3 (number)  

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Train wreck at Montparnasse (October 22, 1895) by Studio Lévy and Sons.
Train wreck at Montparnasse (October 22, 1895) by Studio Lévy and Sons.

3 (three) 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.

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
<math>3 \times x</math> 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
<math>3 \div x</math> 3 1.5 1 0.75 0.6 0.5 <math>0.\overline{428571}</math> 0.375 <math>0.\overline{3}</math> 0.3 <math>0.\overline{27}</math> 0.25 <math>0.\overline{230769}</math> <math>0.2\overline{142857}</math> 0.2
<math>x \div 3</math> <math>0.\overline{3}</math> <math>0.\overline{6}</math> 1 <math>1.\overline{3}</math> <math>1.\overline{6}</math> 2 <math>2.\overline{3}</math> <math>2.\overline{6}</math> 3 <math>3.\overline{3}</math> <math>3.\overline{6}</math> 4 <math>4.\overline{3}</math> <math>4.\overline{6}</math> 5
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
<math>3 ^ x\,</math> 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323
<math>x ^ 3\,</math> 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<ref>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</ref>

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 52px. 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 Template:Unicode (ezh), sometimes used to prevent people from falsifying a 3 into an 8.

In science



Attempts to recognize tripartite patterns in human evolution were somewhat popular in the early-mid 20th century. Today, with new knowledge about the fossil record and phylogeny, they are all but refuted. However, one must wonder why there ever was a recurring predilection for a tripartite organization instead of some other pattern, whether or not a specific enumerative identity (such as the "three") presented itself.

With the realization that the Bonobo represents another and very distinct chimpanzee, humans are instead being referred to as "third chimpanzee", as among living creatures they are most similar to the Bonobo and Common Chimp.


Biology (specific and general)



In religion and myth

Triple deity

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

Georges Dumézil developed the idea of a Tripartite Ideology (Trifunctional Hypothesis) with respect to the Indo-European peoples consisting of three class divisions: Priestly~ Warrior~ Farmers/Craftsmen.

Ancient myths

Abrahamic religions

[[File:Shield-Trinity-Scutum-Fidei-English.png|thumb|The Shield of the Trinity is a diagram of the Christian doctrine of the Trinity]].

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 Vedas are called trayi, i.e., triad.
  • Lord Shiva is Trinetra-Three-eyed.
  • The confluence of the Ganga, Yamuna, and hidden Sarasvati is the famous Triveni-confluence of three rivers.

In Buddhism

  • The Triple Gem - Buddha, Dhamma (Buddha's teaching) and Sangha (the preachers of Dhamma).
  • The Triple Bodhi (ways to understand the end of birth)- Budhu, Pasebudhu, Mahaarahath
  • The Buddha has three bodies.
  • Buddhism's three refuges are Trisharana- Buddhan sharanam gacchami, Dhammam sharanam gacchami, Sangham sharanam gacchami.

