3 in the denominator have a single digit repeating sequences in their decimal expansions, (.000..., .333..., .666...)
- A natural number is divisible by three if the sum of its digits in base 10 is divisible by 3. For example, the number 21 is divisible by three (3 times 7) and the sum of its digits is 2 + 1 = 3. Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc..). See also Divisibility rule. This works in base 10 and in any positional numeral system whose base divided by three leaves a remainder of one (bases 4, 7, 10, etc.).
- A triangle is the only figure which, if all endpoints have hinges, will never change its shape unless the sides themselves are bent.
- 3 is the smallest prime of a Mersenne prime power tower 3, 7, 127, 170141183460469231731687303715884105727. It is not known whether any more of the terms are prime.
- Three of the five regular polyhedra have triangular faces — the tetrahedron, the octahedron, and the icosahedron. Also, three of the five regular polyhedra have vertices where three faces meet — the tetrahedron, the hexahedron (cube), and the dodecahedron. Furthermore, only three different types of polygons comprise the faces of the five regular polyhedra — the triangle, the quadrilateral, and the pentagon.
- There are only three distinct 4×4 panmagic squares.
- Only three tetrahedral numbers are also perfect squares.
- The first number, according to the Pythagoreans, and the first male number.
- The first number, according to Proclus, being the first number such that n2 is greater than 2n.
- The trisection of the angle was one of the three famous problems of antiquity.
- Gauss proved that every integer is the sum of at most 3 triangular numbers.
- Gauss proved that for any prime number p (with the sole exception of 3) the product of its primitive roots is ≡ 1 (mod p).
- Any number not in the form of 4n(8m+7) is the sum of 3 squares.
In numeral systems 
It is frequently noted by historians of numbers that early counting systems often relied on the three-patterned concept of "One- Two- Many" to describe counting limits. In other words, in their own language equivalent way, early peoples had a word to describe the quantities of one and two, but any quantity beyond this point was simply denoted as "Many". As an extension to this insight, it can also be noted that early counting systems appear to have had limits at the numerals 2, 3, and 4. References to counting limits beyond these three indices do not appear to prevail as consistently in the historical record.
List of basic calculations 
Evolution of the glyph 
Three is the largest number still written with as many lines as the number represents. (The Ancient Romans usually wrote 4 as IIII, but this was almost entirely replaced by the subtractive notation IV in the Middle Ages.) To this day 3 is written as three lines in Roman and Chinese numerals. This was the way the Brahmin Indians wrote it, and the Gupta made the three lines more curved. The Nagari started rotating the lines clockwise and ending each line with a slight downward stroke on the right. Eventually they made these strokes connect with the lines below, and evolved it to a character that looks very much like a modern 3 with an extra stroke at the bottom. It was the Western Ghubar Arabs who finally eliminated the extra stroke and created our modern 3. (The "extra" stroke, however, was very important to the Eastern Arabs, and they made it much larger, while rotating the strokes above to lie along a horizontal axis, and to this day Eastern Arabs write a 3 that looks like a mirrored 7 with ridges on its top line): ٣
While the shape of the 3 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in . In some French text-figure typefaces, though, it has an ascender instead of a descender.
A common variant of the digit 3 has a flat top, similar to the character Ʒ (ezh). Since this form is sometimes used to prevent people from fraudulently changing a 3 into an 8, it is sometimes called a banker's 3.
In science 
- A human ear has three semicircular canals.
- A human middle ear has three ossicles.
- Most elbows consist of three bones, the only joint in the human body where three articulations are surrounded by one capsule.
- Humans perceive white light as the mixture of the three additive primary hues: red, green, and blue.
According to French historian Georges Duby
, the three leaves of the fleur-de-lis
symbol represent the three main medieval social classes:
those who prayed,
those who fought and...
those who worked.
Biology (specific and general) 
In religion 
Main article: Triple deity
Many world religions contain triple deities or concepts of trinity, including:
Three major divisions in comparative religion 
There are three major divisions in comparative religion:
Abrahamic religions 
- Christians worship the trinity, which is one God in three persons.
- Three people (including Jesus) were crucified at the Crucifixion.
- Jesus laid dead in a tomb for three days before his resurrection.
- The threefold office of Christ is a Christian doctrine that Christ performs the functions of prophet, priest, and king.
- The three Theological virtues referred to 1 Corinthians 13.
