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'''7''' ('''seven''') is the [[natural number]] following [[6]] and preceding [[8]]. It is the only [[prime number]] preceding a [[cube (algebra)|cube]].
'''7''' ('''EIGHT''') is the [[natural number]] following [[6]] and preceding [[8]]. It is the only [[prime number]] preceding a [[cube (algebra)|cube]].


As an early [[prime number]] in the series of [[positive integers]], the number seven has greatly symbolic associations in [[religion]], [[mythology]], [[superstition]] and [[philosophy]]. The seven [[Classical planet]]s resulted in seven being the number of days in a week.<ref>[[Carl Benjamin Boyer|Carl B. Boyer]], ''A History of Mathematics'' (1968) p.52, 2nd edn.</ref> 7 is often considered [[luck]]y in [[Western culture]] and is often seen as [[Symbolism of the Number 7|highly symbolic]]. Unlike [[Western culture]], in [[Vietnamese culture]], the number seven is sometimes considered unlucky.{{citation needed|date=September 2021}}
As an early [[prime number]] in the series of [[positive integers]], the number seven has greatly symbolic associations in [[religion]], [[mythology]], [[superstition]] and [[philosophy]]. The seven [[Classical planet]]s resulted in seven being the number of days in a week.<ref>[[Carl Benjamin Boyer|Carl B. Boyer]], ''A History of Mathematics'' (1968) p.52, 2nd edn.</ref> 7 is often considered [[luck]]y in [[Western culture]] and is often seen as [[Symbolism of the Number 7|highly symbolic]]. Unlike [[Western culture]], in [[Vietnamese culture]], the number seven is sometimes considered unlucky.{{citation needed|date=September 2021}}

Revision as of 21:24, 4 March 2024

This article is about the number. For the years, see 7 BC and AD 7. For other uses, see 7 (disambiguation) and No. 7 (disambiguation).
← 6 7 8 →
−1 0 1 2 3 4 5 6 7 8 9 →
Cardinalseven
Ordinal7th
(seventh)
Numeral systemseptenary
Factorizationprime
Prime4th
Divisors1, 7
Greek numeralΖ´
Roman numeralVII, vii
Greek prefixhepta-/hept-
Latin prefixseptua-
Binary1112
Ternary213
Senary116
Octal78
Duodecimal712
Hexadecimal716
Greek numeralZ, ζ
Amharic፯
Arabic, Kurdish, Persian٧
Sindhi, Urdu۷
Bengali৭
Chinese numeral七, 柒
Devanāgarī७
Telugu౭
Tamil௭
Hebrewז
Khmer៧
Thai๗
Kannada೭
Malayalam൭

7 (EIGHT) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube.

As an early prime number in the series of positive integers, the number seven has greatly symbolic associations in religion, mythology, superstition and philosophy. The seven Classical planets resulted in seven being the number of days in a week.[1] 7 is often considered lucky in Western culture and is often seen as highly symbolic. Unlike Western culture, in Vietnamese culture, the number seven is sometimes considered unlucky.[citation needed]

Evolution of the Arabic digit

In the beginning, Indians wrote 7 more or less in one stroke as a curve that looks like an uppercase ⟨J⟩ vertically inverted (ᒉ). The western Ghubar Arabs' main contribution was to make the longer line diagonal rather than straight, though they showed some tendencies to making the digit more rectilinear. The eastern Arabs developed the digit from a form that looked something like 6 to one that looked like an uppercase V. Both modern Arab forms influenced the European form, a two-stroke form consisting of a horizontal upper stroke joined at its right to a stroke going down to the bottom left corner, a line that is slightly curved in some font variants. As is the case with the European digit, the Cham and Khmer digit for 7 also evolved to look like their digit 1, though in a different way, so they were also concerned with making their 7 more different. For the Khmer this often involved adding a horizontal line to the top of the digit.[2] This is analogous to the horizontal stroke through the middle that is sometimes used in handwriting in the Western world but which is almost never used in computer fonts. This horizontal stroke is, however, important to distinguish the glyph for seven from the glyph for one in writing that uses a long upstroke in the glyph for 1. In some Greek dialects of the early 12th century the longer line diagonal was drawn in a rather semicircular transverse line.

On seven-segment displays, 7 is the digit with the most common graphic variation (1, 6 and 9 also have variant glyphs). Most calculators use three line segments, but on Sharp, Casio, and a few other brands of calculators, 7 is written with four line segments because in Japan, Korea and Taiwan 7 is written with a "hook" on the left, as ① in the following illustration.

While the shape of the character for the digit 7 has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender (⁊), as, for example, in .

