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−1 0 1 2 3 4 5 6 7 8 9

Cardinal 3
Ordinal 3rd
Numeral system ternary
Factorization prime
Divisors 1, 3
Roman numeral III
Roman numeral (Unicode) Ⅲ, ⅲ
Arabic ٣,3
Chinese numeral 三,弎,叁
Hebrew ג (Gimel)
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

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 Text figures 036.svg. 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

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

3-way Philosophical Distinctions
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[3]: 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[4]: Divine Law, Natural Law, Temporal, positive, or human Law
St. Augustine's 3 characterizations of the soul[5]: Memory, Understanding, Will
Aquinas's 3 causal principles[6] (based in Aristotle): Agent, Patient, Act
Aquinas's 3 acts of intellect[6] (based in Aristotle): Conception, Judgment, Reasoning
Aquinas's 3 transcendentals of being[6]: Unity, Truth, Goodness
Aquinas's 3 requisites for the beautiful[6]: Wholeness or perfection, Harmony or due proportion, Radiance
Albertus Magnus's 3 Universals[7]: Ante rem (Idea in God's mind), In re (potential or actual in things), Post rem (mentally abstracted)
Sir Francis Bacon's 3 Tables[8]: Presence, Absence, Degree
Thomas Hobbes's 3 Fields: Physics, Moral Philosophy, Civil Philosophy
Auguste Comte's Religion of Humanity[9]: Great Being (humanity), Great Medium (the world-space), Great Fetish (the Earth)
Johannes Nikolaus Tetens's 3 powers of mind[10]: Feeling, Understanding, Will
Immanuel Kant's 3 Critiques: Pure Reason, Practical Reason, Judgment
Hegel's 3 Spirits[11]: Subjective Spirit, Objective Spirit, Absolute Spirit
Ludwig Andreas Feuerbach's 3 Thoughts[12]: God (1st thought), Reason (2nd), Man (3rd)
Ferdinand de Saussure's 3 "Signs": Sign, Signified, Signifier
Charles Peirce's 3 semiotic elements: Sign (representamen), Object, Interpretant
Charles Peirce's 3 categories: Quality of feeling, Reaction/resistance, Representation
Charles Peirce's 3 universes of experience: Ideas, Brute fact, Habit (habit-taking)
Charles Peirce's 3 orders of philosophy: Phenomenology, Normative Sciences, Metaphysics
Charles Peirce's 3 normatives: The good (esthetic), The right (ethical), The true (logical)
Charles Peirce's 3 grades of conceptual clearness: By familiarity, Of definition's parts, Of conceivable practical consequences
Charles Peirce's 3 modes of evolution: Fortuitous variation, Mechanical necessity, Creative love
Darwin's essentials of biological evolution[13]: Variation, Heredity, Struggle for existence
James Joyce's 3 aesthetic stages[14]: Arrest (by wholeness), Fascination (by harmony), Enchantment (by radiance)
Louis Zukofsky's 3 aesthetic elements[15] Shape, Rhythm, Style
Pythagoras's "fusion" idea[16]: Monarchy, 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[17]: Aesthetic, Ethical, Religious
Edmund Husserl's 3 Reductions: Phenomenological, Eidetic, Religious
Maurice Merleau-Ponty's 3 fields[18]: Physical, Vital, Human
Maurice Merleau-Ponty's 3 categories[18]: 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"[19]: Acquiescence, Nonviolence, Violence
Max Weber's 3 Authorities: Traditional, Charismatic, Legal-rational
John Maynard Keynes's 3 Eras[20]: 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
Plato's Tripartite soul: Rational, Libidinous, Spirited (various animal qualities)
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

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.

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

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.

In technology

3 as a resin identification code, used in recycling.
Seven-segment 3.svg
  • 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.
  • Any diatonic chord progression's key signature is made obvious with any 3 different triads, as opposed to potential key ambiguities with any 2 chords.
  • 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 a standard jazz combo there are 3 necessary parts: bass, percussion, and chord maker.
  • 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.
  • 3, a song by Britney Spears

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 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

3 is the number used in The Metamorphosis by Kafka

  • 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 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.
  • The Day of the Triffids, 1951 by John Wyndham. Alien plants with three legs invade earth.
  • The number three is a recurring theme in the Series of Unfortunate Events: there are three Baudelaire orphans, three Snickett orphans, three Quagmire orphans, etc...

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

International maritime signal flag for 3 is known as a triband, a form of the tricolour.
Travelling in a troika (three-horse sled).

Three is:

  • There are three golf balls on the moon.
  • Three are the values of French Revolution (liberty, equality, fraternity), and the colors of French flag.
  • Three is a mobile phone operator.
  • The number of stars in "Pacific's triple star" in the God Defend New Zealand, one of New Zealand's two national anthems.
  • 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".
  • 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.
  • 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").


  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. ^
    • Plotinus, the Fifth Ennead, Section 8. Eprint.
    • Plotinus and Corrigan, Kevin (2005), Reading Plotinus: a practical introduction to neoplatonism, p. 26.
  4. ^ Augustine through the Ages (1999), p. 582.
  5. ^ Encyclopedia of Christian Theology v. 1 (2004), p. 54.
  6. ^ a b c d See The Pocket Aquinas (1991).
  7. ^ "St. Albertus Magnus" in the Catholic Encyclopedia. Eprint.
  8. ^ "Francis Bacon, Viscount Saint Alban", Eprint
  9. ^ Pringle-Pattison, Andrew Seth (1917), The idea of God in the light of recent philosophy, p. 149.
  10. ^ Teo, Thomas (2005), The critique of psychology: from Kant to postcolonial theory, p. 43.
  11. ^ Redding, Paul (1997, 2006), "Georg Wilhelm Friedrich Hegel" in the Stanford Encyclopedia of Philosophy. Eprint.
  12. ^ Lange, Friedrich Albert and Thomas, Ernest Chester (1880), History of materialism and criticism of its present importance, v. 2, p. 247, Google Books Eprint.
  13. ^ "Darwinism" in Britannica Concise Encyclopedia via "Darwinism" at
  14. ^ Joyce, James (1914-1915), A Portrait of the Artist as a Young Man, see Chapter 5, especially (but not only) lines 8215-8221.
  15. ^ Zukofsky, Louis, "A" - 12 (1966), and Prepositions (1967, 1981), p. 55.
  16. ^ "Pythagoreanism" at Eprint
  17. ^ McDonald, William (1996, 2009), "Søren Kierkegaard" in the Stanford Encyclopedia of Philosophy. See Section 6.
  18. ^ a b Merleau-Ponty, Maurice (1942), La structure du comportement, and published in English as The Structure of Behavior.
  19. ^ 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.
  20. ^ Mini, Peter V. (1996), "Keynes on markets: a survey of heretical views" in the American Journal of Economics and Sociology, January. Eprint.
  • Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 46 - 48

External links

Simple English

Three – 3
• • •
Order third

The number three is one more than two and one less than four. Three is an important number for many cultures (groups of people living together). Sometimes people think of three as a special number. It is also a prime number. It is the first odd prime.

Famous threes

  • the three stooges
  • the three Doshas (weaknesses) in Ayurvedic medicine in India
  • the Trimurti (three aspects of God) in Hindu religion
  • the Holy Trinity in Christian religion
  • three kings (magi) who visited Christ at his birth in Christian religion
  • the three bears in the fairy tale Goldilocks
  • the three Imperial Regalia of Japankoi:3 (куим)

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