3 (number)

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0 1 2 3 4 5 6 7 8 9

List of numbers — Integers

0 10 20 30 40 50 60 70 80 90

Cardinal 3
three
Ordinal 3rd
third
Numeral system ternary
Factorization prime
Divisors 1, 3
Roman numeral III
Roman numeral (Unicode) Ⅲ, ⅲ
Arabic ٣
Bengali
Chinese numeral
Devanāgarī
Hebrew ג (Gimel)
Khmer
Thai
prefixes tri- (from Greek)

tre-/ter- (from Latin)

Binary 11
Octal 3
Duodecimal 3
Hexadecimal 3
Look up three in
Wiktionary, the free dictionary.

3 (three) is a number, numeral, and glyph. It is the natural number following 2 and preceding 4.

Contents

  • 1 In mathematics
    • 1.1 In numeral systems
    • 1.2 List of basic calculations
  • 2 Evolution of the glyph
  • 3 In science
    • 3.1 Plants and Animals
    • 3.2 Astronomy
    • 3.3 Chemistry
    • 3.4 Physiology
    • 3.5 Physics
    • 3.6 Psychology
    • 3.7 Geology
    • 3.8 Biology (specific and general)
    • 3.9 Anthropology
    • 3.10 History
  • 4 In Mythology
  • 5 In religion
    • 5.1 Abrahamic religions
    • 5.2 Other religions
    • 5.3 In esoteric tradition
  • 6 In philosophy
  • 7 In Education
  • 8 In politics
  • 9 As a lucky or unlucky number
  • 10 In technology
  • 11 In music
  • 12 In Geography
  • 13 In filmography
  • 14 In sports
  • 15 In literature
    • 15.1 Original scholarly articles/reviews about the three
  • 16 In other fields
  • 17 Historical years
  • 18 References
  • 19 External links

[edit] In mathematics

Three is the first odd prime number, and the second smallest prime after two. It is both the first Fermat prime (2 + 1) and the first Mersenne prime (22 - 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 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..., .999...)

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, the only "perfect" figure which if all endpoints have hinges will never change its shape unless the sides themselves are bent.

3 is the only integer between e and π.

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.

[edit] 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 beyound 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 numberals 2, 3, and 4. References to counting limits beyound 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

[edit] 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{4}2857\overline{1} 0.375 0.\overline{3} 0.3 0.\overline{2}\overline{7} 0.25 0.\overline{2}3076\overline{9} 0.2\overline{1}4285\overline{7} 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

[edit] 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

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

[edit] In science

3-patterned general formula of the Scientific Method''
1. The observation of the phenomena and the recording of facts.
2. The formulation of physical laws from the generalization of the phenomena.
3. The development of a theory that is used to predict new phenomena.

[edit] Plants and Animals

[edit] Astronomy

[edit] Chemistry

[edit] Physiology

[edit] Physics

[edit] Psychology

[edit] Geology

[edit] Biology (specific and general)

else can survive: Methanogens~ Halophiles~ Thermoacidophiles.

[edit] Anthropology

3 distinct species of the genus Homo:
[1] Homo habilis "capable man"
[2] Homo erectus "upright man"
[3] Homo sapiens "wise man"

3 distinct species of the genus Paranthropus:
[1] Paranthropus robustus
[2] Paranthropus boisei
[3] Paranthropus aethiopicus

3 Proconsul species:
[1] Proconsul africanus
[2] Proconsul major
[3] Proconsul nyanzae

3 Pan troglodyte sub-species:
[1] Pan Troglodytes Schweinfurthii- (Eastern Common Chimpanzee)
[2] Pan Troglodytes Troglodytes- (Central Common Chimp)
[3] Pan Troglodytes Verus- (Western Common Chimp)

3 types of primates:
[1] Prosimians
[2] Monkeys (old & new world)
[3] Apes (lesser & greater apes, as well as humans)

3 social group types of the Great Apes:
[1] Orangutans (Solitary)
[2] Gorillas (Harems)
[3] Common Chimps (Live in territories defended by related males)

Three traditional families of hominoid:
1. Hylobatidae- include the so-called lesser apes of Asia, the gibbons and siamangs.
2. Hominidae- include living humans and typically fossil apes that possess a suite of characteristics such as bipedalism, reduced canine size, and increasing brain size such as the australopithecines.
3. Pongidae- include the remaining African great apes including gorillas, chimpanzees, and the Asian orangutan.

Present day humans have been referred to as the 3rd chimpanzee.

[edit] History

[edit] In Mythology

Art~ Arms~ Armor for gods and heroes.

were arranged by the gods as a triangular hearth, enclosing the smoke of the fire creation - the nebula.

to as the 3 spinners).

Spartans, Cleta was the third): Aglaia~ Euphrosyne~ Thalia.

sometimes depicted as having wings of gold, brazen claws, and the tusks of boars. Medusa is the only one of the gorgons that is mortal.

Greek belief: Thantos (male)~ Ker (female)~ Gorgo (female).

(the Angry Ones) or Eumenides by the Ancient Greeks (Orestes called them the Solemn Ones, or the Kindly Ones): Alecto ("unceasing")~ Megaera ("grudging")~ Tisiphone ("avenging murder").

[edit] In religion

[edit] Abrahamic religions

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

.

