4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures.

← 3 4 5 →
−1 0 1 2 3 4 5 6 7 8 9
Cardinalfour
Ordinal4th
(fourth)
Numeral systemquaternary
Factorization22
Divisors1, 2, 4
Greek numeralΔ´
Roman numeralIV, iv
Greek prefixtetra-
Latin prefixquadri-/quadr-
Binary1002
Ternary113
Senary46
Octal48
Duodecimal412
Hexadecimal416
Arabic, Kurdish٤
Persian, Sindhi۴
Shahmukhi, Urdu۴
Ge'ez
Bengali, Assamese
Chinese numeral四,亖,肆
Devanagari
Telugu
Malayalam
Tamil
Hebrewד
Khmer
Thai
Kannada
Burmese

Evolution of the Hindu-Arabic digit edit

 
 
Two modern handwritten fours

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  .

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:  .[2]

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".[3]

Mathematics edit

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.

Holistically, there are four elementary arithmetic operations in mathematics: addition (+), subtraction (), multiplication (×), and division (÷); and four basic number systems, the real numbers  , rational numbers  , integers  , and natural numbers  .

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.

Four is the highest degree general polynomial equation for which there is a solution in radicals.[10]

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]

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.[14][15] The regular tetrahedron, also called a 3-simplex, is the simplest Platonic solid.[16] It has four regular triangles as faces that are themselves at dual positions with the vertices of another tetrahedron.[17] Tetrahedra can be inscribed inside all other four Platonic solids, and tessellate space alongside the regular octahedron in the alternated cubic honeycomb.

The third dimension holds a total of four Coxeter groups that generate convex uniform polyhedra: the tetrahedral group, the octahedral group, the icosahedral group, and a dihedral group (of orders 24, 48, 120, and 4 , respectively). There are also four general Coxeter groups of generalized uniform prisms, where two are hosoderal and dihedral groups that form spherical tilings, with another two general prismatic and antiprismatic groups that represent truncated hosohedra (or simply, prisms) and snub antiprisms, respectively.

Four-dimensional space is the highest-dimensional space featuring more than three regular convex figures:

The fourth dimension is also the highest dimension where regular self-intersecting figures exist:

Altogether, sixteen (or 16 = 42) regular convex and star polychora are generated from symmetries of four (4) Coxeter Weyl groups and point groups in the fourth dimension: the   simplex,   hypercube,   icositetrachoric, and   hexacosichoric groups; with the   demihypercube group generating two alternative constructions. There are also sixty-four (or 64 = 43) four-dimensional Bravais lattices, alongside sixty-four uniform polychora in the fourth dimension based on the same  ,  ,   and   Coxeter groups, and extending to prismatic groups of uniform polyhedra, including one special non-Wythoffian form, the grand antiprism. Two infinite families of duoprisms and antiprismatic prisms exist in the fourth dimension.

There are only four polytopes with radial equilateral symmetry: the hexagon, the cuboctahedron, the tesseract, and the 24-cell.

Four-dimensional differential manifolds have some unique properties. There is only one differential structure on   except when   =  , in which case there are uncountably many.

The smallest non-cyclic group has four elements; it is the Klein four-group.[18] An alternating groups are not simple for values   .

There are four Hopf fibrations of hyperspheres:

 

They are defined as locally trivial fibrations that map   for values of   (aside from the trivial fibration mapping between two points and a circle).[19]

Further extensions of the real numbers under Hurwitz's theorem states that there are four normed division algebras: the real numbers  , the complex numbers  , the quaternions  , and the octonions  . Under Cayley–Dickson constructions, the sedenions   constitute a further fourth extension over  . The real numbers are ordered, commutative and associative algebras, as well as alternative algebras with power-associativity. The complex numbers   share all four multiplicative algebraic properties of the reals  , without being ordered. The quaternions loose a further commutative algebraic property, while holding associative, alternative, and power-associative properties. The octonions are alternative and power-associative, while the sedenions are only power-associative. The sedenions and all further extensions of these four normed division algebras are solely power-associative with non-trivial zero divisors, which makes them non-division algebras.   has a vector space of dimension 1, while  ,  ,   and   work in algebraic number fields of dimensions 2, 4, 8, and 16, respectively.

