3 (number)
This article may contain excessive, poor, or irrelevant examples. (July 2012) 



Cardinal  three  
Ordinal  3rd (third) 

Numeral system  ternary  
Factorization  prime  
Divisors  1, 3  
Roman numeral  III  
Roman numeral (unicode)  Ⅲ, ⅲ  
Greek prefix  tri  
Latin prefix  tre/ter  
Binary  11_{2}  
Ternary  10_{3}  
Quaternary  3_{4}  
Quinary  3_{5}  
Senary  3_{6}  
Octal  3_{8}  
Duodecimal  3_{12}  
Hexadecimal  3_{16}  
Vigesimal  3_{20}  
Base 36  3_{36}  
Arabic  ٣,3  
Urdu  
Bengali  ৩  
Chinese  三，弎，叁  
Devanāgarī  ३ (tin)  
Ge'ez  ፫  
Greek  γ (or Γ)  
Hebrew  ג  
Japanese  三  
Khmer  ៣  
Korean  셋,삼  
Malayalam  ൩  
Tamil  ௩  
Telugu  ౩  
Thai  ๓ 
3 (three; /ˈθriː/) is a number, numeral, and glyph. It is the natural number following 2 and preceding 4.
Contents
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^{[1]}
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 textfigure typefaces, though, it has an ascender instead of a descender.
Flat top 3
A common variant of the digit 3 has a flat top, similar to the character Ʒ (ezh). This form is sometimes used to prevent people from fraudulently changing a 3 into an 8. It is usually found on UPCA barcodes and standard 52card decks.
In mathematics
 Three is approximately π (actually closer to 3.14159) when doing rapid guesses or estimates. The same is true if one wants a roughandready estimate of e, which is actually approximately 2.71828.
 Three is the first odd prime number,^{[2]} and the second smallest prime. It is both the first Fermat prime (2^{2n} + 1) and the first Mersenne prime (2^{n} − 1), the only number that is both, as well as the first lucky prime. It is the first superprime. However, it is the second Sophie Germain prime, the second Mersenne prime exponent, the second factorial prime (2! + 1), the second Lucas prime, and 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.
 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.^{[3]}
 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 n^{2} − 1 for some integer n is not prime, since it is (n − 1)(n + 1). This is true for 3 as well (with n = 2), but in this case the smaller factor is 1. If n is greater than 2, both n − 1 and n + 1 are greater than 1 so their product is not prime.
 Three noncollinear 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: 0.000..., 0.333..., 0.666... (See also 0.999..., which = 1.)
 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.).
 3 is the smallest prime of a Mersenne prime power tower: 3, 7, 127, 141183460469231731687303715884105727; it is not known whether any more of the terms are prime. 170
 3 is the smallest number of sides that a simple (nonselfintersecting) polygon can have.
 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, i.e. n^{2} 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 4^{n}(8m + 7) is the sum of 3 squares.
 Each real number belongs to only 1 of the following 3 categories: positive, negative, and zero.
In numeral systems
There is some evidence to suggest that early man may have used counting systems which consisted of "One, Two, Three" and thereafter "Many" to describe counting limits. Early peoples had a word to describe the quantities of one, two, and three but any quantity beyond was simply denoted as "Many". This is most likely based on the prevalence of this phenomena among people in such disparate regions as the deep Amazon and Borneo jungles, where western civilization's explorers have historical records of their first encounters with these indigenous people.^{[4]}
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  10000 

3 × 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  30000 
Division  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  

3 ÷ x  3  1.5  1  0.75  0.6  0.5  0.428571  0.375  0.3  0.3  0.27  0.25  0.230769  0.2142857  0.2  0.1875  0.17647058823529411  0.16  0.157894736842105263  0.15  
x ÷ 3  0.3  0.6  1  1.3  1.6  2  2.3  2.6  3  3.3  3.6  4  4.3  4.6  5  5.3  5.6  6  6.3  6.6 
Exponentiation  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  