Most people in Continental Europe,[3] Indonesia,[4] and some in Britain, Ireland, and Canada, as well as Latin America, write 7 with a line in the middle ("7̵"), sometimes with the top line crooked. The line through the middle is useful to clearly differentiate the digit from the digit one, as the two can appear similar when written in certain styles of handwriting. This form is used in official handwriting rules for primary school in Russia, Ukraine, Bulgaria, Poland, other Slavic countries,[5] France,[6] Italy, Belgium, the Netherlands, Finland,[7] Romania, Germany, Greece,[8] and Hungary.[citation needed]

Mathematics

Seven, the fourth prime number, is not only a Mersenne prime (since 23 − 1 = 7) but also a double Mersenne prime since the exponent, 3, is itself a Mersenne prime.[9] It is also a Newman–Shanks–Williams prime,[10] a Woodall prime,[11] a factorial prime,[12] a Harshad number, a lucky prime,[13] a happy number (happy prime),[14] a safe prime (the only Mersenne safe prime), a Leyland prime of the second kind and the fourth Heegner number.[15]

A heptagon in Euclidean space is unable to generate uniform tilings alongside other polygons, like the regular pentagon. However, it is one of fourteen polygons that can fill a plane-vertex tiling, in its case only alongside a regular triangle and a 42-sided polygon (3.7.42).[24][25] This is also one of twenty-one such configurations from seventeen combinations of polygons, that features the largest and smallest polygons possible.[26][27]
Otherwise, for any regular n-sided polygon, the maximum number of intersecting diagonals (other than through its center) is at most 7.[28]
Seven of eight semiregular tilings are Wythoffian, the only exception is the elongated triangular tiling.[30] Seven of nine uniform colorings of the square tiling are also Wythoffian, and between the triangular tiling and square tiling, there are seven non-Wythoffian uniform colorings of a total twenty-one that belong to regular tilings (all hexagonal tiling uniform colorings are Wythoffian).[31]
In two dimensions, there are precisely seven 7-uniform Krotenheerdt tilings, with no other such k-uniform tilings for k > 7, and it is also the only k for which the count of Krotenheerdt tilings agrees with k.[32][33]
Graph of the probability distribution of the sum of two six-sided dice
Also, the lowest known dimension for an exotic sphere is the seventh dimension, with a total of 28 differentiable structures; there may exist exotic smooth structures on the four-dimensional sphere.[44][45]
In hyperbolic space, 7 is the highest dimension for non-simplex hypercompact Vinberg polytopes of rank n + 4 mirrors, where there is one unique figure with eleven facets.[46] On the other hand, such figures with rank n + 3 mirrors exist in dimensions 4, 5, 6 and 8; not in 7.[47] Hypercompact polytopes with lowest possible rank of n + 2 mirrors exist up through the 17th dimension, where there is a single solution as well.[48]
  • There are seven fundamental types of catastrophes.[49]
  • The positive definite quadratic integer matrix representative of all odd numbers contains the set of seven integers: {1, 3, 5, 7, 11, 15, 33} where seven is the middle indexed member.[50][51]
  • When rolling two standard six-sided dice, seven has a 6 in 62 (or ⁠1/6⁠) probability of being rolled (1–6, 6–1, 2–5, 5–2, 3–4, or 4–3), the greatest of any number.[52] The opposite sides of a standard six-sided dice always add to 7.
  • The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.[53] Currently, six of the problems remain unsolved.[54]

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
7 × x 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 350 700 7000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
7 ÷ x 7 3.5 2.3 1.75 1.4 1.16 1 0.875 0.7 0.7 0.63 0.583 0.538461 0.5 0.46
x ÷ 7 0.142857 0.285714 0.428571 0.571428 0.714285 0.857142 1.142857 1.285714 1.428571 1.571428 1.714285 1.857142 2 2.142857
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
7x 7 49 343 2401 16807 117649 823543 5764801 40353607 282475249 1977326743 13841287201 96889010407
x7 1 128 2187 16384 78125 279936 823543 2097152 4782969 10000000 19487171 35831808 62748517
Radix 1 5 10 15 20 25 50 75 100 125 150 200 250 500 1000 10000 100000 1000000
x7 1 5 137 217 267 347 1017 1357 2027 2367 3037 4047 5057 13137 26267 411047 5643557 113333117

In decimal

999,999 divided by 7 is exactly 142,857. Therefore, when a vulgar fraction with 7 in the denominator is converted to a decimal expansion, the result has the same six-digit repeating sequence after the decimal point, but the sequence can start with any of those six digits.[55] For example, 1/7 = 0.142857 142857... and 2/7 = 0.285714 285714....