List of basic calculations edit

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
4 × x 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 200 400 4000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
4 ÷ x 4 2 1.3 1 0.8 0.6 0.571428 0.5 0.4 0.4 0.36 0.3 0.307692 0.285714 0.26 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
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
4x 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824 4294967296
x4 1 16 81 256 625 1296 2401 4096 6561 10000 14641 20736 28561 38416 50625 65536

In religion edit

Buddhism edit

Judeo-Christian symbolism edit

Hinduism edit

Islam edit

Taoism edit

Other edit

In politics edit

  • 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]

In computing edit

In science edit

In astronomy edit

In biology edit

In chemistry edit

  • 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 atomic number of beryllium[78]
  • There are four basic states of matter: solid, liquid, gas, and plasma.[79]

In physics edit

In logic and philosophy edit

 
Four mugs
  • 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).
  • Aristotle held that there are basically four causes in nature: the material, the formal, the efficient, and the final.[84]
  • 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.
  • Arthur Schopenhauer's doctoral thesis was On the Fourfold Root of the Principle of Sufficient Reason.
  • 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)
  • Four opposed camps of the morality and nature of evil: moral absolutism, amoralism, moral relativism, and moral universalism.

In technology edit

 
4 as a resin identification code, used in recycling

In transport edit

 

In sports edit

  • In the Australian Football League, the top level of Australian rules football, each team is allowed 4 "interchanges" (substitute players), who can be freely substituted at any time, subject to a limit on the total number of substitutions.
  • In baseball:
    • 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.
  • In rugby league:
    • A try is worth 4 points.
    • One of the two starting centres wears the jersey number 4. (An exception to this rule is the Super League, which uses static squad numbering.)
  • In rugby union:
    • 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.
  • In women’s artistic gymnastics, there are four events/apparatus uneven bars, balance beam, floor exercise, and vault.