- In Roman Catholicism, a group of three martyrs, collectively known as Faith, Hope, and Charity (named after the Theological Virtues).
- Also in Roman Catholic doctrine, there are three realms of the afterlife: Heaven, Hell and Purgatory (Limbo is regarded as hypothetical).
- The three members of the Holy Family: Jesus, Mary, and Joseph.
- The Wise Men who visited Jesus after His birth left Him three gifts.
- The Sanctus is a hymn forming part of the Order of Mass in Western Christianity which includes the word "Sanctus" (holy) is repeated three times.
- The Trisagion (Greek: Τρισάγιον "Thrice Holy") is a standard hymn of the Divine Liturgy in most of Eastern Christianity.
- "Holy, Holy, Holy" is a Christian hymn in which the word "holy" is repeated three times.
- During wudhu, the hands, arms, face and feet are each washed three times.
- According to the prophet Muhammad, there are three holy cities of Islam (to which pilgrimage should be made): Mecca, Medina, and Jerusalem.
- King Solomon states in Ecclesiastes 4:12: "A three-ply cord is not easily severed." Examples of this concept of three-ness in Judaism are:
- The three Patriarchs: Abraham, Isaac, and Jacob.
- The Tanakh has 3 sections: Torah, Nevi'im, and Ketuvim.
- There are three main divisions of Jews: Kohen, Levi, and Israel (Israelite).
- Shimon Hatzaddik taught: "On three things the world stands: On Torah, on prayer, and on acts of kindness" (Pirkei Avoth 1:2). Rabban Shimon ben Gamliel taught: "The world continues to exist because of three things: justice, truth, and peace"
In Buddhism 
- The Three Jewels (or Triple Gem) in which Buddhists "take refuge" are the Buddha, the Dharma (the Buddha's teachings), and the Sangha (the community of enlightened beings).
- The Triple Bodhi (ways to understand the end of birth) are Budhu, Pasebudhu, and Mahaarahath.
- The Buddha has three bodies.
In Hinduism 
" symbol, in Devanagari
is also written ओ३म् (ō̄m [õːːm]
), where ३ is दीर्घ (dirgha
times as long")
In Norse mythology 
Three is a very significant number in Norse mythology, along with its powers 9 and 27.
- There were three original beings: the primordial cow Audhumla, Ymir the first giant, and Búri the first god and grandfather of Odin.
- Prior to Ragnarök, there will be three hard winters without an intervening summer, the Fimbulwinter.
- Yggdrasil the World Tree has three roots, and three is the square root of the number of worlds (nine) joined by Yggdrasil. Under the three roots are three sacred wells, one for each, including the Well of Urd in Asgard, the Well of Mimir located "among the frost giants", and Hvergelmir in Niflheim.
- Odin endured three hardships upon the World Tree in his quest for the runes: he hanged himself, wounded himself with a spear, and suffered from hunger and thirst.
- During the onset of Ragnarök three cockerels will begin to crow, heralding the final conflict: Gullinkambi for the gods, Fjalar for the giants and an unnamed third for the dead.
Other religions 
In esoteric tradition 
In cartomancy 
The three cards spread are used in tarot reading with the first representing the past, the second the present, the third the future.
As a lucky or unlucky number 
Three (三, formal writing: 叁, pinyin san1, Cantonese: saam1) is considered a good number in Chinese culture because it sounds like the word "alive" (生 pinyin sheng1, Cantonese: saang1), compared to four (四, pinyin: si4, Cantonese: sei1), which sounds like the word "death" (死 pinyin si3, Cantonese: sei2).
Counting to three is common in situations where a group of people wish to perform an action in synchrony: Now, on the count of three, everybody pull! Assuming the counter is proceeding at a uniform rate, the first two counts are necessary to establish the rate, but then everyone can predict when three" will come based on "one" and "two"; this is likely why three is used instead of some other number.
In Vietnam, there is a superstition that considers it bad luck to take a photo with three people in it; it is professed that the person in the middle will die soon.
There is another superstition that it is unlucky to take a third light, that is, to be the third person to light a cigarette from the same match or lighter. This superstition is sometimes asserted to have originated among soldiers in the trenches of the First World War when a sniper might see the first light, take aim on the second and fire on the third.
The phrase "Third time's the charm" refers to the superstition that after two failures in any endeavor, a third attempt is more likely to succeed. This is also sometimes seen in reverse, as in "third man [to do something, presumably forbidden] gets caught".