In fact, if one sorts the digits in the number 142,857 in ascending order, 124578, it is possible to know from which of the digits the decimal part of the number is going to begin with. The remainder of dividing any number by 7 will give the position in the sequence 124578 that the decimal part of the resulting number will start. For example, 628 ÷ 7 = ⁠89+5/7⁠; here 5 is the remainder, and would correspond to number 7 in the ranking of the ascending sequence. So in this case, 628 ÷ 7 = 89.714285. Another example, 5238 ÷ 7 = ⁠748+2/7⁠, hence the remainder is 2, and this corresponds to number 2 in the sequence. In this case, 5238 ÷ 7 = 748.285714.

In science

In psychology

Classical antiquity

The Pythagoreans invested particular numbers with unique spiritual properties. The number seven was considered to be particularly interesting because it consisted of the union of the physical (number 4) with the spiritual (number 3).[59] In Pythagorean numerology the number 7 means spirituality.

References from classical antiquity to the number seven include:

"Number Seven"
by William Sidney Gibson
Read by Ruth Golding for LibriVox
Audio 00:15:59 (full text)
Problems playing this file? See media help.

Religion and mythology

Judaism

Main article: Significance of numbers in Judaism

The number seven forms a widespread typological pattern within Hebrew scripture, including:

  • Seven days (more precisely yom) of Creation, leading to the seventh day or Sabbath (Genesis 1)
  • Seven-fold vengeance visited on upon Cain for the killing of Abel (Genesis 4:15)
  • Seven pairs of every clean animal loaded onto the ark by Noah (Genesis 7:2)
  • Seven years of plenty and seven years of famine in Pharaoh's dream (Genesis 41)
  • Seventh son of Jacob, Gad, whose name means good luck (Genesis 46:16)
  • Seven times bullock's blood is sprinkled before God (Leviticus 4:6)
  • Seven nations God told the Israelites they would displace when they entered the land of Israel (Deuteronomy 7:1)
  • Seven days (de jure, but de facto eight days) of the Passover feast (Exodus 13:3–10)
  • Seven-branched candelabrum or Menorah (Exodus 25)
  • Seven trumpets played by seven priests for seven days to bring down the walls of Jericho (Joshua 6:8)
  • Seven things that are detestable to God (Proverbs 6:16–19)
  • Seven Pillars of the House of Wisdom (Proverbs 9:1)
  • Seven archangels in the deuterocanonical Book of Tobit (12:15)

References to the number seven in Jewish knowledge and practice include:

  • Seven divisions of the weekly readings or aliyah of the Torah
  • Seven aliyot on Shabbat
  • Seven blessings recited under the chuppah during a Jewish wedding ceremony
  • Seven days of festive meals for a Jewish bride and groom after their wedding, known as Sheva Berachot or Seven Blessings
  • Seven Ushpizzin prayers to the Jewish patriarchs during the holiday of Sukkot

Christianity

Following the tradition of the Hebrew Bible, the New Testament likewise uses the number seven as part of a typological pattern:

Seven lampstands in The Vision of John on Patmos by Julius Schnorr von Carolsfeld, 1860

References to the number seven in Christian knowledge and practice include:

Islam

References to the number seven in Islamic knowledge and practice include:

Hinduism

References to the number seven in Hindu knowledge and practice include:

Eastern tradition

Other references to the number seven in Eastern traditions include:

The Seven Lucky Gods in Japanese mythology

Other references

Other references to the number seven in traditions from around the world include:

See also

Wikiquote has quotations related to 7 (number).
Wikimedia Commons has media related to 7 (number).
Look up seven in Wiktionary, the free dictionary.

