Brahmic numerals represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign. The
Shunga would add a horizontal line on top of the digit, and the Kshatrapa and Pallava evolved the digit to a point where the speed of writing was a secondary concern. The
Arabs' 4 still had the early concept of the cross, but for the sake of efficiency, was made in one stroke by connecting the "western" end to the "northern" end; the "eastern" end was finished off with a curve. The Europeans dropped the finishing curve and gradually made the digit less cursive, ending up with a digit very close to the original Brahmin cross.[1]
While the shape of the character for the digit 4 has an
ascender in most modern
typefaces, in typefaces with
text figures the glyph usually has a
descender, as, for example, in .
Four is the smallest
composite number, its proper
divisors being
1 and
2.[4] Four is the sum and product of
two with itself: , the only non-zero number such that , which also makes four the smallest and only even squared
prime number and hence the first squared prime of the form , where is a prime. Four, as the first composite number, has a prime aliquot sum of
3; and as such it is part of the first
aliquot sequence with a single composite member, expressly (4, 3,
1,
0). It is the smallest non-unitary
tetrahedral number.[5]
In
Knuth's up-arrow notation, , and so forth, for any number of up arrows.[6] By consequence, four is the only square one more than a prime number, specifically
three.
The sum of the first four prime numbers
two +
three +
five +
seven is the only sum of four consecutive prime numbers that yields an
odd prime number,
seventeen, which is the fourth
super-prime. Four lies between the first proper pair of
twin primes,
three and
five, which are the first two
Fermat primes, like
seventeen, which is the third. On the other hand, the
square of four (), equivalently the
fourth power of two (), is
sixteen; the only number that has as a form of
factorization.
Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. . A number is a multiple of 4 if its last two digits are a multiple of 4 (for example, 1092 is a multiple of 4 because 92 = 4 × 23).[7]
Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four
square numbers.[8] Three are not always sufficient;
7 for instance cannot be written as the sum of three squares.[9]
There are four
all-Harshad numbers:
1,
2, 4, and
6.
12, which is divisible by four thrice over, is a Harshad number in all bases except
octal.
A four-sided plane figure is a
quadrilateral or quadrangle, sometimes also called a tetragon. It can be further classified as a
rectangle or oblong,
kite,
rhombus, and
square.
The
four-color theorem states that a
planar graph (or, equivalently, a flat
map of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors.[11] Three colors are not, in general, sufficient to guarantee this.[12] The largest planar
complete graph has four vertices.[13]
Five-dimensional and every higher dimension: three regular convex -
polytopes, all within the infinite family of regular -
simplexes, -
hypercubes, and -
orthoplexes.
The fourth dimension is also the highest dimension where regular
self-intersecting figures exist:
Two-dimensional: infinitely many regular
star polygons.
Five-dimensional and every higher dimension: zero regular
star-polytopes;
uniform star polytopes in dimensions > are the most symmetric, which mainly originate from
stellations of regular -polytopes.
Four sights – observations which affected Prince Siddhartha deeply and made him realize the sufferings of all beings, and compelled him to begin his spiritual journey—an
old man, a
sick man, a
dead man, and an
ascetic[21]
The four primary castes or strata of society:
Brahmana (priest/teacher),
Kshatriya (warrior/politician),
Vaishya (landowner/entrepreneur) and
Shudra (servant/manual laborer).[42]
The
swastika symbol is traditionally used in
Hindu religions as a sign of good luck and signifies good from all four directions.[43]
When Abraham said: "My Lord, show me how You give life to the dead," Allah said: "Why! Do you have no faith?" Abraham replied: "Yes, but in order that my heart be at rest." He said: "Then take four birds, and tame them to yourself, then put a part of them on every hill, and summon them; they will come to you flying. [Al-Baqara 2:260][53]
The respite of four months was granted to give time to the mushriks in Surah
At-Tawba so that they should consider their position carefully and decide whether to make preparation for war or to emigrate from the country or to accept Islam.[54]
Those who accuse honorable women (of unchastity) but do not produce four witnesses, flog them with eighty lashes, and do not admit their testimony ever after. They are indeed transgressors. [An-Noor 24:4][55]
In a more general sense, numerous mythological and cosmogonical systems consider
Four corners of the world as essentially corresponding to the four points of the compass.[57]
Four is the sacred number of the
Zia, an indigenous tribe located in the U.S. state of
New Mexico.[58]
Four Freedoms: four fundamental freedoms that
Franklin D. Roosevelt declared ought to be enjoyed by everyone in the world: Freedom of Speech, Freedom of Religion, Freedom from Want, Freedom from Fear.[61]
Gang of Four: Popular name for four Chinese Communist Party leaders who rose to prominence during China's Cultural Revolution, but were ousted in 1976 following the death of Chairman