Luck, especially bad luck, is often said to "come in threes".
In philosophy 
- The three Doshas (weaknesses) and their antidotes are the basis of Ayurvedic medicine in India.
- Philosophers such as Aquinas, Kant, Hegel, and C. S. Peirce have made threefold divisions, or trichotomies, which have been important in their work.
- Hegel's dialectic of Thesis + Antithesis = Synthesis creates three-ness from two-ness.
- According to Pythagoras and the Pythagorean school, the number 3, which they called triad, is the noblest of all digits, as it is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.
In technology 
- The glyph "3" may be used as a substitute for yogh (Ȝ, ȝ) or Greek xi (Ξ, ξ) or ze (З, з) when those characters are not available.
- Three is the minimum odd number of voting components for simple easy redundancy checks by direct comparison.
- Three is approximately pi (actually closer to 3.14159) when doing rapid engineering guesses or estimates. The same is true if one wants a rough-and-ready estimate of e, which is actually approximately 2.7183.
- "3" is the DVD region code for many East Asian countries, except for Japan (which is Region 2) and China (which is Region 6).
- "3" is the trading name of mobile network operator Hutchison 3G.
- Channel 3 is the television channel traditionally associated with ITV in the UK, and, since 1990, the broadcaster's legal name.
- The television VHF channel most often used in North America for hooking up VCRs and/or video game systems. If it is otherwise occupied by a local broadcaster, then channel 4 is used instead.
- Some may use "3" as an alternate to the letter "E", often in jest or when using Leetspeak, to denote being experienced in certain technology related fields.
- In Resource Description Framework, subject-predicate-object expressions are referred to as triples, because they contain 3 values.
In music 
Two forms of triplets featuring number 3 and an irregular tuplet.
- In music, the Roman numeral iii is the mediant scale degree, chord, or diatonic function, when distinguished III = major and iii = minor.
- Three is the number of performers in a trio.
- There are 3 notes in a triad, the basic form of any chord.
- The tritone, which divides the octave into 3 equally spaced notes (root, tritone, octave).
- In musical notation, the number 3 is often used above tuplets, in particular triplets, denoting that three notes are to be played in the time of one (e.g. three quavers in the time of a crotchet).
- In Indian classical music, three equal repetitions of a rhythmic pattern is a common device called tihai.
Artists, albums, songs 
In geography 
- Several cities are known as Tripoli from Greek for "three cities".
- Sicilia was known as Trinacria for its triangle-shape.
- Three Mile Island is known for a nuclear accident.
- Several cities are also known as Triad Winston-Salem, High Point, and Greensboro NC
In filmography 
In sports 
- In association football:
- The squad number 3 is assigned in most cases to the starting left defender or fullback.
- In almost all leagues, and in the group phases of most international competitions, 3 competition points are awarded for a win.
- In bowling, 3 strikes in a row is called a turkey.
- In Gaelic football, hurling and camogie, a "goal", with a scoring value of 3, is awarded when the attacking team legally sends the ball into the opponent's goal.
- In ice hockey, a game consists of 3 periods of twenty minutes each.
- In rugby union, 3 is the jersey number of the starting tighthead prop. It is also the number of points received for a successful drop goal or penalty kick.
- In rugby league, 3 is the jersey number of the starting right centre threequarter (except in the European Super League, which uses static squad numbering).
- In baseball, 3 is the number of strikes before the batter is out and the number of outs per side per inning. It also represents the first baseman's position.
- In basketball:
- A shot made from behind the three-point arc is worth 3 points (except in the 3x3 variant, in which it is worth 2 points).
- 3 is used to represent the small forward position.
- A potential "three-point play" exists when a player is fouled while successfully completing a two-point field goal, thus being awarded one additional free throw attempt.
- On offense, the "3-second rule" states that an offensive player cannot remain in the opponent's free throw lane for more than 3 seconds while his team is in possession of the ball and the clock is running.
- In the NBA only, the defensive 3-second violation, also known as "illegal defense", states that a defensive player cannot remain in his own free throw lane for more than 3 seconds unless he is actively guarding an offensive player.
- The number of the famous NASCAR stock car that Dale Earnhardt drove for nearly 20 years before his death in 2001. In IROC, Hélio Castroneves had his car number changed from his standard 3 (which he drives in the Indy Racing League) to number 03. In NASCAR's Nationwide Series, the #3 car is currently driven by Austin Dillon, grandson of Earnhardt's friend and former employer Richard Childress.