Notes

  1. ^ Carl B. Boyer, A History of Mathematics (1968) p.52, 2nd edn.
  2. ^ 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): 395, Fig. 24.67
  3. ^ Eeva Törmänen (September 8, 2011). "Aamulehti: Opetushallitus harkitsee numero 7 viivan palauttamista". Tekniikka & Talous (in Finnish). Archived from the original on September 17, 2011. Retrieved September 9, 2011.
  4. ^ "Mengapa orang Indonesia menambahkan garis kecil pada penulisan angka tujuh (7)?" (in Indonesian). Quora. Retrieved June 12, 2023.
  5. ^ "Education writing numerals in grade 1." Archived 2008-10-02 at the Wayback Machine(Russian)
  6. ^ "Example of teaching materials for pre-schoolers"(French)
  7. ^ Elli Harju (August 6, 2015). ""Nenosen seiska" teki paluun: Tiesitkö, mistä poikkiviiva on peräisin?". Iltalehti (in Finnish).
  8. ^ "Μαθηματικά Α' Δημοτικού" [Mathematics for the First Grade] (PDF) (in Greek). Ministry of Education, Research, and Religions. p. 33. Retrieved May 7, 2018.
  9. ^ Weisstein, Eric W. "Double Mersenne Number". mathworld.wolfram.com. Retrieved 2020-08-06.
  10. ^ "Sloane's A088165 : NSW primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  11. ^ "Sloane's A050918 : Woodall primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  12. ^ "Sloane's A088054 : Factorial primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  13. ^ "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  14. ^ "Sloane's A035497 : Happy primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  15. ^ "Sloane's A003173 : Heegner numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  16. ^ Heyden, Anders; Sparr, Gunnar; Nielsen, Mads; Johansen, Peter (2003-08-02). Computer Vision – ECCV 2002: 7th European Conference on Computer Vision, Copenhagen, Denmark, May 28–31, 2002. Proceedings. Part II. Springer. p. 661. ISBN 978-3-540-47967-3. A frieze pattern can be classified into one of the 7 frieze groups...
  17. ^ Grünbaum, Branko; Shephard, G. C. (1987). "Section 1.4 Symmetry Groups of Tilings". Tilings and Patterns. New York: W. H. Freeman and Company. pp. 40–45. doi:10.2307/2323457. ISBN 0-7167-1193-1. JSTOR 2323457. OCLC 13092426. S2CID 119730123.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A004029 (Number of n-dimensional space groups.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-30.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-02-01.
  20. ^ Weisstein, Eric W. "Heptagon". mathworld.wolfram.com. Retrieved 2020-08-25.
  21. ^ Weisstein, Eric W. "7". mathworld.wolfram.com. Retrieved 2020-08-07.
  22. ^ Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers (or 7-gonal numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-09.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A003215". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  24. ^ Grünbaum, Branko; Shepard, Geoffrey (November 1977). "Tilings by Regular Polygons" (PDF). Mathematics Magazine. 50 (5). Taylor & Francis, Ltd.: 231. doi:10.2307/2689529. JSTOR 2689529. S2CID 123776612. Zbl 0385.51006.
  25. ^ Jardine, Kevin. "Shield - a 3.7.42 tiling". Imperfect Congruence. Retrieved 2023-01-09. 3.7.42 as a unit facet in an irregular tiling.
  26. ^ Grünbaum, Branko; Shepard, Geoffrey (November 1977). "Tilings by Regular Polygons" (PDF). Mathematics Magazine. 50 (5). Taylor & Francis, Ltd.: 229–230. doi:10.2307/2689529. JSTOR 2689529. S2CID 123776612. Zbl 0385.51006.
  27. ^ Dallas, Elmslie William (1855). "Part II. (VII): Of the Circle, with its Inscribed and Circumscribed Figures − Equal Division and the Construction of Polygons". The Elements of Plane Practical Geometry. London: John W. Parker & Son, West Strand. p. 134.
    "...It will thus be found that, including the employment of the same figures, there are seventeen different combinations of regular polygons by which this may be effected; namely, —
    When three polygons are employed, there are ten ways; viz., 6,6,6 – 3.7.42 — 3,8,24 – 3,9,18 — 3,10,15 — 3,12,12 — 4,5,20 — 4,6,12 — 4,8,8 — 5,5,10.
    With four polygons there are four ways, viz., 4,4,4,4 — 3,3,4,12 — 3,3,6,6 — 3,4,4,6.
    With five polygons there are two ways, viz., 3,3,3,4,4 — 3,3,3,3,6.
    With six polygons one way — all equilateral triangles [ 3.3.3.3.3.3 ]."
