← 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 numeral
Greek prefixtetra-
Latin prefixquadri-/quadr-
Binary1002
Ternary113
Senary46
Octal48
Duodecimal412
Hexadecimal416
ArmenianԴ
Arabic, Kurdish٤
Persian, Sindhi۴
Shahmukhi, Urdu۴
Ge'ez
Bengali, Assamese
Chinese numeral四,亖,肆
Devanagari
Telugu
Malayalam
Tamil
Hebrewד
Khmer
Thai
Kannada
Burmese
Babylonian numeral𒐘
Egyptian hieroglyph, Chinese counting rod||||
Maya numerals••••
Morse code.... _

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.

Evolution of the Hindu-Arabic digit

This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources in this section. Unsourced material may be challenged and removed. (May 2024) (Learn how and when to remove this message)
Two modern handwritten fours
Sculpted date "1481" in the Convent church of Maria Steinach in Algund, South Tirol, Italy. The upward loop signifies the number 4.

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

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). Four is therefore also the smallest semiprime, where the fourth such distinct semiprime is the product between the smallest pair of twin primes (3, 5); meanwhile the fourth prime and composite are (7, 9), where twice four lies between these. Also,

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 .

Four is the smallest non-unitary tetrahedral number.[6]

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]

The unit (1) is the fourth distinct entry in the continued fraction for pi (), by order of appearances of entries.[20]

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

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

Buddhism

Biblical

Judaism

Hinduism

Islam

Taoism

Other

In politics

In computing

In science

In astronomy

In biology

In chemistry

In physics

In logic and philosophy

Four mugs

In technology

4 as a resin identification code, used in recycling

In transport

In sports

In other fields

See also: 4 (disambiguation)

