7

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

As an early

In the

On the seven-segment displays of pocket calculators and digital watches, 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,^[2] Indonesia,^[3] and some in Britain, Ireland, and Canada, as well as Latin America, write 7 with a line in the middle ("7"), 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,^[4] France,^[5] Italy, Belgium, the Netherlands, Finland,^[6] Romania, Germany, Greece,^[7] and Hungary.^{[citation needed]}

Mathematics

Seven, the fourth

• Seven is the lowest natural number that cannot be represented as the sum of the squares of three integers. (See Lagrange's four-square theorem#Historical development.)

• Seven is the
  8
  and is the base of the 7-aliquot tree.

• 7 is the only number D for which the equation 2ⁿ − D = x² has more than two solutions for n and x natural. In particular, the equation 2ⁿ − 7 = x² is known as the Ramanujan–Nagell equation.

• There are 7
  isomorphic to the group of integers.^[15] These are related to the 17 wallpaper groups whose transformations and isometries repeat two-dimensional patterns in the plane.^[16][17] The seventh indexed prime number is seventeen.^[18]

• A seven-sided shape is a
  compass and straightedge alone, which makes the heptagon the first regular polygon that cannot be directly constructed with these simple tools.^[20] Figurate numbers representing heptagons are called heptagonal numbers.^[21] 7 is also a centered hexagonal number.^[22]

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).^[23][24] This is also one of twenty-one such configurations from seventeen combinations of polygons, that features the largest and smallest polygons possible.^[25][26]

• In Wythoff's kaleidoscopic constructions, seven distinct generator points that lie on mirror edges of a three-sided Schwarz triangle are used to create most uniform tilings and polyhedra; an eighth point lying on all three mirrors is technically degenerate, reserved to represent snub forms only.^[27]

Seven of eight semiregular tilings are Wythoffian, the only exception is the elongated triangular tiling.^[28] 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).^[29]

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.^[30][31]

• The
  group order 168 = 2³·3·7, this plane holds 35 total triples of points where 7 are collinear and another 28 are non-collinear, whose incidence graph is the 3-regular bipartate Heawood graph with 14 vertices and 21 edges.^[33] This graph embeds in three dimensions as the Szilassi polyhedron, the simplest toroidal polyhedron alongside its dual with 7 vertices, the Császár polyhedron.^[34][35]

• In three-dimensional space there are seven
  crystal systems and fourteen Bravais lattices which classify under seven lattice systems, six of which are shared with the seven crystal systems.^[36][37][38] There are also collectively seventy-seven Wythoff symbols that represent all uniform figures in three dimensions.^[39]

• The seventh dimension is the only dimension aside from the familiar three where a vector cross product can be defined.^[40] This is related to the octonions over the imaginary subspace Im(O) in 7-space whose commutator between two octonions defines this vector product, wherein the Fano plane describes the multiplicative algebraic structure of the unit octonions {e₀, e₁, e₂, ..., e₇}, with e₀ an identity element.^[41]

Also, the lowest known dimension for an

four-dimensional sphere.^[42][43]

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.^[44] On the other hand, such figures with rank n + 3 mirrors exist in dimensions 4, 5, 6 and 8; not in 7.^[45] Hypercompact polytopes with lowest possible rank of n + 2 mirrors exist up through the 17th dimension, where there is a single solution as well.^[46]

• There are seven fundamental types of catastrophes.^[47]

• 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.^[48] The opposite sides of a standard six-sided dice always add to 7.

• The
  unsolved.^[50]

• Seven colors in a rainbow: ROYGBIV
• Seven Continents
• Seven Seas
• Seven climes
• The neutral
  pH balance
• Number of music notes in a scale
• Number of spots most commonly found on
  ladybugs
• Atomic number for nitrogen

In psychology

• Seven, plus or minus two as a model of working memory.
• Seven
  Alice A. Bailey
• In Western culture, Seven is consistently listed as people's favorite number.^[52][53]
• When guessing numbers 1–10, the number 7 is most likely to be picked.^[54]
• Seven-year itch: happiness in marriage said to decline after 7 years

Classical antiquity

The

"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.

