8

8 (eight) is the natural number following 7 and preceding 9.

Etymology

English eight, from Old English eahta, æhta,

The modern digit 8, like all modern Arabic numerals other than zero, originates with the Brahmi numerals. The Brahmi digit for eight by the 1st century was written in one stroke as a curve └┐ looking like an uppercase H with the bottom half of the left line and the upper half of the right line removed. However, the digit for eight used in India in the early centuries of the Common Era developed considerable graphic variation, and in some cases took the shape of a single wedge, which was adopted into the Perso-Arabic tradition as ٨ (and also gave rise to the later Devanagari form ८); the alternative curved glyph also existed as a variant in Perso-Arabic tradition, where it came to look similar to our digit 5.^{[year needed]}

The digits as used in Al-Andalus by the 10th century were a distinctive western variant of the glyphs used in the Arabic-speaking world, known as ghubār numerals (ghubār translating to "sand table"). In these digits, the line of the 5-like glyph used in Indian manuscripts for eight came to be formed in ghubār as a closed loop, which was the 8-shape that became adopted into European use in the 10th century.^[3]

Just as in most modern typefaces, in typefaces with text figures the character for the digit 8 usually has an ascender, as, for example, in .

The

Mathematics

Eight is the third

• 8 is the first proper Leyland number of the form x^y + y^x, where in its case x and y both equal 2.^[4]
• 8 is the sum between the first pair of twin-primes (3, 5), and the only twin-prime sum that is not a multiple of 3 or 12.
• 8 is the sixth
  perfect cube.^[5]
• 8 is the third refactorable number, as it has exactly four positive divisors, and 4 is one of them.
• 8 is the only composite number with a prime aliquot sum of 7 (1 + 2 + 4)^[6] that is part of the aliquot sequence (8, 7, 1, 0).
• 8 is the first number to be the aliquot sum of two numbers: the discrete semiprime 10 = 5 × 2, and squared prime 49 = 7².
• 8 is surrounded by (7, 9) which multiply to equal the forty-fourth composite number 63,^[7] where the eighth triangular number and twenty-fourth composite is 36.^[8]
• 8 is the number of known primary pseudoperfect numbers,^[9] the smallest four (2, 6, 42, 1806) are one less than the first four numbers in Sylvester's sequence.

Sphenic numbers always have exactly eight divisors.^[10]

Octagon

A

A cube is a regular polyhedron with eight vertices that also forms the cubic honeycomb, the only regular honeycomb in three-dimensional space.^[17] Through various truncation operations, the cubic honeycomb generates eight other convex uniform honeycombs under the cubic group ${\displaystyle {\tilde {C}}_{3}}$.

The truncated tetrahedron is the simplest Archimedean solid, made of four triangles and four hexagons, the hexagonal prism, which classifies as an irregular octahedron and parallelohedron, is able to tessellate space as a three-dimensional analogue of the hexagon, and the gyrobifastigium, with four square faces and four triangular faces, is the only Johnson solid that is able to tessellate space. The truncated octahedron, also a parallelohedron, is the permutohedron of order four, with eight hexagonal faces alongside six squares is likewise the only Archimedean solid that can generate a honeycomb on its own.

Polychora

A

The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. If ${\displaystyle O(\infty )}$ is the direct limit of the inclusions of real orthogonal groups ${\displaystyle O(1)\hookrightarrow O(2)\hookrightarrow \ldots \hookrightarrow O(k)\hookrightarrow \ldots }$, the following holds:

${\displaystyle \pi _{k+8}(O(\infty ))\cong \pi _{k}(O(\infty ))}$.

E₈

The ${\displaystyle \mathrm {E} _{8}}$ lattice Γ₈ is the smallest positive even unimodular lattice. As a lattice, it holds the optimal structure for the densest packing of 240 spheres in eight dimensions, whose lattice points also represent the root system of Lie group E₈. This honeycomb arrangement is shared by a unique complex tessellation of Witting polytopes, also with 240 vertices. Each complex Witting polytope is made of Hessian polyhedral cells that have Möbius–Kantor polygons as faces, each with eight vertices and eight complex equilateral triangles as edges, whose Petrie polygons form regular octagons. In general, positive even unimodular lattices only exist in dimensions proportional to eight. In the 16th dimension, there are two such lattices : Γ₈ ⊕ Γ₈ and Γ₁₆, while in the 24th dimension there are precisely twenty-four such lattices that are called the Niemeier lattices, the most important being the Leech lattice, which can be constructed using the octonions as well as with three copies of the ring of icosians that are isomorphic to the ${\displaystyle \mathrm {E} _{8}}$ lattice.^[24][25] The order of the smallest non-abelian group all of whose subgroups are normal is 8.