International maritime signal flag for 4
Playing cards for 4

In music

In fiction

Other groups of four

See also

References

  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. ^ 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
  6. ^ 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.
  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. ^ Sloane, N. J. A. (ed.). "Sequence A154883 (Distinct entries in continued fraction for Pi in the order of their appearance.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 16 June 2024.
  21. ^ 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
  22. ^ 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
  23. ^ 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...
  24. ^ 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
  25. ^ 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...
  26. ^ 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
  27. ^ 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
  28. ^ Jayatilleke, K. N. (16 October 2013). Early Buddhist Theory of Knowledge. Routledge. ISBN 978-1-134-54294-9. ...the states of the four arupajhanas.
  29. ^ 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.
  30. ^ 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)
  31. ^ 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.
  32. ^ 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
  33. ^ 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.
  34. ^ 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
  35. ^ 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
  36. ^ 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
  37. ^ 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.
  38. ^ "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
  39. ^ 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.
  40. ^ Frawley, David (7 October 2014). Vedic Yoga: The Path of the Rishi. Lotus Press. ISBN 978-0-940676-25-1. There are four Vedas
  41. ^ 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
  42. ^ Maanas - Individual and Society. Rapid Publications. ISBN 978-1-937192-06-8. The Four Stages of Life
  43. ^ 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:...
  44. ^ Kulendiren, Pon (11 October 2012). Hinduism a Scientific Religion: & Some Temples in Sri Lanka. iUniverse. p. 32. ISBN 978-1-4759-3675-9.
  45. ^ 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,...
  46. ^ "Definition of yuga". Dictionary.com. Archived from the original on 28 July 2020. Retrieved 28 July 2020.
  47. ^ 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 ...
  48. ^ 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,...
  49. ^ 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. According to Islam, the Four Arch Angels are: Jibraeel (Gabriel), Mikaeel (Michael), Izraeel (Azrael), and Israfil (Raphael).
  50. ^ 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...
  51. ^ Shabazz, Hassan (6 January 2020). Al Islaam, and the Transformation of Society. Lulu.com. p. 15. ISBN 978-1-7948-3337-1. There are four books in Islam: Torah, Zaboor, Injeel and Holy Qur'an...
  52. ^ Bukhari, Muohammad Ben Ismail Al (1 January 2007). THE CORRECT TRADITIONS OF AL'BUKHARI 1-4 VOL 3: صحيح البخاري 1/4 [عربي/انكليزي] ج3. Dar Al Kotob Al Ilmiyah دار الكتب العلمية. p. 840. For those who take an oath for abstention from their wives, awaiting for four months is ordained;
  53. ^ Ahmad, Yusuf Al-Hajj. The Book Of Nikkah: Encyclopaedia of Islamic Law. Darussalam Publishers. ...for four months and ten days.
  54. ^ Mawdudi, Sayyid Abul A'la (15 December 2016). Towards Understanding the Qur'an: English Only Edition. Kube Publishing Ltd. p. 59. ISBN 978-0-86037-613-2. Then take four birds, ...
  55. ^ Maudoodi, Syed Abul ʻAla (2000). Sūrah al-Aʻarāf to Sūrah bani Isrāel. Islamic Publications. p. 177. The respite of four months...
  56. ^ Barazangi, Nimat Hafez (9 March 2016). Woman's Identity and Rethinking the Hadith. Routledge. p. 138. ISBN 978-1-134-77065-6. And those who launch a charge against chaste women and do not produce four witnesses...
  57. ^ SK, Lim. Origins of Chinese Auspicious Symbols. Asiapac Books Pte Ltd. p. 16. ISBN 978-981-317-026-1. Taoism later incorporated the four symbols into its immortality system...
  58. ^ Terry, Milton Spenser (1883). Biblical Hermeneutics: A Treatise on the Interpretation of the Old and New Testaments. Phillips & Hunt. p. 382. the four corners or extremities of the earth (Isa. xi, 12; Ezek. vii, 2.; Rev. vii, 1; xx, 8), corresponding, doubtless, with the four points of the compass
  59. ^ Bulletin - State Department of Education. Department of Education. 1955. p. 151. Four was a sacred number of Zia
  60. ^ Lachenmeyer, Nathaniel (2005). 13: The Story of the World's Most Notorious Superstition. Penguin Group (USA) Incorporated. p. 187. ISBN 978-0-452-28496-8. In Chinese, Japanese, and Korean, the word for four is, unfortunately, an exact homonym for death
  61. ^ Maberry, Jonathan; Kramer, David F. (2007). The Cryptopedia: A Dictionary of the Weird, Strange & Downright Bizarre. Citadel Press. p. 211. ISBN 978-0-8065-2819-9. Svetovid is portrayed as having four heads ...