Other religions

In esoteric tradition

In philosophy

3-way Philosophical Distinctions
Plato's Tripartite soul: Rational. Libidinous. Spirited (various animal qualities).
Aristotle's 3-in-1 idea: Mind. Self-knowledge. Self-love.
Aristotle's 3 Dramatic Unities: Unity of Action. Unity of Time. Unity of Place.
Plotinus's Philosophy<ref>Plotinus, the Fifth Ennead, Section 8. Eprint.
Plotinus and Corrigan, Kevin (2005), Reading Plotinus: a practical introduction to neoplatonism, p. 26.</ref>:
One. One Many. One and Many.
Lucretius's 3 Ages (see also Christian Thomsen): Stone Age. Bronze Age. Iron Age.
St. Augustine's 3 Laws<ref>Augustine through the Ages (1999), p. 582.</ref>: Divine Law. Natural Law. Temporal, positive, or human Law.
St. Augustine's 3 characterizations of the soul<ref>Encyclopedia of Christian Theology v. 1 (2004), p. 54.</ref>: Memory. Understanding. Will.
Aquinas's 3 causal principles<ref name=Aq>See The Pocket Aquinas (1991).</ref> (based in Aristotle): Agent. Patient. Act.
Aquinas's 3 acts of intellect<ref name=Aq /> (based in Aristotle): Conception. Judgment. Reasoning.
Aquinas's 3 transcendentals of being<ref name=Aq />: Unity. Truth. Goodness.
Aquinas's 3 requisites for the beautiful<ref name=Aq />: Wholeness or perfection. Harmony or due proportion. Radiance.
Albertus Magnus's 3 Universals<ref>"St. Albertus Magnus" in the Catholic Encyclopedia. Eprint.</ref>: Ante rem (Idea in God's mind). In re (potential or actual in things). Post rem (mentally abstracted).
Sir Francis Bacon's 3 Tables<ref>"Francis Bacon, Viscount Saint Alban", Britannica.com Eprint</ref>: Presence. Absence. Degree.
Thomas Hobbes's 3 Fields: Physics. Moral Philosophy. Civil Philosophy.
Auguste Comte's Religion of Humanity<ref>Pringle-Pattison, Andrew Seth (1917), The idea of God in the light of recent philosophy, p. 149.</ref>: Great Being (humanity). Great Medium (the world-space). Great Fetish (the Earth).
Johannes Nikolaus Tetens's 3 powers of mind<ref>Teo, Thomas (2005), The critique of psychology: from Kant to postcolonial theory, p. 43.</ref>: Feeling. Understanding. Will.
Immanuel Kant's 3 Critiques: Pure Reason. Practical Reason. Judgment.
Hegel's 3 Spirits<ref>Redding, Paul (1997, 2006), "Georg Wilhelm Friedrich Hegel" in the Stanford Encyclopedia of Philosophy. Eprint.</ref>: Subjective Spirit. Objective Spirit. Absolute Spirit.
Ludwig Andreas Feuerbach's 3 Thoughts<ref>Lange, Friedrich Albert and Thomas, Ernest Chester (1880), History of materialism and criticism of its present importance, v. 2, p. 247, Google Books Eprint.</ref>: God (1st thought). Reason (2nd). Man (3rd).
Ferdinand de Saussure's 3 "Signs": Sign. Signified. Signifier.
Charles Sanders Peirce's 3 semiotic elements: Sign (representamen). Object. Interpretant.
C. S. Peirce's 3 categories: Quality of feeling. Reaction, resistance. Representation, mediation.
C. S. Peirce's 3 universes of experience: Ideas. Brute fact. Habit (habit-taking).
C. S. Peirce's 3 orders of philosophy: Phenomenology. Normative sciences. Metaphysics.
C. S. Peirce's 3 normatives: The good (esthetic). The right (ethical). The true (logical).
C. S. Peirce's 3 grades of conceptual clearness: By familiarity. Of definition's parts,. Of conceivable practical implications.
C. S. Peirce's 3 modes of evolution: Fortuitous variation. Mechanical necessity. Creative love.
Darwin's essentials of biological evolution<ref>"Darwinism" in Britannica Concise Encyclopedia via "Darwinism" at Answers.com.</ref>: Variation. Heredity. Struggle for existence.
Friedrich Nietzsche's revaluation of values: The Will to Power. The Overman. The Eternal Recurrence.
Nietzsche's Zarathustra's 3 metamorphoses: The Camel. The Lion. The Child.
Freud's conceptualization of the psyche: Id. Ego. Super-Ego.
James Joyce's 3 aesthetic stages<ref>Joyce, James (1914-1915), A Portrait of the Artist as a Young Man, see Chapter 5, especially (but not only) lines 8215-8221.</ref>: Arrest (by wholeness). Fascination (by harmony). Enchantment (by radiance).
Louis Zukofsky's 3 aesthetic elements<ref>Zukofsky, Louis, "A" – 12 (1966), and Prepositions (1967, 1981), p. 55.</ref> Shape. Rhythm. Style.
Pythagoras's "fusion" idea<ref>"Pythagoreanism" at Britannica.com. Eprint</ref>: Monarch, Oligarchy. Democracy (into harmonic whole).
Karl Marx's 3 isms: Communism. Socialism. Capitalism.
Woodrow Wilson's 3 isms: Colonialism. Racism. Anti-Communism.
Hippocrates's Mind Disorders: Mania. Melancholia. Phrenitis.
Émile Durkheim's 3 Suicides: Egoistic. Altruistic. Anomic.
David Riesman's 3 Social Characters: Tradition-directed. Inner-directed. Other-directed.
Erich Fromm's 3 Symbols: The Conventional. The Accidental. The Universal.
Søren Kierkegaard's 3 Stages<ref>McDonald, William (1996, 2009), "Søren Kierkegaard" in the Stanford Encyclopedia of Philosophy. See Section 6.</ref>: Aesthetic. Ethical. Religious.
Edmund Husserl's 3 Reductions: Phenomenological. Eidetic. Religious.
Maurice Merleau-Ponty's 3 fields<ref name=MP>Merleau-Ponty, Maurice (1942), La structure du comportement, and published in English as The Structure of Behavior.</ref>: Physical. Vital. Human.
Maurice Merleau-Ponty's 3 categories<ref name=MP />: Quantity. Order. Meaning.
Alan Watts's 3 world views: Life as machine (Western). Life as organism (Chinese). Life as drama (Indian).
3-monkey Philosophy: Hear no Evil. See no Evil. Speak no Evil.
Mark Twain's (Samuel Clemens) 3 lies: Lies. Damned Lies. Statistics.
Witness Stand truths: The Truth. The whole truth. Nothing but the truth.
Abraham Lincoln's 3-For-All: Of the People, By the People. For the People.
Martin Luther King, Jr.'s "Middle Road"<ref>King, Martin Luther, Jr. (1959), "My Trip to the Land of Ghandi", published in A Testament of Hope: The Essential Writings and Speeches of Martin Luther King by Martin Luther King, edited by James M. Washington, 6th ed. 1990, see p. 25.</ref>: Acquiescence. Nonviolence. Violence.
Max Weber's 3 Authorities: Traditional. Charismatic. Legal-rational.
John Maynard Keynes's 3 Eras<ref>Mini, Peter V. (1996), "Keynes on markets: a survey of heretical views" in the American Journal of Economics and Sociology, January. Eprint.</ref>: Scarcity. Abundance. Stabilization.
George Herbert Mead's 3 Distinctions: Self. I. Me.
Frederic Thrasher's 3-group Gangs: Inner Circle. Rank & File. Fringers.
J.W.S. Pringle's 3 intellectual problems: Religious & Ethical. Practical. Scientific.
Jerome Bruner's 3 cognitive processing modes: Enactive. Iconic. Symbolic.
Wilhelm Wundt's 3 mind elements: Sensations. Images. Feelings.
Ezra Pound's 3 poetic modes: Melopoeia (sound). Phanopoeia (image). Logopoeia (meaning).
Robert Sternberg's 3 love components: Passion. Intimacy. Commitment.
Sternberg's Triarchic Intelligence: Analytic. Creative. Practical.
Paul D. MacLean's Triune Brain: R-System (Reptilian). Limbic System. Neocortex.
J.A. Fodor's mind Taxonomy: Central Processes. Input Processes. Transducers.
William Herbert Sheldon's body types: Endomorph. Mesomorph. Ectomorph.
Ernst Kretschmer's body types: Pyknic. Asthenic. Athletic.
K.J.W. Craik's 3 reasoning processes: Translation. Reasoning. Retranslation.
Francis Galton's 3 genius traits: Intellect. Zeal. Power of working.
Yukio Mishima's harmony of pen and sword: Art. Beauty. Action.