Mao Zedong. Among the four was Mao's widow,
Jiang Qing. Since then, many other political factions headed by four people have been called "Gangs of Four".[62]
Insects of the superorder
Holometabola, also known as Endopterygota, such as butterflies, ants, bees, beetles, fleas, flies, moths, and wasps, undergo
holometabolism—complete metamorphism in four stages—from (1) embryo (ovum, egg), to (2) larva (such as grub, caterpillar), then (3) pupa (such as the chrysalis), and finally (4) the imago.[73]
The cow's stomach is divided in four digestive compartments: reticulum, rumen, omasum and abomasum.[76]
In chemistry
Valency of
carbon (that is basis of life on the Earth) is four. Also because of its tetrahedral crystal bond structure,
diamond (one of the natural allotropes of carbon) is the hardest known naturally occurring material. It is also the valence of
silicon, whose compounds form the majority of the mass of the Earth's crust.[77]
The symbolic meanings of the number four are linked to those of the cross and the square. "Almost from prehistoric times, the number four was employed to signify what was solid, what could be touched and felt. Its relationship to the cross (four points) made it an outstanding symbol of wholeness and universality, a symbol which drew all to itself". Where lines of latitude and longitude intersect, they divide the earth into four proportions. Throughout the world kings and chieftains have been called "lord of the four suns" or "lord of the four quarters of the earth",[83] which is understood to refer to the extent of their powers both territorially and in terms of total control of their subjects' doings.
The
Square of Opposition, in both its Aristotelian version and its
Boolean version, consists of four forms: A ("All S is R"), I ("Some S is R"), E ("No S is R"), and O ("Some S is not R").
In regard to whether two given propositions can have the same
truth value, there are four separate logical possibilities: the propositions are subalterns (possibly both are true, and possibly both are false); subcontraries (both may be true, but not that both are false); contraries (both may be false, but not that both are true); or contradictories (it is not possible that both are true, and it is not possible that both are false).
The
Stoics held with four basic
categories, all viewed as bodies (substantial and insubstantial): (1) substance in the sense of substrate, primary formless matter; (2) quality, matter's organization to differentiate and individualize something, and coming down to a physical ingredient such as pneuma, breath; (3) somehow holding (or disposed), as in a posture, state, shape, size, action, and (4) somehow holding (or disposed) toward something, as in relative location, familial relation, and so forth.
Immanuel Kant expounded a
table of judgments involving four three-way alternatives, in regard to (1) Quantity, (2) Quality, (3) Relation, (4) Modality, and, based thereupon, a
table of four categories, named by the terms just listed, and each with three subcategories.
Franz Brentano held that any major philosophical period has four phases: (1) Creative and rapidly progressing with scientific interest and results; then declining through the remaining phases, (2) practical, (3) increasingly skeptical, and (4) literary, mystical, and scientifically worthless—until philosophy is renewed through a new period's first phase. (See Brentano's essay "The Four Phases of Philosophy and Its Current State" 1895, tr. by Mezei and Smith 1998.)
C. S. Peirce, usually a
trichotomist, discussed four methods for overcoming troublesome uncertainties and achieving secure beliefs: (1) the method of tenacity (policy of sticking to initial belief), (2) the method of authority, (3) the method of congruity (following a fashionable
paradigm), and (4) the
fallibilistic, self-correcting method of science (see "
The Fixation of Belief", 1877); and four barriers to inquiry, barriers refused by the fallibilist: (1) assertion of absolute certainty; (2) maintaining that something is unknowable; (3) maintaining that something is inexplicable because absolutely basic or ultimate; (4) holding that perfect exactitude is possible, especially such as to quite preclude unusual and anomalous phenomena (see "
F.R.L." [First Rule of Logic], 1899).
Paul Weiss built a system involving four modes of being: Actualities (substances in the sense of substantial, spatiotemporally finite beings), Ideality or Possibility (pure normative form), Existence (the dynamic field), and God (unity). (See Weiss's Modes of Being, 1958).
Karl Popper outlined a tetradic schema to describe the growth of theories and, via generalization, also the emergence of new behaviors and living organisms: (1) problem, (2) tentative theory, (3) (attempted) error-elimination (especially by way of critical discussion), and (4) new problem(s). (See Popper's Objective Knowledge, 1972, revised 1979.)
John Boyd (military strategist) made his key concept the decision cycle or
OODA loop, consisting of four stages: (1) observation (data intake through the senses), (2) orientation (analysis and synthesis of data), (3) decision, and (4) action.[85] Boyd held that his decision cycle has philosophical generality, though for strategists the point remains that, through swift decisions, one can disrupt an opponent's decision cycle.