• Seven
  Seven Heavens
• Seven Wonders of the Ancient World
• Seven metals of antiquity
• Seven days in the week
• Seven Seas
• Seven Sages
• Seven champions that fought Thebes
• Seven Kings of Rome
• Seven Sisters, the daughters of Atlas also known as the Pleiades

Religion and mythology

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Judaism

The number seven forms a widespread

• 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
  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 Jewish men (over the age of 13) called to read aliyahs in Shabbat morning services
• 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

• Seven loaves multiplied into seven basketfuls of surplus (Matthew 15:32–37)
• Seven
  demons were driven out of Mary Magdalene
  (Luke 8:2)
• Seven last sayings of Jesus on the cross
• Seven men of honest report, full of the Holy Ghost and wisdom (Acts 6:3)
• Seven Seals in the Book of Revelation

• Seven Gifts of the Holy Spirit
• Seven Spiritual Acts of Mercy
• Seven deadly sins: lust, gluttony, greed, sloth, wrath, envy, and pride, and seven terraces of Mount Purgatory
• Seven Virtues
  : chastity, temperance, charity, diligence, kindness, patience, and humility
• Seven Joys and Seven Sorrows of the Virgin Mary
• Seven Sleepers of Christian myth
• Seven
  Sacraments
  in the Catholic Church (though some traditions assign a different number)

Islam

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

• Seven
  Qur'an
• Seven
  circumambulations of Muslim pilgrims around the Kaaba in Mecca during the Hajj and the Umrah
• Seven walks between
  Al-Safa and Al-Marwah performed Muslim pilgrims during the Hajj and the Umrah
• Seven doors to hell (for heaven the number of doors is eight)
• Seven heavens
  (plural of sky) mentioned in Qur'an (S. 65:12)
• Night Journey to the Seventh Heaven, (reported ascension to heaven to meet God) Isra' and Mi'raj of the Qur'an and surah Al-Isra'.
• Seventh day naming ceremony held for babies
• Seven enunciators of divine revelation (nāṭiqs) according to the celebrated Fatimid Ismaili dignitary Nasir Khusraw^[56]
• Circle Seven Koran
  , the holy scripture of the Moorish Science Temple of America

Hinduism

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

• Seven worlds in the universe and seven seas in the world in Hindu cosmology
• Seven sages or
  Saptarishi and their seven wives or Sapta Matrka in Hindu mythology
• Seven
  Chakras
  in eastern philosophy
• Seven stars in a constellation called "Saptharishi Mandalam" in Indian astronomy
• Seven promises, or Saptapadi, and seven circumambulations around a fire at Hindu weddings
• Seven virgin goddesses or Saptha Kannimar worshipped in temples in Tamil Nadu, India^[57][58]
• Seven hills at Tirumala known as Yedu Kondalavadu in Telugu, or ezhu malaiyan in Tamil, meaning "Sevenhills God"
• Seven steps taken by the
  Buddha
  at birth
• Seven divine ancestresses of humankind in Khasi mythology
• Seven octets or
  Ragas
  compositions
• Seven Social Sins listed by Mahatma Gandhi

Eastern tradition

Other references to the number seven in Eastern traditions include:

• Seven Lucky Gods or gods of good fortune in Japanese mythology
• Seven-Branched Sword in Japanese mythology
• Seven Sages of the Bamboo Grove in China
• Seven minor symbols of
  yin-yang