3^{x}  3  9  27  81  243  729  2187  6561  19683  59049  177147  531441  1594323  4782969  14348907  43046721  129140163  387420489  1162261467  3486784401  
x^{3}  1  8  27  64  125  216  343  512  729  1000  1331  1728  2197  2744  3375  4096  4913  5832  6859  8000 
In science
 The Roman numeral III stands for giant star in the Yerkes spectral classification scheme.
 Three is the atomic number of lithium.
 Three is the ASCII code of "End of Text".
 Three is the number of dimensions that humans can perceive. Humans perceive the universe to have three spatial dimensions, but some theories, such as string theory, suggest there are more.
 The triangle, a polygon with three edges and three vertices, is the most stable physical shape. For this reason it is widely utilized in construction, engineering and design.^{[5]}
 The ability of the human eye to distinguish colors is based upon the varying sensitivity of different cells in the retina to light of different wavelengths. Humans being trichromatic, the retina contains three types of color receptor cells, or cones.
In protoscience
 In European alchemy, the three primes (Latin: tria prima) were salt (), sulfur () and mercury ().^{[6]}^{[7]}
 The three doshas (weaknesses) and their antidotes are the basis of Ayurvedic medicine in India.
In astronomy
 The Saros number of the solar eclipse series which began on April 24, 2814 BC and ended on June 1, 1534 BC. The duration of Saros series 3 was 1280.14 years, and it contained 72 solar eclipses.
 The Saros number of the lunar eclipse series which began on December 30, 2567 BC and ended on March 21, 1214 BC. The duration of Saros series 3 was 1352.26 years, and it contained 76 lunar eclipses.
In philosophy
 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 threeness from twoness.
In religion
Many world religions contain triple deities or concepts of trinity, including:
 the Christian Holy Trinity
 the Hindu Trimurti
 the Hindu Tridevi
 the Three Jewels of Buddhism
 the Three Pure Ones of Taoism
 the Triple Goddess of Wicca
In Christianity
 The threefold office of Christ is a Christian doctrine that Christ performs the functions of prophet, priest, and king.
 The ministry of Jesus lasted three years.
 Jesus rose from the dead on the third day after his death.
 The devil tempted Jesus three times.
 Saint Peter thrice denied Jesus and thrice affirmed his faith in Jesus
 The Magi gave Jesus three gifts.
 There are three Synoptic Gospels and three epistles of John.
In Judaism
 Noah had three sons: Ham, Shem and Japheth
 The Three Patriarchs: Abraham, Isaac and Jacob
 The prophet Balaam beat his donkey three times.
 The prophet Jonah spent three days and nights in the belly of a large fish
 Three divisions of the Written Torah: Torah (Five Book of Moses), Nevi'im (Prophets), Ketuvim (Writings)^{[8]}
 Three divisions of the Jewish people: Kohen, Levite, Yisrael
 Three daily prayers: Shacharit, Mincha, Maariv
 Three Shabbat meals
 Shabbat ends when three stars are visible in the night sky^{[9]}
 Three Pilgrimage Festivals: Passover, Shavuot, Sukkot
 Three matzos on the Passover Seder table^{[10]}
 The Three Weeks, a period of mourning bridging the fast days of Seventeenth of Tammuz and Tisha B'Av
 Three cardinal sins for which a Jew must die rather than transgress: idolatry, murder, sexual immorality^{[11]}
 Upsherin, a Jewish boy's first haircut at age 3^{[12]}
 A Beth din is composed of three members
 Potential converts are traditionally turned away three times to test their sincerity^{[13]}
 In the Jewish mystical tradition of the Kabbalah, it is believed that the soul consists of three parts, with the highest being nefesh ("repose"), the middle being ruach ("wind" or "spirit") and the lowest being neshamah ("breath").^{[14]} Sometimes the two elements of Chayah ("life" or "animal") and Yechidah ("unit") are additionally mentioned.
 In the Kabbalah, the Tree of Life (Hebrew: Etz haChayim, עץ החיים) refers to a latter 3pillar diagrammatic representation of its central mystical symbol, known as the 10 Sephirot.
In Buddhism
 The Triple Bodhi (ways to understand the end of birth) are Budhu, Pasebudhu, and Mahaarahath.
 The Three Jewels, the three things that Buddhists take refuge in.
In Taoism
 The Three Treasures (Chinese: 三寶; pinyin: sānbǎo; Wade–Giles: sanpao), the basic virtues in Taoism.
In Hinduism
 The Trimurti: Brahma the Creator, Vishnu the Preserver, and Shiva the Destroyer.
 The three Gunas underlie action, in the Vedic system of knowledge.
 The Three Yogas in the context of monotheistic Hinduism are three religious paths for the human spirit to achieve union (yoga) with Ishvara, Supreme Being, i.e. God. They are Karma Yoga, Bhakti Yoga and Jnana Yoga.
In Zoroastrianism
 The three virtues of Humata, Hukhta and Huvarshta (Good Thoughts, Good Words and Good Deeds) are a basic tenet in Zoroastrianism.
In Norse mythology
Three is a very significant number in Norse mythology, along with its powers 9 and 27.
 Prior to Ragnarök, there will be three hard winters without an intervening summer, the Fimbulwinter.
 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.
 Bor had three sons, Odin, Vili, and Vé.
In other religions
 The Wiccan Rule of Three.