${\displaystyle \mathrm {E} _{8}}$ lattice

In the classification of sporadic groups, the third generation consists of eight groups, four of which are centralizers of ${\displaystyle \mathrm {F_{1}} }$ (itself the largest group of this generation), with another three transpositions of Fischer group ${\displaystyle \mathrm {F_{3+}} }$.

of ${\displaystyle \mathrm {F_{1}} }$ is

${\displaystyle \mathrm {Ly} }$ and Fischer group ${\displaystyle \mathrm {Fi_{23}} }$),

${\displaystyle \mathrm {M_{23}} }$

${\displaystyle o{\bigl (}(ab)^{2}(abab^{2})^{2}ab^{2}{\bigr )}=8}$

List of basic calculations

In other bases

A number is divisible by 8 if its last three digits, when written in decimal, are also divisible by 8, or its last three digits are 0 when written in binary.

8 is the base of the octal number system, which is mostly used with computers.^[30] In octal, one digit represents three bits. In modern computers, a byte is a grouping of eight bits, also called an octet.

In science

Physics

• In nuclear physics, the second magic number.^[31]
• In
  eightfold way is used to classify sub-atomic particles.^[32]
• In statistical mechanics, the eight-vertex model has 8 possible configurations of arrows at each vertex.^[33]

Astronomy

• Messier object M8, a magnitude 5.0 nebula in the constellation of Sagittarius.^[34]
• The New General Catalogue object NGC 8, a double star in the constellation Pegasus.
• Since the demotion of Pluto to a dwarf planet on 24 August 2006, in our Solar System, eight of the bodies orbiting the Sun are considered to be planets.

Chemistry

• The atomic number of oxygen.^[35]
• The most stable allotrope of a sulfur molecule is made of eight sulfur atoms arranged in a rhombic form.^[36]
• The maximum number of electrons that can occupy a valence shell (except for transitional elements), see the octet rule.
• The red pigment lycopene consists of eight isoprene units.^[37]

Geology

• A disphenoid crystal is bounded by eight scalene triangles arranged in pairs. A ditetragonal prism in the tetragonal crystal system has eight similar faces whose alternate interfacial angles only are equal.

Biology

• All spiders, and more generally all arachnids, have eight legs.^[38] Orb-weaver spiders of the cosmopolitan family Areneidae have eight similar eyes.^[39]
• The octopus and its cephalopod relatives in genus Argonauta have eight arms (tentacles).
• Compound coelenterates of the subclass or order Alcyonaria have polyps with eight-branched tentacles and eight septa.^[40]
• Sea anemones of genus Edwardsia have eight mesenteries.^[41]
• Animals of phylum Ctenophora swim by means of eight meridional bands of transverse ciliated plates, each plate representing a row of large modified cilia.^[42]
• The eight-spotted forester (genus Alypia, family Zygaenidae) is a diurnal moth having black wings with brilliant white spots.
• The ascus in fungi of the class Ascomycetes, following nuclear fusion, bears within it typically eight ascospores.^[43]
• Herbs of genus Coreopsis (tickseed) have showy flower heads with involucral bracts in two distinct series of eight each.
• In human
  adult dentition there are eight teeth in each quadrant.^[44] The eighth tooth is the so-called wisdom tooth
  .
• There are eight
  cervical nerves on each side in man and most mammals.^[45]

• There are eight
  MBTI models by John Beebe and Linda Berens.^[46]
• Timothy Leary identified a hierarchy of eight levels of consciousness.

In technology

• A byte is eight bits.^[47]
• Many (mostly historic) computer architectures are eight-bit, among them the Nintendo Entertainment System.
• film formats.^[48]
• Video8, Hi8 and Digital8 are related 8 mm video formats.^[49]
• On most phones, the 8 key is associated with the letters T, U, and V, but on the BlackBerry Pearl it is the key for B and N.
• An eight may refer to an eight-cylinder engine or automobile.^[50] A V8 engine is an internal combustion engine with eight cylinders configured in two banks (rows) of four forming a "V" when seen from the end.
• A figure-eight knot (so named for its configuration) is a kind of stopper knot.^[51]
• The number eight written in parentheses is the code for the musical note in
  Windows Live Messenger
  .
• In a seven-segment display, when an 8 is illuminated, all the display bulbs are on.