    Note: the only four other configurations from the same combinations of polygons are: 3.4.3.12, (3.6)2, 3.4.6.4, and 3.3.4.3.4.
  28. ^ Poonen, Bjorn; Rubinstein, Michael (1998). "The Number of Intersection Points Made by the Diagonals of a Regular Polygon" (PDF). SIAM Journal on Discrete Mathematics. 11 (1). Philadelphia: Society for Industrial and Applied Mathematics: 135–156. arXiv:math/9508209. doi:10.1137/S0895480195281246. MR 1612877. S2CID 8673508. Zbl 0913.51005.
  29. ^ Coxeter, H. S. M. (1999). "Chapter 3: Wythoff's Construction for Uniform Polytopes". The Beauty of Geometry: Twelve Essays. Mineola, NY: Dover Publications. pp. 326–339. ISBN 9780486409191. OCLC 41565220. S2CID 227201939. Zbl 0941.51001.
  30. ^ Grünbaum, Branko; Shephard, G. C. (1987). "Section 2.1: Regular and uniform tilings". Tilings and Patterns. New York: W. H. Freeman and Company. pp. 62–64. doi:10.2307/2323457. ISBN 0-7167-1193-1. JSTOR 2323457. OCLC 13092426. S2CID 119730123.
  31. ^ Grünbaum, Branko; Shephard, G. C. (1987). "Section 2.9 Archimedean and uniform colorings". Tilings and Patterns. New York: W. H. Freeman and Company. pp. 102–107. doi:10.2307/2323457. ISBN 0-7167-1193-1. JSTOR 2323457. OCLC 13092426. S2CID 119730123.
  32. ^ Sloane, N. J. A. (ed.). "Sequence A068600 (Number of n-uniform tilings having n different arrangements of polygons about their vertices.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-09.
  33. ^ Grünbaum, Branko; Shepard, Geoffrey (November 1977). "Tilings by Regular Polygons" (PDF). Mathematics Magazine. 50 (5). Taylor & Francis, Ltd.: 236. doi:10.2307/2689529. JSTOR 2689529. S2CID 123776612. Zbl 0385.51006.
  34. ^ Pisanski, Tomaž; Servatius, Brigitte (2013). "Section 1.1: Hexagrammum Mysticum". Configurations from a Graphical Viewpoint. Birkhäuser Advanced Texts (1 ed.). Boston, MA: Birkhäuser. pp. 5–6. doi:10.1007/978-0-8176-8364-1. ISBN 978-0-8176-8363-4. OCLC 811773514. Zbl 1277.05001.
  35. ^ Pisanski, Tomaž; Servatius, Brigitte (2013). "Chapter 5.3: Classical Configurations". Configurations from a Graphical Viewpoint. Birkhäuser Advanced Texts (1 ed.). Boston, MA: Birkhäuser. pp. 170–173. doi:10.1007/978-0-8176-8364-1. ISBN 978-0-8176-8363-4. OCLC 811773514. Zbl 1277.05001.
  36. ^ Szilassi, Lajos (1986). "Regular toroids" (PDF). Structural Topology. 13: 74. Zbl 0605.52002.
  37. ^ Császár, Ákos (1949). "A polyhedron without diagonals" (PDF). Acta Scientiarum Mathematicarum (Szeged). 13: 140–142. Archived from the original (PDF) on 2017-09-18.
  38. ^ Sloane, N. J. A. (ed.). "Sequence A004031 (Number of n-dimensional crystal systems.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-30.
  39. ^ Wang, Gwo-Ching; Lu, Toh-Ming (2014). "Crystal Lattices and Reciprocal Lattices". RHEED Transmission Mode and Pole Figures (1 ed.). New York: Springer Publishing. pp. 8–9. doi:10.1007/978-1-4614-9287-0_2. ISBN 978-1-4614-9286-3. S2CID 124399480.
  40. ^ Sloane, N. J. A. (ed.). "Sequence A256413 (Number of n-dimensional Bravais lattices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-30.
  41. ^ Messer, Peter W. (2002). "Closed-Form Expressions for Uniform Polyhedra and Their Duals" (PDF). Discrete & Computational Geometry. 27 (3). Springer: 353–355, 372–373. doi:10.1007/s00454-001-0078-2. MR 1921559. S2CID 206996937. Zbl 1003.52006.
  42. ^ Massey, William S. (December 1983). "Cross products of vectors in higher dimensional Euclidean spaces" (PDF). The American Mathematical Monthly. 90 (10). Taylor & Francis, Ltd: 697–701. doi:10.2307/2323537. JSTOR 2323537. S2CID 43318100. Zbl 0532.55011. Archived from the original (PDF) on 2021-02-26. Retrieved 2023-02-23.
  43. ^ Baez, John C. (2002). "The Octonions". Bulletin of the American Mathematical Society. 39 (2). American Mathematical Society: 152–153. doi:10.1090/S0273-0979-01-00934-X. MR 1886087. S2CID 586512.
  44. ^ Behrens, M.; Hill, M.; Hopkins, M. J.; Mahowald, M. (2020). "Detecting exotic spheres in low dimensions using coker J". Journal of the London Mathematical Society. 101 (3). London Mathematical Society: 1173. arXiv:1708.06854. doi:10.1112/jlms.12301. MR 4111938. S2CID 119170255. Zbl 1460.55017.
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References

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