Richard McKeon outlined four classes (each with four subclasses) of modes of philosophical inquiry: (1) Modes of Being (Being); (2) Modes of Thought (That which is); (3) Modes of Fact (Existence); (4) Modes of Simplicity (Experience)—and, corresponding to them, four classes (each with four subclasses) of philosophical semantics: Principles, Methods, Interpretations, and Selections. (See McKeon's "Philosophic Semantics and Philosophic Inquiry" in Freedom and History and Other Essays, 1989.)
Jonathan Lowe (E.J. Lowe) argues in The Four-Category Ontology, 2006, for four categories: kinds (substantial universals), attributes (relational universals and property-universals), objects (substantial particulars), and modes (relational particulars and property-particulars, also known as "
tropes"). (See Lowe's "Recent Advances in Metaphysics," 2001,
Eprint)
Wide use of
rectangles (with four angles and four sides) because they have effective form and capability for close adjacency to each other (houses, rooms, tables, bricks, sheets of paper, screens, film frames).
In the
Rich Text Format specification, language code 4 is for the
Chinese language. Codes for regional variants of Chinese are congruent to 4 mod 256.
Credit card machines have four-twelve function keys.
On most phones, the 4 key is associated with the letters
G,
H, and
I,[88] but on the
BlackBerry Pearl, it is the key for
D and
F.
Many
internal combustion engines are called
four-stroke engines because they complete one thermodynamic cycle in four distinct steps: Intake, compression, power, and exhaust.
"
Quattro", meaning four in the Italian language, is used by
Audi as a trademark to indicate that
all-wheel drive (AWD) technologies are used on Audi-branded cars.[91] The word "Quattro" was initially used by Audi in 1980 in its original 4WD coupé, the
Audi Quattro. Audi also has a privately held subsidiary company called
quattro GmbH.
There are four bases in the game:
first base,
second base,
third base, and
home plate; to score a run, an offensive player must complete, in the sequence shown, a circuit of those four bases.
When a batter receives four pitches that the umpire declares to be "
balls" in a single at-bat, a
base on balls, informally known as a "walk", is awarded, with the batter sent to first base.
For scoring, number 4 is assigned to the
second baseman.
Four is the most runs that can be scored on any single at bat, whereby all three baserunners and the batter score (the most common being via a
grand slam).
The fourth batter in the batting lineup is called the
cleanup hitter.
In
basketball, the number four is used to designate the
power forward position, often referred to as "the four spot" or "the four".[92]
In
cricket, a four is a specific type of scoring event, whereby the ball crosses the
boundary after touching the ground at least one time, scoring four runs. Taking four wickets in four consecutive balls is typically referred to as a double hat trick (two consecutive, overlapping hat tricks).
In
American Football teams get four downs to reach the line of gain.
In
rowing, a four refers to a
boat for four rowers, with or without
coxswain. In rowing nomenclature, 4− represents a coxless four and 4+ represents a coxed four.
One of the two starting
locks wears the jersey number 4.
In the standard
bonus points system, a point is awarded in the league standings to a team that scores at least 4 tries in a match, regardless of the match result.
Four is the only number whose name in English has the same number of letters as its value.
Four (四, formal writing: 肆,
pinyin sì) is considered an
unlucky number in
Chinese,
Korean,
Vietnamese and
Japanese cultures mostly in Eastern Asia because it sounds like the word "death" (死,
pinyin sǐ). To avoid complaints from people with tetraphobia, many numbered product lines skip the "four": e.g.
Nokiacell phones (there was no series beginning with a 4 until the
Nokia 4.2),
PalmPDAs, etc. Some buildings skip floor 4 or replace the number with the letter "F", particularly in heavily Asian areas. See
tetraphobia and Numbers in Chinese culture.
In Tetris, a game named for the Greek word for 4, every shape in the game is formed of 4 blocks each.[97]
4 represents the number of Justices on the
Supreme Court of the United States necessary to grant a writ of
certiorari (i.e., agree to hear a case; it is one less than the number necessary to render a majority decision) at the court's current size.[98]
In the
performing arts, the
fourth wall is an imaginary barrier which separates the audience from the performers, and is "broken" when performers communicate directly to the audience.[100]
In music
In
written music,
common time is constructed of four beats per measure and a quarter note receives one beat.The whole note also receives four beats[101]
The common
major scale is built on two sets of four notes (e.g., CDEF, GABC), where the first and last notes create an
octave interval (a pair-of-four relationship).
The interval of a
perfect fourth is a foundational element of many genres of music, represented in
music theory as the
tonic and
subdominant relationship. Four is also embodied within the
circle of fifths (also known as circle of fourths), which reveals the interval of four in more active harmonic contexts.
Approximately four weeks (4 times 7 days) to a lunar month (
synodic month = 29.53 days). Thus the number four is universally an integral part of primitive sacred calendars.