[edit] Other religions

[edit] In esoteric tradition

[edit] In philosophy

3-patterned Philosophical Distinctions
St. Augustine's Philosophy: Memory~ Understanding~ Will
Comte's Philosophy: Great Being~ Great Medium~ Great Fetish
Hegel's 3 Spirits: Subjective Spirit~ Objective Spirit~ Absolute Spirit
Plotinu's Philosophy: One~ One Many~ One and Many
Aristotle's 3 Unities: Unity of Action~ Unity of Time~ Unity of Place
Sir F. Bacon's 3 Tables: Presence~ Absence~ Degree
Thomas Hobbes's 3 Fields: Physics~ Moral Philosophy~ Civil Philosophy
Immanuel Kant's 3 Critiques: Pure Reason~ Practical Reason~ Judgment
Averroes's 3 Commentaries: Little~ Middle~ Great
Karl Marx's 3 isms: Communism~ Socialism~ Capitalism
Woodrow Wilson's 3 isms: Colonialism~ Racism~ Anti-Communism
Hippocrates's Mind Disorders: Mania~ Melancholia~ Phrenitis
Emile Durkeim's 3 Suicides: Egoistic~ Altruistic~ Anomic
D. Liesman's 3 Social Characters: Tradition-directed~ Inner-directed~ Other-directed
Erich Fromm's 3 Symbols: The Conventional~ The Accidental~ The Universal
Pythagoras's "fusion" idea: Monarchy~ Oligarchy~ Democracy (into harmonic whole)
M.L. King Jr.'s "Middle Road": Acquiescence~ Nonviolence~ Violence
Kierkegaard's 3 Stages: Aesthetic~ Ethical~ Religious
Husserl's 3 Reductions: Phenomenological~ Eidetic~ Religious
St. Augustine's 3 Laws: Divine Law~ Natural Law~ Temporal, or positive Law
Witness Stand truths: The Truth~ The whole Truth~ Nothing but the Truth
Titus Carus's 3 Ages: Stone Age~ Bronze Age~ Iron Age
Feuerbach's 3 Thoughts: God, 1st Thought~ Reason, 2nd~ Man, 3rd
Magnus's 3 Universals: Ante Rem~ In Rem~ Post Rem
Max Weber's 3 Authorities: Traditional~ Charismatic~ Legal-rational
F.  de Sausure's 3 "Signs": Sign~ Signified~ Signifier
Charles Pierces 3 "Signs": Qualisign~ Sinsign (token)~ Legisign
John Keynes's 3 Eras: Scarcity~ Abundance~ Stabilization
George Mead's 3 Distinctions: Self~ I~ Me
Thrasher's 3-group Gangs: Inner Circle~ Rank & File~ Fringers
Abe Lincoln's 3-For-All: Of the People~ By the People~ For the People
Jesus Christ's 3 Praises: In the name of the Father~ Son~ Holy Spirit
Samuel Clemmons' (Mark Twain) 3 lies: Lies~ Damned Lies~ Statistics
J.W.S. Pringle's 3 intellectual problems: Religious & Ethical~ Practical~ Scientific
J. Bruner's 3 cognitive processing modes: Enactive~ Iconic~ Symbolic
Wilhelm Wundt's 3 mind elements: Sensations~ Images~ Feelings
Robert Sternberg's 3 love components: Passion~ Intimacy~ Commitment
Sternberg's Triarchic Intelligence: Analytic~ Creative~ Practica
Paul D. Maclean's Triune Brain: R-System (Reptilian)~ Limbic System~ Neocortex
3-monkey Philosophy: Hear no Evil~ See no Evil~ Speak no Evil
J.A. Fodor's mind Taxonomy: Central Processes~ Input Processes~ Transducers
Plato's Tripartite soul: Rational~ Libidinous~ Spirited (various animal qualities)
Hjalmar Wennerberg's philosophy orders: Phenomenology~ Normative Science~ Metaphysics
W.H. Sheldon's body types: Endomorph~ Mesomorph~ Ectomorph
Ernst Kretschmer's body types: Pyknic~ Asthenic~ Athletic
Aristotle's 3 in 1 idea: Mind~ Self-knowledge~ Self-love
K.J.W. Craik's 3 reasoning processes: Translation~ Reasoning~ Retranslation
Galton's 3 genius traits: Intellect~ Zeal~ Power of working
Gregor Mendel "laws": Independent Unit Characters~ Segregation~ Dominance
Darwinian essentials of Evolution: Variation~ Heredity~ Struggle for existence

[edit] In Education

[edit] In politics

Christ sorting people into prayers, protectors and workers.

law-making process. To this end, every man, woman, and worker must have access to such a role, thus constituting a true 3rd branch legislative body. For example, each State in the United States would adopt an ongoing list of self-elected candidates from which the 3 aforementioned persons would be randomly selected to fulfill one-year terms of office with at least the same pay, privileges and legislative power commensurate to all other congressional members.

[edit] 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: sei3) 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.

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

Some cultures in history have a place for people of third gender.

[edit] In technology

[edit] In music

[edit] In Geography

Flag of Trinacria with a three-legged symbol.

[edit] In filmography

[edit] In sports

[edit] In literature

[edit] Original scholarly articles/reviews about the three

[edit] 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).

For other uses and related terms, see also 3 (disambiguation) Three is:

[edit] Historical years

3 A.D., 3 B.C., 1903, 2003, etc.