 The Triple Goddess: Maiden, Mother, Crone; the three fates.
 The sons of Cronus: Zeus, Poseidon, and Hades.
In esoteric tradition
 The Theosophical Society has three conditions of membership.
 Gurdjieff's Three Centers and the Law of Three.
 Liber AL vel Legis, the central scripture of the religion of Thelema, consists of three chapters, corresponding to three divine narrators respectively: Nuit, Hadit and RaHoorKhuit.
 The Triple Greatness of Hermes Trismegistus is an important theme in Hermeticism.
As a lucky or unlucky number
Three (三, formal writing: 叁, pinyin sān, Cantonese: saam^{1}) is considered a good number in Chinese culture because it sounds like the word "alive" (生 pinyin shēng, Cantonese: saang^{1}), compared to four (四, pinyin: sì, Cantonese: sei^{1}), which sounds like the word "death" (死 pinyin sǐ, Cantonese: sei^{2}).
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, and the count of "three" is predicted based on the timing of the "one" and "two" before it. Three is likely used instead of some other number because it requires the minimal amount counts while setting a rate.
In East and Southeast Asia, there is a widespread superstition that considers it inauspicious to take a photo with three people in it; it is professed that the person in the middle will die first.
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".^{[15]}
In sports
 In association football in almost all leagues, and in the group phases of most international competitions, three competition points are awarded for a win.
 In Gaelic football, hurling and camogie, a "goal", with a scoring value of three, is awarded when the attacking team legally sends the ball into the opponent's goal.
 In baseball, three is the number of strikes before the batter is out and the number of outs per side per inning; in scorekeeping, "3" denotes the first baseman.
 In basketball:
 A shot made from behind the threepoint arc is worth three points (except in the 3x3 variant, in which it is worth two points).
 A potential "threepoint play" exists when a player is fouled while successfully completing a twopoint field goal, thus being awarded one additional free throw attempt.
 On offense, the "threesecond rule" states that an offensive player cannot remain in the opponent's freethrow lane for more than three seconds while his team is in possession of the ball and the clock is running.
 In the NBA only, the defensive threesecond violation, also known as "illegal defense", states that a defensive player cannot remain in his own freethrow lane for more than three seconds unless he is actively guarding an offensive player.
 The "3 position" is the small forward.
 In gridiron football, a field goal is a scoring play in which a kicker kicks the football from behind the line of scrimmage through the goalposts on the opponent's side of the field. This play, if successful, is worth three points.
 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 three wickets in a row it is called a hat trick.
 A "threepeat" is a term for winning three consecutive championships.
 A triathlon consists of three events: swimming, bicycling, and running.
 A pin (professional wrestling) in professional wrestling is when one's shoulders are held the opponent's shoulders against the mat for a count of three.
 NASCAR driver Dale Earnhardt, Sr. drove under number 3 for most of his career for car owner Richard Childress.
See also
 Cube (algebra) – (3 superscript)
 Third
 Triad
References
 ↑ 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
 ↑ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 39
 ↑ Priya Hemenway (2005), Divine Proportion: Phi In Art, Nature, and Science, Sterling Publishing Company Inc., pp. 53–54, ISBN 1402735227
 ↑ Big Numbers. ISBN 1840464313.
 ↑ "Most stable shape triange". Maths in the city. Retrieved February 23, 2015.
 ↑ Eric John Holmyard. Alchemy. 1995. p.153
 ↑ Walter J. Friedlander. The golden wand of medicine: a history of the caduceus symbol in medicine. 1992. p.7677
 ↑ Marcus, Rabbi Yossi (2015). "Why are many things in Judaism done three times?". Ask Moses. Retrieved 16 March 2015.
 ↑ "Shabbat". Judaism 101. 2011. Retrieved 16 March 2015.
 ↑ Kitov, Eliyahu (2015). "The Three Matzot". Chabad.org. Retrieved 16 March 2015.
 ↑ Kaplan, Rabbi Aryeh (28 August 2004). "Judaism and Martyrdom". Aish.com. Retrieved 16 March 2015.
 ↑ "The Basics of the Upsherin: A Boy's First Haircut". Chabad.org. 2015. Retrieved 16 March 2015.
 ↑ "The Conversion Process". Center for Conversion to Judaism. Retrieved 16 March 2015.
 ↑ Kaplan, Aryeh. "The Soul". Aish. From The Handbook of Jewish Thought (Vol. 2, Maznaim Publishing. Reprinted with permission.) September 4, 2004. Retrieved February 24, 2015.
 ↑ See "bad" in the Oxford Dictionary of Phrase and Fable, 2006, via Encyclopedia.com.
 Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 46–48
External links
Look up three in Wiktionary, the free dictionary. 
Wikimedia Commons has media related to 3 (number). 
 Tricyclopedic Book of Threes by Michael Eck
 Threes in Human Anatomy by Dr. John A. McNulty
 Grime, James. "3 is everywhere". Numberphile. Brady Haran.
 The Number 3
 The Positive Integer 3
 Prime curiosities: 3