Four Houses of
Hogwarts in the
Harry Potter series: Gryffindor, Hufflepuff, Ravenclaw, Slytherin.[111]
Four known continents of the world in the A Song of Ice and Fire series: Westeros, Essos, Sothoryos, Ulthos.
Each Grand Prix in
Nintendo's Mario Kart series is divided into four cups and each cup is divided into four courses. The Mushroom Cup, Flower Cup, Star Cup, and Special Cup make up the Nitro Grand Prix, while the Shell Cup, Banana Cup, Leaf Cup, and the Lightning Cup make up the Retro Grand Prix.
^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): 394, Fig. 24.64
^Spencer, Joel (1996), Chudnovsky, David V.; Chudnovsky, Gregory V.; Nathanson, Melvyn B. (eds.), "Four Squares with Few Squares", Number Theory: New York Seminar 1991–1995, New York, NY: Springer US, pp. 295–297,
doi:
10.1007/978-1-4612-2418-1_22,
ISBN978-1-4612-2418-1
^Hilbert, David; Cohn-Vossen, Stephan (1999).
Geometry and the Imagination. American Mathematical Soc. p. 143.
ISBN978-0-8218-1998-2. ...the tetrahedron plays an anomalous role in that it is self-dual, whereas the four remaining polyhedra are mutually dual in pairs...
^Van Voorst, Robert (1 January 2012).
RELG: World. Cengage Learning. p. 108.
ISBN978-1-111-72620-1. He first observed the suffering of the world in the Four Passing Sites
^Stevenson, Kenneth; Glerup, Michael (19 March 2014).
Ezekiel, Daniel. InterVarsity Press. pp. xlv.
ISBN978-0-8308-9738-4. We have already mentioned the four living creatures—the man, the lion, the ox and the eagle
^Wagner, Richard; Helyer, Larry R. (31 January 2011).
The Book of Revelation For Dummies. John Wiley & Sons. p. 308.
ISBN978-1-118-05086-6. The four horsemen of the Apocalypse are one of the most familiar images of Revelation
^Raphael, Howard A., ed. (November 1974).
"The Functions Of A Computer: Instruction Register And Decoder"(PDF). MCS-40 User's Manual For Logic Designers. Santa Clara, California, USA:
Intel Corporation. p. viii.
Archived(PDF) from the original on 3 March 2020. Retrieved 3 March 2020. [...] The characteristic eight
bit field is sometimes referred to as a
byte, a four bit field can be referred to as a nibble. [...]
^Petsko, Gregory A.; Ringe, Dagmar (2004).
Protein Structure and Function. New Science Press. p. 40.
ISBN978-0-87893-663-2. Oligomers containing two, three, four, five, six or even more subunits are known as dimers, trimers, tetramers, pentamers, hexamers, and so on.
^Encrenaz, Therese; Bibring, Jean-Pierre; Blanc, M.; Barucci, Maria-Antonietta; Roques, Francoise; Zarka, Philippe (26 January 2004).
The Solar System. Springer Science & Business Media. p. 283.
ISBN978-3-540-00241-3.
Archived from the original on 12 March 2022. Retrieved 4 November 2020. ...the gas giants (Jupiter and Saturn), and the icy giants (Uranus and Neptune)
^Darpan, Pratiyogita (2008).
Pratiyogita Darpan. Pratiyogita Darpan. p. 85. In the 'ABO' system, all blood belongs one of four major groups — A, B, AB or O
^Woodward, Thompson Elwyn; Nystrom, Amer Benjamin (1930).
Feeding Dairy Cows. U.S. Department of Agriculture. p. 4. The cow's stomach is divided into four compartments.
^Conover, Charles (8 November 2011).
Designing for Print. John Wiley & Sons. p. 62.
ISBN978-1-118-13088-9. CMYK is the standard four-color model used for all full-color print jobs that will be output on an offset printing press
^Vermaat, Misty E.; Sebok, Susan L.; Freund, Steven M.; Campbell, Jennifer T.; Frydenberg, Mark (1 January 2015).
Discovering Computers, Essentials. Cengage Learning. p. 123.
ISBN978-1-305-53402-5. ...the 4 key (labeled with the letters g, h and i)...
^Touche, Fred; Price, Anne (2005).
Wilderness Navigation Handbook. Touche Publishing. p. 48.
ISBN978-0-9732527-0-5. Each of the familiar cardinal directions is equivalent to a particular true bearing: north (0°), east (90°), south (180°), and west (270°)
^Medley, H. Anthony (1997).
Bridge. Penguin. p. 6.
ISBN978-0-02-861735-0. The four playing card suits, as you probably already know, are spades, hearts, diamonds, and clubs