In other fields edit

 
International maritime signal flag for 4
 
Playing cards for 4

In music edit

Groups of four edit

See also edit

References edit

  1. ^ 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
  2. ^ "Seven Segment Displays (7-Segment) | Pinout, Types and Applications". Electronics Hub. 22 April 2019. Archived from the original on 28 July 2020. Retrieved 28 July 2020.
  3. ^ "Battle of the MICR Fonts: Which Is Better, E13B or CMC7? - Digital Check". Digital Check. 2 February 2017. Archived from the original on 3 August 2020. Retrieved 28 July 2020.
  4. ^ Fiore, Gregory (1 August 1993). Basic mathematics for college students: concepts and applications. HarperCollins College. p. 162. ISBN 978-0-06-042046-8. The smallest composite number is 4.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers: a(n) is C(n+2,3) equal to n*(n+1)*(n+2)/6.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 February 2024.
  6. ^ Hodges, Andrew (17 May 2008). One to Nine: The Inner Life of Numbers. W. W. Norton & Company. p. 249. ISBN 978-0-393-06863-4. 2 ↑↑ ... ↑↑ 2 is always 4
  7. ^ Kaplan Test Prep (3 January 2017). SAT Subject Test Mathematics Level 1. Simon and Schuster. p. 289. ISBN 978-1-5062-0922-7. An integer is divisible by 4 if the last two digits form a multiple of 4.
  8. ^ 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, ISBN 978-1-4612-2418-1
  9. ^ Peterson, Ivars (2002). Mathematical Treks: From Surreal Numbers to Magic Circles. MAA. p. 95. ISBN 978-0-88385-537-9. 7 is an example of an integer that can't be written as the sum of three squares.
  10. ^ Bajnok, Béla (13 May 2013). An Invitation to Abstract Mathematics. Springer Science & Business Media. ISBN 978-1-4614-6636-9. There is no algebraic formula for the roots of the general polynomial of degrees 5 or higher.
  11. ^ Bunch, Bryan (2000). The Kingdom of Infinite Number. New York: W. H. Freeman & Company. p. 48.
  12. ^ Ben-Menahem, Ari (6 March 2009). Historical Encyclopedia of Natural and Mathematical Sciences. Springer Science & Business Media. p. 2147. ISBN 978-3-540-68831-0. (i.e. That there are maps for which three colors are not sufficient)
  13. ^ Molitierno, Jason J. (19 April 2016). Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs. CRC Press. p. 197. ISBN 978-1-4398-6339-8. ... The complete graph on the largest number of vertices that is planar is K4 and that a(K4) equals 4.
  14. ^ Weisstein, Eric W. "Tetrahedron". mathworld.wolfram.com. Archived from the original on 20 August 2020. Retrieved 28 July 2020.
  15. ^ Grossnickle, Foster Earl; Reckzeh, John (1968). Discovering Meanings in Elementary School Mathematics. Holt, Rinehart and Winston. p. 337. ISBN 9780030676451. ...the smallest possible number of faces that a polyhedron may have is four
  16. ^ Grossnickle, Foster Earl; Reckzeh, John (1968). Discovering Meanings in Elementary School Mathematics. Holt, Rinehart and Winston. p. 337. ISBN 9780030676451. ...face of the platonic solid. The simplest of these shapes is the tetrahedron...
  17. ^ Hilbert, David; Cohn-Vossen, Stephan (1999). Geometry and the Imagination. American Mathematical Soc. p. 143. ISBN 978-0-8218-1998-2. ...the tetrahedron plays an anomalous role in that it is self-dual, whereas the four remaining polyhedra are mutually dual in pairs...
  18. ^ Horne, Jeremy (19 May 2017). Philosophical Perceptions on Logic and Order. IGI Global. p. 299. ISBN 978-1-5225-2444-1. Archived from the original on 31 October 2022. Retrieved 31 October 2022. The Klein four-group is the smallest noncyclic group,...
  19. ^ Shokurov, A.V. (2002). "Hopf fibration". In Michiel Hazewinkel (ed.). Encyclopedia of Mathematics. Helsinki: European Mathematical Society. ISBN 1402006098. OCLC 1013220521. Archived from the original on 1 May 2023. Retrieved 30 April 2023.
  20. ^ a b c Chwalkowski, Farrin (14 December 2016). Symbols in Arts, Religion and Culture: The Soul of Nature. Cambridge Scholars Publishing. p. 22. ISBN 978-1-4438-5728-4. The four main pilgrimages sites are: Lumbini, Bodh Gaya, Sarnath and Kusinara....four Noble Truths of Buddhism
  21. ^ Van Voorst, Robert (1 January 2012). RELG: World. Cengage Learning. p. 108. ISBN 978-1-111-72620-1. He first observed the suffering of the world in the Four Passing Sites
  22. ^ Yun, Hsing; Xingyun (2010). The Great Realizations: A Commentary on the Eight Realizations of a Bodhisattva Sutra. Buddha's Light Publishing. p. 27. ISBN 978-1-932293-44-9. The four great elements, earth, water, fire and wind...
  23. ^ Chaudhuri, Saroj Kumar (2003). Hindu Gods and Goddesses in Japan. Vedams eBooks (P) Ltd. p. 20. ISBN 978-81-7936-009-5. The Buddhists adopted him as one of the four Devarajas or Heavenly Kings
  24. ^ Bronkhorst, Johannes (22 December 2009). Buddhist Teaching in India. Simon and Schuster. p. 66. ISBN 978-0-86171-566-4. The four right exertions are...
  25. ^ Mistry, Freny (2 May 2011). Nietzsche and Buddhism: Prolegomenon to a Comparative Study. Walter de Gruyter. p. 69. ISBN 978-3-11-083724-7. these four bases of psychic power