  62. ^ "FDR, 'The Four Freedoms,' Speech Text". Voices of Democracy. Archived from the original on 1 August 2020. Retrieved 30 July 2020.
  63. ^ "Yao Wenyuan". The Economist. ISSN 0013-0613. Archived from the original on 1 May 2018. Retrieved 30 July 2020.
  64. ^ 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. [...]
  65. ^ Petsko, Gregory A.; Ringe, Dagmar (2004). Protein Structure and Function. New Science Press. p. 40. ISBN 978-0-87893-663-2. Oligomers containing two, three, four, five, six or even more subunits are known as dimers, trimers, tetramers, pentamers, hexamers, and so on.
  66. ^ Yaqoob, Tahir (2011). Exoplanets and Alien Solar Systems. New Earth Labs. p. 12. ISBN 978-0-9741689-2-0. The four inner planets (known as terrestrial, or rocky planets
  67. ^ 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. ISBN 978-3-540-00241-3. 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)
  68. ^ Pidwirny, Michael (7 May 2020). Chapter 3: Matter, Energy and the Universe: Single chapter from the eBook Understanding Physical Geography. Our Planet Earth Publishing. p. 10. including the four large Galilean moons that are easily visible from a hobby telescope
  69. ^ Pugh, Philip (2 November 2011). Observing the Messier Objects with a Small Telescope: In the Footsteps of a Great Observer. Springer Science & Business Media. p. 41. ISBN 978-0-387-85357-4. M4 is a globular star cluster near Antares in Scorpius.
  70. ^ Bok, Bart Jan; Bok, Priscilla Fairfield (1981). The Milky Way. Harvard University Press. p. 66. ISBN 978-0-674-57503-5. IV, subgiants
  71. ^ Encyclopedia of Cell Biology. Academic Press. 7 August 2015. p. 25. ISBN 978-0-12-394796-3.
  72. ^ Chien, Shu; Chen, Peter C. Y.; Fung, Yuan-cheng (2008). An Introductory Text to Bioengineering. World Scientific. p. 54. ISBN 978-981-270-793-2. The mammalian heart consists of four chambers,...
  73. ^ Creation Research Society Textbook Committee (1970). Biology: a search for order in complexity. Zondervan Pub. House. p. 209. ISBN 978-0-310-29490-0. Except for the flies, mosquitoes, and some others, insects with wings have four wings.
  74. ^ Pittenger, Dennis (15 December 2014). California Master Gardener Handbook, 2nd Edition. UCANR Publications. p. 180. ISBN 978-1-60107-857-5. metamorphosis is marked by four distinct stages
  75. ^ 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
  76. ^ Daniels, Patricia; Stein, Lisa (2009). Body: The Complete Human : how it Grows, how it Works, and how to Keep it Healthy and Strong. National Geographic Books. p. 94. ISBN 978-1-4262-0449-4. Four canines for tearing + Eight premolars for crushing +Twelve molars (including four wisdom teeth)
  77. ^ 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.
  78. ^ Lucas, Jerry (1993). Great unsolved mysteries of science. F & W Pubns Inc. p. 168. ISBN 978-1-55870-291-2. Of course, carbon is not the only chemical element with a valence of +4 or -4
  79. ^ Walsh, Kenneth A. (1 January 2009). Beryllium Chemistry and Processing. ASM International. p. 93. ISBN 978-0-87170-721-5. Beryllium has an atomic number of four
  80. ^ Ebeling, Werner; Fortov, Vladimir E.; Filinov, Vladimir (27 November 2017). Quantum Statistics of Dense Gases and Nonideal Plasmas. Springer. p. 39. ISBN 978-3-319-66637-2. Plasma is one of the four fundamental states of matter, the others being solid, liquid, and gas.
  81. ^ Petkov, Vesselin (23 June 2009). Relativity and the Nature of Spacetime. Springer Science & Business Media. p. 124. ISBN 978-3-642-01962-3. should be regarded as a four-dimensional world
  82. ^ Giordano, Nicholas (13 February 2009). College Physics: Reasoning and Relationships. Cengage Learning. p. 1073. ISBN 978-0-534-42471-8. We have referred to the four fundamental forces in nature,...
  83. ^ Alon, Noga; Spencer, Joel H. (20 September 2011). The Probabilistic Method. John Wiley & Sons. p. 6.1. ISBN 978-1-118-21044-4. The Four Functions Theorem of Ahlswede Daykin
  84. ^ Chevalier, Jean and Gheerbrant, Alain (1994), The Dictionary of Symbols. The quote beginning "Almost from prehistoric times..." is on p. 402.
  85. ^ Hennig, Boris (5 December 2018). Aristotle's Four Causes. Peter Lang. ISBN 978-1-4331-5929-9. This book examines Aristotle's four causes (material, formal, efficient, and final)
  86. ^ Wilkinson, Amy (17 February 2015). The Creator's Code: The Six Essential Skills of Extraordinary Entrepreneurs. Simon and Schuster. p. 79. ISBN 978-1-4516-6609-0. The OODA loop consists of four steps.
  87. ^ Howard, Brian Clark; Abdelrahman, Amina Lake; Good Housekeeping Institute (26 February 2020). "You Might Be Recycling Wrong — Here's Everything You Need to Know About Recycling Symbols". Good Housekeeping. Archived from the original on 13 March 2015. Retrieved 28 July 2020. Plastic Recycling Symbol #4: LDPE
  88. ^ Conover, Charles (8 November 2011). Designing for Print. John Wiley & Sons. p. 62. ISBN 978-1-118-13088-9. CMYK is the standard four-color model used for all full-color print jobs that will be output on an offset printing press