In measurement

• The
  SI prefix
  for 1000⁸ is yotta (Y), and for its reciprocal, yocto (y).
• In liquid measurement (
  gill.^[52]
• There are eight furlongs in a mile.^[53]
• The clove, an old English unit of weight, was equal to eight pounds when measuring cheese.^[54]
• An eight may be an article of clothing of the eighth size.
• Force eight is the first wind strength attributed to a gale on the Beaufort scale when announced on a Shipping Forecast.^[55]

In culture

Currency

• Sailors and civilians alike from the 1500s onward referred to evenly divided parts of the Spanish dollar as "pieces of eight", or "bits".

Architecture

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• Various types of buildings are usually eight-sided (octagonal), such as single-roomed gazebos^[56] and multi-roomed pagodas (descended from stupas; see religion section below).
• Eight
  volutes
  .

In religion, folk belief and divination

Hinduism

• As sourced from the Mahabharata, there are 8 vasus who are given elemental names:^[57]
  1. Anala or Agni (fire)
  2. Dhara or Prithvi (earth)
  3. Anila or Vayudeva (wind)
  4. Apa (water)
  5. Prabhasa or Dyauh (sky)
  6. Pratyusha
  7. Soma
  8. Dhruva
• The goddess of wealth and prosperity, Lakshmi, has eight forms known as Ashta Lakshmi and worshipped as:
  "Maha-lakshmi, Dhana-lakshmi, Dhanya-lakshmi, Gaja-lakshmi,
  Santana-lakshmi, Veera-lakshmi, Vijaya-lakshmi and Vidhya-lakshmi"^[58]
• There are eight nidhi, or seats of wealth, according to Hinduism.
• There are eight guardians of the directions known as Astha-dikpalas.^[59]
• There are eight
  Hindu monasteries established by the saint Madhvacharya in Udupi, India popularly known as the Ashta Mathas of Udupi.^[60]

• The
  Dharmacakra, a Buddhist symbol, has eight spokes.^[61] The Buddha's principal teaching—the Four Noble Truths—ramifies as the Noble Eightfold Path
  and the Buddha emphasizes the importance of the eight attainments or jhanas.
• In
  Yogacara school of thought: consciousness in the five senses, thought-consciousness, self-consciousness, and unconsciousness-"consciousness" or "store-house consciousness" (alaya-vijñana). The "irreversible" state of enlightenment, at which point a Bodhisattva goes on "autopilot", is the Eight Ground or bhūmi. In general, "eight" seems to be an auspicious number for Buddhists, e.g., the "eight auspicious symbols" (the jewel-encrusted parasol; the goldfish (always shown as a pair, e.g., the glyph of Pisces); the self-replenishing amphora; the white kamala lotus-flower; the white conch; the eternal (Celtic-style, infinitely looping) knot; the banner of imperial victory; the eight-spoked wheel that guides the ship of state, or that symbolizes the Buddha's teaching). Similarly, Buddha's birthday falls on the 8th day of the 4th month of the Chinese calendar
  .

• The religious rite of brit milah (commonly known as circumcision) is held on a baby boy's eighth day of life.^[63]
• Hanukkah is an eight-day Jewish holiday that starts on the 25th day of Kislev.^[64]
• Shemini Atzeret (Hebrew: "Eighth Day of Assembly") is a one-day Jewish holiday immediately following the seven-day holiday of Sukkot.^[65]

Christianity

• The spiritual
  Eighth Day
  , because the number 7 refers to the days of the week (which repeat themselves).
• The number of Beatitudes.^[66]
• 1 Peter 3:20 states that there were eight people on Noah's Ark.^[67]
• The Antichrist is the eighth king in the Book of Revelation.^[68]

Islam

• In Islam, eight is the number of angels carrying the throne of Allah in heaven.^[69]
• The number of gates of heaven.^[70]
• The octagram Rub el Hizb is often used in Islamic symbology.

Taoism

• Bagua^[71]
• Ba Xian^[72]
• Baduanjin

• In Wicca, there are eight Sabbats, festivals, seasons, or spokes in the Wheel of the Year.^[73]
• In
  Ancient Egyptian mythology, the Ogdoad represents the eight primordial deities of creation.^[74]
• In Scientology there are eight dynamics of existence.^[75]: 39
• There is also the Ogdoad in Gnosticism.^[76]