- A hat-trick in sports is associated with succeeding at anything three times in three consecutive attempts, as well as when any player in ice hockey or soccer scores three goals in one game (whether or not in succession). In cricket, if a bowler takes 3 wickets in a row it is called a hat trick.
- In volleyball, 3 is the number of sets needed to be won to win the whole match. The number is also important because of the "3-metre line", a line on either side of the court 3 metres from the net, which restricts certain attacking plays by back-row players.
- In both American football and Canadian football, the number of points received for a successful field goal. (An exception is in six-man football where the field goal is worth four points.)
- In Canadian football, the last down before a team loses possession on downs. Usually, a team faced with a third down will punt (if far from the opponent's goal line) or attempt a field goal (if relatively close).
- A triathlon consists of three events: swimming, bicycling, and running.
- The jersey number 3 has been retired by several North American sports teams in honor of past playing greats or other key figures:
- Five association football clubs are also known to have retired the number 3:
- In cricket, each wicket, located on each each of the pitch, is made of 3 stumps.
In games 
- The game rock-paper-scissors involves three hand shapes. Rock, paper, and scissors.
- The number is notorious in the gaming community since developer Valve is yet to release a second sequel to any of their major games, with Half-Life 3 being known as one of the industry's most famous cases of vaporware.
In literature 
- It is a peculiarity of Semitic linguistics that a large majority of consonantal roots are triliterals.
- 3 is the number of witches in William Shakespeare's Macbeth.
- 3 is the number of words or phrases in a Tripartite motto.
- 3 is the number of novels or films in a trilogy and the number of interconnected works of art in a triptych.
- Thr3e is a 2003 suspense novel written by thriller author Ted Dekker.
- Dante Alighieri's Divine Comedy has three parts each of thirty-three cantos (plus one introductory canto totaling 100). It was written in terza rima, a combination of tercets. All of this is an allusion to the Christian Trinity.
- The number three recurs several times in Tolkien's The Lord of the Rings and also in The Silmarillion. Three Rings of Power were given to the Elves. There are three Silmarils. The unions of the Eldar (Elves) and the Edain (Men) were three in number: Beren and Lúthien, Tuor and Idril, and Aragorn and Arwen.
- Three Blind Mice is a children's nursery rhyme and musical round.
- The Three Musketeers is a novel by Alexandre Dumas, and is part of a trilogy.
- Three Sisters is a play by Anton Chekhov.
- A recurring theme in Arthur C. Clarke's Rama series is the observation that "the Ramans do everything in threes."
- The Three Bears – children's classic literature
- The Three Little Pigs – children's classic literature.
- 3 is the number of wishes normally granted in most fairy tales and stories. Likewise, the protagonist in most stories faces 3 conflicts, whether mental or physical before his or her great triumph.
- "Threes" is a poem by Carl Sandburg.
- In many Czech folktales, a great beast of some sort will, if bound in some manner, usually be bound by three chains, hooks, ropes, etc., and a menial task must be repeated three times to free it.
- The Day of the Triffids, 1951 by John Wyndham. Genetically modified plants with three legs take over the earth.
- The number three is a recurring theme in the Series of Unfortunate Events: there are three Baudelaire orphans, three Snicket orphans, three Quagmire orphans, etc.
- The Good, the Bad and the Ugly centers around a theme of 3
Original scholarly articles/reviews about the three 
Travelling in a troika
- "The Number Three in The American Culture". A selected chapter found in the book entitled Every Man His Way (1967–68) by Alan Dundes.
- "People in Threes Going Up in Smoke and Other Triplicities in Russian Literature and Culture" (Fall 2005, Rocky Mountain Review) by Lee B. Croft.
- "Buckland's Third Revolution" (1997–98) and "Three Wise Men" (1984–85) posters by Herb O. Buckland.
See also 
- ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 39
- ^ 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): 393, Fig. 24.63
- ^ Georges Duby, France in the Middle Ages 987–1460: From Hugh Capet to Joan of Arc
- ^ See "bad" in the Oxford Dictionary of Phrase and Fable, 2006, via Encyclopedia.com.
- ^ Priya Hemenway (2005), Divine Proportion: Phi In Art, Nature, and Science, Sterling Publishing Company Inc., pp. 53–54, ISBN 1-4027-3522-7
- ^ Three at the Internet Movie Database
- ^ 10 Cases of Vaporware
External links