As a lucky or unlucky number

Template:Unreferenced section 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

50px|right|3 as a resin identification code, used in recycling.


  • The glyph "3" may be used as a substitute for yogh (Template:Unicode) or ze (Template:Unicode) 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

[[File:Flag of Sicily (revised).svg|thumb|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 filmography

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.
  • Is the number of the famous NASCAR stock car that Dale Earnhardt drove for nearly 20 years before his death in 2001. He won 6 out of his 7 championships while driving the #3 car. Although NASCAR does not officially retire numbers, no one has driven the 3 car since his death. In IROC, Hélio Castroneves had his car number changed from his standard 3 (which he drives in the Indy Racing League) to number 03.
  • Traditional number for the Tyrrell Formula One team's first car along with number 4 for the second until the end of the 1995 Formula One Season.
  • 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).
  • An Ironman triathlon consists of three events, a 2.4 mile (3.86 kilometer) swim, a 112 mile (180.2 kilometer) bike ride, and a 26.2 mile (42.2 kilometer) marathon run.
  • 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

Original scholarly articles/reviews about the three

  • "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.

In other fields


Template:/doc<noinclude> [[File:ICS Three.svg|right|thumb|100px|International maritime signal flag for 3 is known as a triband, a form of the tricolour.]] [[File:Orlowski podrozny.jpg|thumb|Travelling in a troika (three-horse sled).]] Three is:

  • The number of golf balls on the moon.
  • The number of values promoted in the French Revolution (liberty, equality, fraternity), and the number of colors in the French flag.
  • A brand of 3G mobile phones.
  • The number of stars in "Pacific's triple star" referred to in "God Defend New Zealand", one of New Zealand's two national anthems.
  • 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.


  • The phrase "Third time's the charm" (or, rarely, "Three time's the charm") usually means that the third time a person attempts something, he or she will succeed. This is also sometimes seen in reverse, as in "third man [to do something, presumably forbidden] gets caught".
  • In Astrology, Gemini is the 3rd astrological sign of the Zodiac.
  • In paleontology, trilobites are named as such because their bodies are divided in three longitudinal lobes.
  • In leet, the numeral "3" can be used to represent the letter "E" due to their obvious visual similarities, as in: "3}{4|\/|/>13" ("example").


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