3

3
	Template:Numbers (digits)
Cardinal	3 ; three
Ordinal	3rd ; third
Numeral system	ternary
Factorization	prime
Divisors	1, 3
Roman numeral	III
Roman numeral (Unicode)	Ⅲ, ⅲ
Arabic	٣,3
Ge'ez	፫
Bengali	৩
Chinese numeral	三，弎，叁
Devanāgarī	३
Japanese	三
Tamil	௩
Hebrew	ג (Gimel)
Khmer	៣
Thai	๓
prefixes	tri- (from Greek) tre-/ter- (from Latin)
Binary	11
Octal	3
Duodecimal	3
Hexadecimal	3

3 (three) 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,^[1] and the second smallest prime. It is both the first Fermat prime (2^2ⁿ + 1) and the first Mersenne prime (2ⁿ − 1), as well as the first lucky prime. However, it's 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 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 is the third Heegner number.

Three non-collinear points determine a plane and a circle.

Three is the fourth Fibonacci number and the third that is unique. 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.

A triangle is the most durable shape possible^{[citation needed]}, the only "perfect" figure which if all endpoints have hinges will never change its shape unless the sides themselves are bent.

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.

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.

Base	Numeral system
2	binary	11
3	ternary	10
over 3 (decimal, hexadecimal)		3

List of basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20		21	22	23	24	25		50	100	1000
$3\times x$	3	6	9	12	15	18	21	24	27	30		33	36	39	42	45	48	51	54	57	60		63	66	69	72	75		150	300	3000

Division	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15
$3\div x$	3	1.5	1	0.75	0.6	0.5	$0.{\overline {428571}}$	0.375	$0.{\overline {3}}$	0.3		$0.{\overline {27}}$	0.25	$0.{\overline {230769}}$	$0.2{\overline {142857}}$	0.2
$x\div 3$	$0.{\overline {3}}$	$0.{\overline {6}}$	1	$1.{\overline {3}}$	$1.{\overline {6}}$	2	$2.{\overline {3}}$	$2.{\overline {6}}$	3	$3.{\overline {3}}$		$3.{\overline {6}}$	4	$4.{\overline {3}}$	$4.{\overline {6}}$	5

Exponentiation	1	2	3	4	5	6	7	8	9	10		11	12	13
$3^{x}\,$	3	9	27	81	243	729	2187	6561	19683	59049		177147	531441	1594323
$x^{3}\,$	1	8	27	64	125	216	343	512	729	1000		1331	1728	2197

Evolution of the glyph

Three is often the largest number written with as many lines as the number represents. The Romans tired of writing 4 as IIII, but 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^[2]

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), sometimes used to prevent people from falsifying a 3 into an 8.

In science

Genetic information is encoded in a triplet codon system.
Three is the atomic number of lithium
There are three generations of fundamental leptons (electron, muon, tauon and their neutrinos) and three groups of flavours of quarks (up-down, charmed-strange, top-bottom).
A proton consists of three quarks: two up quarks and one down quark. A neutron also consists of three quarks: two down quarks and one up quark.
We perceive our universe to have three spatial dimensions.
White light is composed of the mixture of the three additive primary hues: red, green, and blue.

In religion and mythology

The Shield of the Trinity is a diagram of the Christian doctrine of the Trinity

Many world religions contain triple deities or concepts of trinity, including:

Three is also a symbolic number in Judaism. King Solomon states in Ecclesiastes 4:12: "A three-ply cord is not easily severed." Threes in Judaism include the Three Patriarchs, the Three Pilgrim Festivals, and the three sections of the Hebrew Bible.

In philosophy

Plato split the soul into three parts: the appetitive, the spirited, and the rational
Hegel's dialectic of Thesis + Antithesis = Synthesis creates three-ness from two-ness.
According to the Pythagoreans, 3 was the noblest of all digits.
The three Doshas (weaknesses) and their antidotes are the basis of Ayurvedic medicine in India.
Charles Sanders Peirce made many trichotomies and framed the "Reduction Thesis" that every predicate is essentially either monadic (quality), dyadic (relation of reaction or resistance), or triadic (representational relation), and never genuinely and irreducibly tetradic or larger.

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) that 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, it is bad luck to take a photo with three people in it. The person in the middle is believed to die soon.

There is a superstition that states 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 is commonly believed to date from 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.

Luck, especially bad luck, is often said to "come in threes".

In technology

3 as a resin identification code, used in recycling.

The resin identification code used in recycling to identify polyvinyl chloride.
On most telephone keypads, the "3" key is also associated with the letters "D", "E", and "F".

The glyph "3" may be used as a substitute for yogh (Ȝ, ȝ) 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.
Some computer users may use "3" as an alternate to the letter "E", often in jest or to prevent search engines from reading their messages. This form of code is an example of basic Leetspeak.
"3" is the DVD region code for many East Asian countries, except for Japan (which is Region 2) and China (which is Region 6).

In music

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 most important and basic form of any chord.
The tritone, which divides the octave into 3 equally spaced notes (root, tritone, octave) is the rarest interval of any mode, only occurring semantically twice, and physically once. It is the only interval that, when inverted, remains unchanged functionally and harmonically.
The 3/4 time signature of Western classical music tradition (Three beats to a measure, with the quarter note comprising the beat.) is said to represent the Holy Trinity of Christian doctrine, Father, Son and Holy Spirit. It is for this reason that it is often utilized in compositions which were written for use in ecclesiastical rites, or that are inspired by scriptural/spiritual themes and texts.
In Indian classical music, three equal repetitions of a rhythmic pattern is a common device called tihai.
3rd Bridge, an extended technique on string instruments.

In geography

Several cities are known as Tripoli from Greek for "three cities," while Sicilia was known as Trinacria for its triangle-shape. Several cities are also known as Triad Winston-Salem, High Point, and Greensboro in North Carolina.

In sports

In bowling, 3 strikes in a row is called a turkey.
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.
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. The number 3 position in the batting order is generally occupied by the team's best hitter. In high school and college, 3 is the maximum "drop" (inches of length minus ounces of weight) for a legal bat. 3 is the retired number of Baseball Hall of Fame players Babe Ruth, Joe Medwick, Bill Terry, and Harmon Killebrew. Gary Sheffield and Ken Griffey Jr wear the number three.
In basketball, a shot made from behind the three-point arc is worth 3 points. 3 is used to represent the small forward position. In addition, 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.
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, 3 outs in a row is called a hat trick.
In volleyball, is the number of sets needed to be won to win the whole match.
In both American 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).
In football, number 3 is assigned in most cases to the left defender or fullback.
On March 24, 2006 the number 3 became the second number retired by the New Jersey Devils in honor of defenseman Ken Daneyko.

In 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.
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 number 3 is often used as a literary device to provoke a feeling of unnaturalness, as twos are much more common in nature (limbs, hemispheres, eyes, etc). This is a prevailing theme in Ray Bradbury's novel Fahrenheit 451. The aliens and their machines in the 2005 film War of the Worlds were associated with features recurring in threes: eyes, legs, fingers, etc, for this same reason.

In other fields

Three is:

The number of golf balls on the moon.^{[citation needed]}
The television VHF channel most often used for hooking up VCRs and/or video game systems. If it is otherwise occupied by a local broadcaster, then channel 4 is used instead.

References

^ 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

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 46–48

External links

Tricyclopedic Book of Threes by Michael Eck
Three at IMDb
Threes in Human Anatomy by Dr. John A. McNulty

[1] Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 39

[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): 393, Fig. 24.63

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