  89. ^ Vermaat, Misty E.; Sebok, Susan L.; Freund, Steven M.; Campbell, Jennifer T.; Frydenberg, Mark (1 January 2015). Discovering Computers, Essentials. Cengage Learning. p. 123. ISBN 978-1-305-53402-5. ...the 4 key (labeled with the letters g, h and i)...
  90. ^ Bunting, Steve; Wei, William (6 March 2006). EnCase Computer Forensics: The Official EnCE: EnCase?Certified Examiner Study Guide. John Wiley & Sons. p. 246. ISBN 978-0-7821-4435-2. A byte also contains two 4-bit nibbles...
  91. ^ Braden, R. (1989). Braden, R (ed.). "Requirements for Internet Hosts - Communication Layers". tools.ietf.org: 9–10. doi:10.17487/RFC1122. Archived from the original on 28 July 2020. Retrieved 28 July 2020.
  92. ^ Assenza, Tony (June 1982). "Audi Quattro: Germany's 4x4 Cruise Missile". Popular Mechanics. Hearst Magazines.
  93. ^ Schaller, Bob; Harnish, Dave (18 September 2009). The Everything Kids' Basketball Book: The all-time greats, legendary teams, today's superstars - and tips on playing like a pro. Simon and Schuster. ISBN 978-1-4405-0177-7. Power forward Referred to as the number 4 spot
  94. ^ "Definition of FOUR-LETTER WORD". merriam-webster.com. Archived from the original on 22 August 2016. Retrieved 28 July 2020.
  95. ^ Wells, J. C. (25 September 2014). Sounds Interesting: Observations on English and General Phonetics. Cambridge University Press. p. 33. ISBN 978-1-316-12385-0. But one confused re-spelling is fower for 'four'.
  96. ^ Guttman, Ariel; Guttman, Gail; Johnson, Kenneth (1993). Mythic Astrology: Archetypal Powers in the Horoscope. Llewellyn Worldwide. p. 263. ISBN 978-0-87542-248-0. Sign: Cancer, the fourth Zodiacal Sign
  97. ^ Curtiss, Harriette A. (1996). The Key to the Universe. Health Research Books. p. 161. ISBN 978-0-7873-1233-6. The 4th Tarot Card is called "The Emperor."
  98. ^ Weller, David; Lobao, Alexandre Santos; Hatton, Ellen (20 September 2004). Beginning .NET Game Programming in VB .NET. Apress. p. 383. ISBN 978-1-4302-0724-5. ...tetraminos (the shapes used in Tetris) are all just a collection of four blocks
  99. ^ Bardes, Barbara; Shelley, Mack; Schmidt, Steffen (16 December 2008). American Government and Politics Today: The Essentials 2009 - 2010 Edition. Cengage Learning. p. 453. ISBN 978-0-495-57170-4. The court will not issue a writ unless at least four justices approve of it. This is called the rule of four.
  100. ^ "Movie Projector: 'I Am Number Four' to be No. 1 at holiday weekend box office [Updated]". LA Times Blogs - Company Town. 17 February 2011. Archived from the original on 20 August 2020. Retrieved 28 July 2020.
  101. ^ "fourth wall". dictionary.cambridge.org. Retrieved 29 November 2021.
  102. ^ Roberts, Gareth E. (15 February 2016). From Music to Mathematics: Exploring the Connections. JHU Press. p. 3. ISBN 978-1-4214-1918-3. ... called common time and denoted by C, which has four beats per measure
  103. ^ Bonds, Mark Evan (10 January 2009). Music as Thought: Listening to the Symphony in the Age of Beethoven. Princeton University Press. p. 1. ISBN 978-1-4008-2739-8. The number, character and sequence of movements in the symphony, moreover, did not stabilize until the 1770s when the familiar format of four movements...
  104. ^ Frisch, Walter (2003). Brahms: The Four Symphonies. Yale University Press. ISBN 978-0-300-09965-2.
  105. ^ Brech, Lewis (2010). Storybook Advent Carols Collection Songbook. Couples Company, Inc. p. 26. ISBN 978-1-4524-7763-3.
  106. ^ Baker, Felicity (2017). Houses of Hogwarts: Cinematic Guide. Scholastic Incorporated. ISBN 978-1-338-12861-1. ...the four houses of Hogwarts School of Witchcraft and Wizardry: Gryffindor, Ravenclaw, Hufflepuff, and Slytherin
  107. ^ Wright, Robert J.; Ellemor-Collins, David; Tabor, Pamela D. (4 November 2011). Developing Number Knowledge: Assessment, Teaching and Intervention with 7-11 year olds. SAGE. ISBN 978-1-4462-5368-7.
  108. ^ Macauley, David (29 September 2010). Elemental Philosophy: Earth, Air, Fire, and Water as Environmental Ideas. SUNY Press. ISBN 978-1-4384-3246-5.
  109. ^ Brooks, Edward (1876). Normal Higher Arithmetic Designed for Advanced Classes in Common Schools, Normal Schools, and High Schools, Academics, Etc. Sower. p. 227. Every year that is divisible by four, except the Centennial years, and every Centennial year divisible by 400, is a leap year...
  110. ^ Touche, Fred; Price, Anne (2005). Wilderness Navigation Handbook. Touche Publishing. p. 48. ISBN 978-0-9732527-0-5. Each of the familiar cardinal directions is equivalent to a particular true bearing: north (0°), east (90°), south (180°), and west (270°)
  111. ^ Roeckelein, J. E. (19 January 2006). Elsevier's Dictionary of Psychological Theories. Elsevier. p. 235. ISBN 978-0-08-046064-2. ...four substances or humors: blood, yellow bile, black bile and phlegm
  112. ^ Medley, H. Anthony (1997). Bridge. Penguin. p. 6. ISBN 978-0-02-861735-0. The four playing card suits, as you probably already know, are spades, hearts, diamonds, and clubs