3
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
Bengali
Chinese 三，弎，叁
Devanāgarī
Ge'ez
Greek γ (or Γ)
Hebrew ג
Japanese
Khmer
Korean 셋,삼
Malayalam
Tamil
Telugu
Thai
prefixes tri- (from Greek)

tre-/ter- (from Latin)

Binary 11
Ternary 10
Octal 3
Duodecimal 3

3 (three; pron.: /ˈθr/) is a number, numeral, and glyph. It is the natural number following 2 and preceding 4.

## In mathematics

### 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

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 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[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). 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

### Anatomy

• 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.

### Anthropology

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.[3]

## In religion

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

The Shield of the Trinity is a diagram of the Christian doctrine of the Trinity
Christianity
Islam
• 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.
Judaism

### 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.[citation needed]

### In Hinduism

The "Om" symbol, in Devanagari is also written ओ३म् (ō̄m [õːːm]), where ३ is दीर्घ (dirgha, "three 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.

### 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".[4]

## 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 geography

Flag of Trinacria with a three-legged symbol.
• 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 games

International maritime signal flag for 3 is known as a triband, a form of the tricolour.
• 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.[7]

## In literature

### Original scholarly articles/reviews about the three

Travelling in a troika (three-horse sled).
• "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.

## References

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
3. ^ Georges Duby, France in the Middle Ages 987–1460: From Hugh Capet to Joan of Arc
4. ^ See "bad" in the Oxford Dictionary of Phrase and Fable, 2006, via Encyclopedia.com.
5. ^ Priya Hemenway (2005), Divine Proportion: Phi In Art, Nature, and Science, Sterling Publishing Company Inc., pp. 53–54, ISBN 1-4027-3522-7
6. ^
7. ^ 10 Cases of Vaporware