As a lucky number

• The number eight is considered to be a
  lucky number in Chinese culture because it sounds like the word meaning to generate wealth (發(T) 发(S); Pinyin: fā). Property with the number 8 may be valued greatly by Chinese. For example, a Hong Kong number plate with the number 8 was sold for $640,000.^[78] The opening ceremony of the Summer Olympics in Beijing started at 8 seconds and 8 minutes past 8 pm (local time) on 8 August 2008.^[79]
• In Pythagorean numerology the number 8 represents victory, prosperity and overcoming.
• Eight (八, hachi, ya) is also considered a lucky number in Japan, but the reason is different from that in Chinese culture.^[80] Eight gives an idea of growing prosperous, because the letter (八) broadens gradually.
• The Japanese thought of eight (や, ya) as a holy number in the ancient times. The reason is less well-understood, but it is thought that it is related to the fact they used eight to express large numbers vaguely such as manyfold (やえはたえ, Yae Hatae) (literally, eightfold and twentyfold), many clouds (やくも, Yakumo) (literally, eight clouds), millions and millions of Gods (やおよろずのかみ, Yaoyorozu no Kami) (literally, eight millions of Gods), etc. It is also guessed that the ancient Japanese gave importance to pairs, so some researchers guess twice as four (よ, yo), which is also guessed to be a holy number in those times because it indicates the world (north, south, east, and west) might be considered a very holy number.
• In numerology, 8 is the number of building, and in some theories, also the number of destruction.

In astrology

• In astrology, Scorpio is the 8th astrological sign of the Zodiac.^[81]
• In the Middle Ages, 8 was the number of "unmoving" stars in the sky, and symbolized the perfection of incoming planetary energy.

In music and dance

• A note played for one-eighth the duration of a whole note is called an eighth note, or quaver.^[82]
• An
  modes
  are ascending diatonic musical scales of eight notes or tones comprising an octave.
• There are eight notes in the octatonic scale.
• There are eight musicians in a double quartet or an octet.^[84] Both terms may also refer to a musical composition for eight voices or instruments.^[85]
• Caledonians is a square dance for eight, resembling the quadrille.
• Albums with the number eight in their title include 8 by the Swedish band Arvingarna, 8 by the American rock band Incubus,^[86] The Meaning of 8 by Minnesota indie rock band Cloud Cult and 8ight by Anglo-American singer-songwriter Beatie Wolfe.^[87]
• Octavarium
  contains many different references to the number 8, including the number of songs and various aspects of the music and cover artwork.
• "Eight maids a-milking" is the gift on the eighth day of Christmas in the carol "The Twelve Days of Christmas".^[88]
• The
  8-track cartridge
  is a musical recording format.
• "#8" is the stage name of Slipknot vocalist Corey Taylor.
• "Too Many Eights" is a song by Athens, Georgia's Supercluster.^[89]
• Eight Seconds, a Canadian musical group popular in the 1980s with their most notable song "Kiss You (When It's Dangerous)".^[90]
• "
  Eight Days a Week" is a #1 single for the music group the Beatles.^[91]
• Figure 8 is the fifth studio album by singer-songwriter Elliott Smith, released in the year 2000,^[92] an album released by Julia Darling in 1999,^[93] and an album released by Outasight in 2011.^[94]
• Ming Hao from the k-pop group Seventeen goes by the name "The8".^[95]
• "8 (circle)" is the eighth song on the album 22, A Million by the American band Bon Iver.^[96]
• "8" is the eighth song on the album When We All Fall Asleep, Where Do We Go? by Billie Eilish.^[97]

In film and television

• 8 Guys is a 2003 short film written and directed by Dane Cook.
• 8 Man (or Eightman): 1963 Japanese manga and anime superhero.
• 8 Mile is a 2002 film directed by Curtis Hanson.^[98]
• 8 mm is a 1999 film directed by Joel Schumacher.^[99]
• 8 Women (Original French title: 8 femmes) is a 2001 film directed by François Ozon.^[100]
• Frank Marshall.^[101]
• Eight Legged Freaks is a 2002 film directed by Ellory Elkayem.^[102]
• Eight Men Out is a 1988 film directed by John Sayles.^[103]
• Jennifer Eight, also known as Jennifer 8, is a 1992 film written and directed by Bruce Robinson.^[104]
• Eight Is Enough is an American television comedy-drama series.
• In Stargate SG-1 and Stargate Atlantis, dialing an 8-chevron address will open a wormhole to another galaxy.
• The Hateful Eight is a 2015 American western mystery film written and directed by Quentin Tarantino.^[105]
• Kate Plus 8 is an American reality television show.^[106]
• Ocean's 8 is an American heist comedy film directed by Gary Ross.^[107]

