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4

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Evolution of the Hindu-A..
Mathematics
List of basic calculatio..
In culture
In logic and philosophy
Religion
In technology
Other groups of four
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4 ( four) is a number, numeral and numerical digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is tetraphobia in many East Asian cultures.

Evolution of the Hindu-Arabic digit

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 Empire would add a horizontal line on top of the digit, and the Northern Satraps and Pallava dynasty evolved the digit to a point where the speed of writing was a secondary concern. The ' 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.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

While the shape of the character for the digit 4 has an ascender in most modern , in typefaces with text figures the glyph usually has a descender, as, for example, in .

On the seven-segment displays of pocket calculators and digital watches, as well as certain optical character recognition fonts, 4 is seen with an open top: .

Television stations that operate on channel 4 have occasionally made use of another variation of the "open 4", with the open portion being on the side, rather than the top. This version resembles the Canadian Aboriginal syllabics letter ᔦ. The magnetic ink character recognition "CMC-7" font also uses this variety of "4".

Mathematics

There are four elementary arithmetic operations in mathematics: addition ( +), subtraction ( −), multiplication ( ×), and division ( ÷).

Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four square number.

Ivars Peterson (2025). 9780883855379, MAA. . ISBN 9780883855379

Four is one of four Harshad number. Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e.

4x=y^{2}-z^{2}

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.

Four is the highest degree general polynomial equation for which there is a solution in radicals.

Béla Bajnok (2013). 9781461466369, Springer Science & Business Media. . ISBN 9781461466369

Four is the only square number $I=i\times i$ where $I - 1$ is a prime number.

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. Three colors are not, in general, sufficient to guarantee this.

Ari Ben-Menahem (2009). 9783540688310, Springer Science & Business Media. . ISBN 9783540688310

The largest planar complete graph has four vertices.

Jason J. Molitierno (2016). 9781439863398, CRC Press. . ISBN 9781439863398

A solid figure with four faces as well as four vertices is a tetrahedron, which is the smallest possible number of faces and vertices a polyhedron can have.

(1968). 9780030676451, Holt, Rinehart and Winston. . ISBN 9780030676451

The regular tetrahedron, also called a 3-simplex, is the simplest Platonic solid.

(1968). 9780030676451, Holt, Rinehart and Winston. . ISBN 9780030676451

It has four as faces that are themselves at dual positions with the vertices of another tetrahedron.

(1999). 9780821819982, American Mathematical Soc.. . ISBN 9780821819982

The smallest non-cyclic group has four elements; it is the Klein four-group.

Jeremy Horne (2017). 9781522524441, IGI Global. . ISBN 9781522524441

A alternating groups are not simple group for values

n

≤

4

There are four of :

$\begin{align}
S^0 & \hookrightarrow S^1 \to S^1, \\
S^1 & \hookrightarrow S^3 \to S^2, \\
S^3 & \hookrightarrow S^7 \to S^4, \\
S^7 & \hookrightarrow S^{15}\to S^8. \\
\end{align}$

They are defined as locally trivial that map $f : S^{2n-1} \rightarrow S^{n}$ for values of $n=2,4,8$ (aside from the trivial fibration mapping between two points and a circle).

A.V. Shokurov (2025). 9781402006098, European Mathematical Society. ISBN 9781402006098

In Knuth's up-arrow notation, $2+2=2\times2=2^{2}=2\uparrow\uparrow 2=2\uparrow\uparrow\uparrow2=\;...\; = 4$ , and so forth, for any number of up arrows.

Andrew Hodges (2008). 9780393068634, W. W. Norton & Company. . ISBN 9780393068634

There are four dimensions in the theory of Minkowski space, three of space and the one being time.

List of basic calculations

4 × x

4 ÷ x	4	2	1.	1	0.8	0.	0.	0.5	0.	0.4	0.	0.	0.	0.	0.2	0.25
x ÷ 4	0.25	0.5	0.75	1	1.25	1.5	1.75	2	2.25	2.5	2.75	3	3.25	3.5	3.75	4

4	4			256	1024	4096	16384	65536	262144	1048576	4194304	16777216	67108864	268435456	1073741824	4294967296
x	1		81	256	625	1296	2401	4096	6561	10000	14641	20736	28561	38416	50625	65536

In culture

Four is the sacred number of the Zia, an indigenous tribe located in the U.S. state of New Mexico.
tetraphobia is most common in nations, where it is a homonym for "death" in their languages.
Nathaniel Lachenmeyer (2025). 9780452284968, Penguin Group (USA) Incorporated. . ISBN 9780452284968

In logic and philosophy

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",Chevalier, Jean and Gheerbrant, Alain (1994), The Dictionary of Symbols. The quote beginning "Almost from prehistoric times..." is on p. 402. 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").

Religion

Judaism

Four represents the four matriarchs (Sarah, Rebecca, Rachel, and Leah); the four sides of the world, the four extremes.

Christianity

Four represents the 3+1 of the Trinity engendered as the one God and has a particular significance in Christian Theology because of that. In Augustinian numerology, four represents the earth and earthly affairs.

In technology

In internet slang, "4" can replace the word "for" (as "four" and "for" are pronounced similarly). For example, typing "4u" instead of "for you".
In , "4" may be used to replace the letter "A".

Other groups of four

Approximately four weeks (4 times 7 days) to a lunar month (synodic month = 29.54 days). Thus the number four is universally an integral part of primitive sacred calendars.
Four seasons in a year: spring, summer, autumn and winter.