  26. ^ Arbel, Keren (16 March 2017). Early Buddhist Meditation: The Four Jhanas as the Actualization of Insight. Taylor & Francis. p. 1. ISBN 978-1-317-38399-4. This book is about the four jhanas
  27. ^ Jayatilleke, K. N. (16 October 2013). Early Buddhist Theory of Knowledge. Routledge. ISBN 978-1-134-54294-9. ...the states of the four arupajhanas.
  28. ^ van Gorkom, Nina. The Perfections Leading to Enlightenment. Рипол Классик. p. 171. ISBN 978-5-88139-786-9. There are four of them: loving-kindness, metta, compassion, karuna, sympathetic joy, mudita and equanimity, upekkha.
  29. ^ Rinpoche, Khenchen Konchog Gyaltshen; Milarepa; Sumgon, Jigten (8 October 2013). Opening the Treasure of the Profound: Teachings on the Songs of Jigten Sumgon and Milarepa. Shambhala Publications. ISBN 978-0-8348-2896-4. ...four types of shravaka (stream enterer, oncereturner, nonreturner, and arhat)
  30. ^ Fahlbusch, Erwin; Bromiley, Geoffrey William; Lochman, Jan Milic; Mbiti, John; Pelikan, Jaroslav (14 February 2008). The Encyclodedia of Christianity, Vol. 5. Wm. B. Eerdmans Publishing. p. 823. ISBN 978-0-8028-2417-2.
  31. ^ Stevenson, Kenneth; Glerup, Michael (19 March 2014). Ezekiel, Daniel. InterVarsity Press. pp. xlv. ISBN 978-0-8308-9738-4. We have already mentioned the four living creatures—the man, the lion, the ox and the eagle
  32. ^ Butnick, Stephanie; Leibovitz, Liel; Oppenheimer, Mark (1 October 2019). The Newish Jewish Encyclopedia: From Abraham to Zabar's and Everything in Between. Artisan Books. ISBN 978-1-57965-893-9. ...be like Sarah, Rachel, Rebecca, and Leah, the foremothers of Judaism
  33. ^ Kaplan, Aryeh (1990). Innerspace: Introduction to Kabbalah, Meditation and Prophecy. Moznaim. p. 109. ISBN 9780940118560. ...as well as to the palm ( lulav ), myrtle ( hadas ), willow ( aravah ) and citron ( etrog ), the four species of plants
  34. ^ a b c Dennis, Geoffrey W. (2007). The Encyclopedia of Jewish Myth, Magic and Mysticism. Llewellyn Worldwide. p. 188. ISBN 978-0-7387-0905-5. The Passover Seder is particularly structured around fours: the Four Questions, the Four Sons, and four cups of wine.
  35. ^ "Four Expressions of Redemption to be said on the Jewish holiday of Passover - Google Search". p. 46. Archived from the original on 25 October 2022. Retrieved 29 July 2020. There are four expressions of redemption in the Torah
  36. ^ Templeton, Charles (1973). Jesus: the four Gospels, Matthew, Mark, Luke, and John, combined in one narrative and rendered in modern English. Simon and Schuster. ISBN 9780671217150.
  37. ^ Wagner, Richard; Helyer, Larry R. (31 January 2011). The Book of Revelation For Dummies. John Wiley & Sons. p. 308. ISBN 978-1-118-05086-6. The four horsemen of the Apocalypse are one of the most familiar images of Revelation
  38. ^ Turfe, Tallal Alie (19 July 2013). Children of Abraham: United We Prevail, Divided We Fail. iUniverse. p. 91. ISBN 978-1-4759-9047-8. The four holy cities of Judaism are Jerusalem, Hebron, Safed, and Tiberius.
  39. ^ Frawley, David (7 October 2014). Vedic Yoga: The Path of the Rishi. Lotus Press. ISBN 978-0-940676-25-1. There are four Vedas
  40. ^ Fritz, Stephen Martin (14 May 2019). Our Human Herds: The Theory of Dual Morality (Second Edition, Unabridged). Dog Ear Publishing. p. 491. ISBN 978-1-4575-6755-1. that these four proper aims and objects
  41. ^ Maanas - Individual and Society. Rapid Publications. ISBN 978-1-937192-06-8. The Four Stages of Life
  42. ^ Chwalkowski, Farrin (14 December 2016). Symbols in Arts, Religion and Culture: The Soul of Nature. Cambridge Scholars Publishing. p. 23. ISBN 978-1-4438-5728-4. The four primary castes or strata of society:...
  43. ^ Kulendiren, Pon (11 October 2012). Hinduism a Scientific Religion: & Some Temples in Sri Lanka. iUniverse. p. 32. ISBN 978-1-4759-3675-9.
  44. ^ Jansen, Eva Rudy (1993). The Book of Hindu Imagery: Gods, Manifestations and Their Meaning. Binkey Kok Publications. p. 87. ISBN 978-90-74597-07-4. Brahma has four faces,...
  45. ^ "Definition of yuga". Dictionary.com. Archived from the original on 28 July 2020. Retrieved 28 July 2020.
  46. ^ Çakmak, Cenap (18 May 2017). Islam: A Worldwide Encyclopedia [4 volumes]. ABC-CLIO. p. 397. ISBN 978-1-61069-217-5. ...Eid al-Adha (Feast of Sacrifice) lasts four days ...
  47. ^ Leonard, Timothy; Willis, Peter (11 June 2008). Pedagogies of the Imagination: Mythopoetic Curriculum in Educational Practice. Springer Science & Business Media. p. 144. ISBN 978-1-4020-8350-1. ... four Rightly Guided Caliphs, Abu-Bakr, Umar ibn al-Khattab, Uthman ibn Affan and Ali ibn Abi Talib,...
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  49. ^ Busool, Assad Nimer (28 December 2010). The Wise Qur'an: These are the Verses of the Wise Book: These are the verses of the Wise Book. Xlibris Corporation. p. 50. ISBN 978-1-4535-2526-5. The sacred months are four, Rajab, Dhu al-Qi'dah, Dhu al-Hijjah, and al-Muharram. During those four sacred months there were no war...
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