Other references

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

• The number seven had mystical and religious significance in Mesopotamian culture by the 22nd century BCE at the latest. This was likely because in the Sumerian
  repeating fractions.^[59]
• Seven palms in an Egyptian Sacred Cubit
• Seven ranks in Mithraism
• Seven hills of Istanbul
• Seven islands of Atlantis
• Seven Cherokee clans
• Seven lives of cats in
  Romance language-speaking cultures^[60]
• Seven fingers on each hand, seven toes on each foot and seven pupils in each eye of the Irish epic hero
  Cúchulainn
• Seventh sons will be werewolves in Galician folklore, or the son of a woman and a werewolf in other European folklores
• Seventh sons of a seventh son will be magicians with special powers of healing and clairvoyance in some cultures, or vampires in others
• Seven prominent
  Guaraní mythology
• Seven gateways traversed by Inanna during her descent into the underworld
• Seven Wise Masters, a cycle of medieval stories
• Seven sister goddesses or fates in Baltic mythology called the Deivės Valdytojos.^[61]
• Seven legendary Cities of Gold, such as
  Cibola
  , that the Spanish thought existed in South America
• Seven years spent by Thomas the Rhymer in the faerie kingdom in the eponymous British folk tale
• Seven-year cycle in which the Queen of the Fairies pays a tithe to Hell (or possibly Hel) in the tale of Tam Lin
• Bahá'u'lláh
  in the Bahá'í faith
• Seven superuniverses in the cosmology of
  Urantia^[62]
• Seven
  Alice A. Bailey
• Seven, the sacred number of
  Yemaya^[63]
• Seven holes representing eyes (سبع عيون) in an Assyrian evil eye bead – though occasionally two, and sometimes nine [64]

In culture

This section appears to contain trivial, minor, or unrelated references to popular culture. Please reorganize this content to explain the subject's impact on popular culture, providing citations to reliable, secondary sources, rather than simply listing appearances. Unsourced material may be challenged and removed. (April 2023)

In literature

• Seven Dwarfs
• The Seven Brothers, an 1870 novel by Aleksis Kivi
• Seven features prominently in A Song of Ice and Fire by George R. R. Martin, namely, the Seven Kingdoms and the Faith of the Seven

In visual art

• The Group of Seven Canadian landscape painters

In sports

• Sports with seven players per side
  • Kabaddi
  • Rugby sevens
  • Water Polo
  • Netball
  • Handball
  • Flag Football
  • Ultimate Frisbee
• Seven is the least number of players a soccer team must have on the field in order for a match to start and continue.
• A touchdown plus an extra point is worth seven points.

See also

Wikimedia Commons has media related to 7 (number).

Look up seven in Wiktionary, the free dictionary.

• Diatonic scale (7 notes)
• Seven colors in the rainbow
• Seven continents
• Seven liberal arts
• Seven Wonders of the Ancient World
• Seven days of the Week
• Septenary (numeral system)
• Year Seven (School)
• Se7en (disambiguation)
• Sevens (disambiguation)
• One-seventh area triangle
• Z with stroke (Ƶ)
• List of highways numbered 7

Notes

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): 395, Fig. 24.67
2. ^ 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.
3. ^ "Mengapa orang Indonesia menambahkan garis kecil pada penulisan angka tujuh (7)?" (in Indonesian). Quora. Retrieved June 12, 2023.
4. ^ "Education writing numerals in grade 1." Archived 2008-10-02 at the Wayback Machine(Russian)
5. ^ "Example of teaching materials for pre-schoolers"(French)
6. ^ Elli Harju (August 6, 2015). ""Nenosen seiska" teki paluun: Tiesitkö, mistä poikkiviiva on peräisin?". Iltalehti (in Finnish).
7. ^ "Μαθηματικά Α' Δημοτικού" [Mathematics for the First Grade] (PDF) (in Greek). Ministry of Education, Research, and Religions. p. 33. Retrieved May 7, 2018.
8. ^ Weisstein, Eric W. "Double Mersenne Number". mathworld.wolfram.com. Retrieved 2020-08-06.
9. ^ "Sloane's A088165 : NSW primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
10. ^ "Sloane's A050918 : Woodall primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
11. ^ "Sloane's A088054 : Factorial primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
12. ^ "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
13. ^ "Sloane's A035497 : Happy primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
14. ^ "Sloane's A003173 : Heegner numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
15. ISBN 978-3-540-47967-3
    . A frieze pattern can be classified into one of the 7 frieze groups...
16. S2CID 119730123
    .
17. ^ 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.
18. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-02-01.
19. ^ Weisstein, Eric W. "Heptagon". mathworld.wolfram.com. Retrieved 2020-08-25.
20. ^ Weisstein, Eric W. "7". mathworld.wolfram.com. Retrieved 2020-08-07.
21. ^ 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.
22. ^ Sloane, N. J. A. (ed.). "Sequence A003215". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
23. Zbl 0385.51006
    .
24. ^ 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.
25. Zbl 0385.51006
    .
26. ^ 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.
27. Zbl 0941.51001
    .
28. S2CID 119730123
    .
29. S2CID 119730123
    .
30. ^ 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.
31. Zbl 0385.51006
    .
32. Zbl 1277.05001
    .
33. Zbl 1277.05001
    .
34. Zbl 0605.52002
    .
35. ^ Császár, Ákos (1949). "A polyhedron without diagonals" (PDF). Acta Scientiarum Mathematicarum (Szeged). 13: 140–142. Archived from the original (PDF) on 2017-09-18.
36. ^ 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.
37. S2CID 124399480
    .
38. ^ 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.
39. Zbl 1003.52006
    .
40. Zbl 0532.55011. Archived from the original
    (PDF) on 2021-02-26. Retrieved 2023-02-23.
41. S2CID 586512
    .
42. Zbl 1460.55017
    .
43. ^ Sloane, N. J. A. (ed.). "Sequence A001676 (Number of h-cobordism classes of smooth homotopy n-spheres.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-02-23.
44. Zbl 1208.52012
    .
45. Zbl 1168.51311
    .
46. Zbl 1062.52012
    .
47. ISBN 978-3-642-46890-2
    . ...every catastrophe can be composed from the set of so called elementary catastrophes, which are of seven fundamental types.
48. ^ Weisstein, Eric W. "Dice". mathworld.wolfram.com. Retrieved 2020-08-25.
49. ^ "Millennium Problems | Clay Mathematics Institute". www.claymath.org. Retrieved 2020-08-25.
50. ^ "Poincaré Conjecture | Clay Mathematics Institute". 2013-12-15. Archived from the original on 2013-12-15. Retrieved 2020-08-25.
51. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 82
52. ^ Gonzalez, Robbie (4 December 2014). "Why Do People Love The Number Seven?". Gizmodo. Retrieved 20 February 2022.
53. ^ Bellos, Alex. "The World's Most Popular Numbers [Excerpt]". Scientific American. Retrieved 20 February 2022.
54. doi:10.1037/0096-1523.2.2.291
    . Retrieved 20 February 2022.
55. ^ "Number symbolism - 7".
56. ISBN 978-1-84511-542-5
    , retrieved 2020-11-17
57. S2CID 226326183
    .
58. S2CID 226373749
    .
59. ^ The Origin of the Mystical Number Seven in Mesopotamian Culture: Division by Seven in the Sexagesimal Number System
60. ^ "Encyclopædia Britannica "Number Symbolism"". Britannica.com. Retrieved 2012-09-07.
61. ISSN 0235-716X
    .
62. ^ "Chapter I. The Creative Thesis of Perfection by William S. Sadler, Jr. - Urantia Book - Urantia Foundation". urantia.org. 17 August 2011.
63. ^ Yemaya. Santeria Church of the Orishas. Retrieved 25 November 2022
64. ^ Ergil, Leyla Yvonne (2021-06-10). "Turkey's talisman superstitions: Evil eyes, pomegranates and more". Daily Sabah. Retrieved 2023-04-05.

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group (1987): 70–71