In sports and other games

• Eight-ball pool is played with a cue ball and 15 numbered balls, the black ball numbered 8 being the middle and most important one, as the winner is the player or side that legally pockets it after first pocketing its numerical group of 7 object balls (for other meanings see Eight ball (disambiguation)).
• In chess, each side has eight pawns and the board is made of 64 squares arranged in an eight by eight lattice. The eight queens puzzle is a challenge to arrange eight queens on the board so that none can capture any of the others.
• In the game of eights or Crazy Eights, each successive player must play a card either of the same suit or of the same rank as that played by the preceding player, or may play an eight and call for any suit. The object is to get rid of all one's cards first.
• In association football, the number 8 has historically been the number of the Central Midfielder.
• In Australian rules football, the top eight teams at the end of the Australian Football League regular season qualify for the finals series (i.e. playoffs).
• In baseball:
  • The center fielder is designated as number 8 for scorekeeping purposes.
  • The
    NCAA Division I tournament
    , features eight teams.
• In
  Number 8
  , a forward position.
• In rugby league:
  • Most competitions (though not the Super League, which uses static squad numbering) use a position-based player numbering system in which one of the two starting props wears the number 8.
  • The Australia-based National Rugby League has its own 8-team finals series, similar but not identical in structure to that of the Australian Football League.
• In rowing, an "eight" refers to a sweep-oar racing boat with a crew of eight rowers plus a coxswain.^[108]
• In the
  CST
  .
• In rock climbing, climbers frequently use the figure-eight knot to tie into their harnesses.
• The Women's College World Series, the final phase of the NCAA Division I softball tournament, like its men's counterpart in baseball, features eight teams.
• In curling an 8-point 'Eight Ender' is a perfect end. Each team delivers 8 Stones per end.

In foods

• Nestlé sells a brand of chocolates filled with peppermint-flavoured cream called After Eight, referring to the time 8 p.m.^[109]
• There are eight vegetables in
  V8 juice.^[110]

In literature

• Eights may refer to
  lines
  of verse.
• The drott-kvaett, an
  Old Icelandic verse, consisted of a stanza of eight regular lines.^[111]
• In
  octarine
  .
• Lewis Carroll's poem The Hunting of the Snark has 8 "fits" (cantos), which is noted in the full name "The Hunting of the Snark – An Agony, in Eight Fits".^[113]
• Eight apparitions appear to Macbeth in Act 4 scene 1 of Shakespeare's Macbeth as representations of the eight descendants of Banquo.

In slang

• An "eighth" is a common measurement of
  psilocybin mushrooms.^[114]
• Avril Lavigne's song "Sk8er Boi" uses this convention in the title.
• The Housing Choice Voucher Program, operated by the United States Department of Housing and Urban Development, is commonly referred to as the Section 8 program, as this was the original section of the Act which instituted the program.^[115]
• In Colombia and Venezuela, "volverse un ocho" (meaning to tie oneself in a figure 8) refers to getting in trouble or contradicting oneself.
• In China, "8" is used in chat speak as a term for parting. This is due to the closeness in pronunciation of "8" (bā) and the English word "bye".

Other uses

• A figure 8 is the common name of a geometric shape, often used in the context of sports, such as skating.^[116] Figure-eight turns of a rope or cable around a cleat, pin, or bitt are used to belay something.^[117]

See also

• The Magical Number Seven, Plus or Minus Two
• List of highways numbered 8

References

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3. ^ 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. 24.68.
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31. ^ Ilangovan, K. (10 June 2019). Nuclear Physics. MJP Publisher. p. 30.
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34. ^ "Messier Object 8". www.messier.seds.org. Retrieved 7 August 2020.
35. ISBN 978-1-4042-0159-0
    . Knowing that oxygen has an atomic number of 8,
36. ISBN 978-0-201-01022-0
    . under normal conditions the most stable allotropic form (Fig. 23-8a). Sulfur molecules within the crystal consist of puckered rings of eight sulfur atoms linked by single...
37. ISBN 978-0-203-48375-6
    . The chemical structure of lycopene consists of a long chain of eight isoprene units joined head to tail
38. ISBN 978-0-8225-6464-5
    . Arachnids have eight legs
39. ISBN 978-0-87719-264-0
    . Araneids have eight eyes
40. ^ Fisher, James; Huxley, Julian (1961). The Doubleday Pictorial Library of Nature: Earth, Plants, Animals. Doubleday. p. 311. Polyps with eight branched tentacles and eight septa
41. ^ Bourne, Gilbert Charles (1911). "Anthozoa" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 02 (11th ed.). Cambridge University Press. pp. 97–105, see page 100. Zoantharia.....It is not known whether all the eight mesenteries of Edwardsia are developed simultaneously or not, but in the youngest form which has been studied all the eight mesenteries were present
42. ^ The Century Dictionary and Cyclopedia: A work of Universal Reference in all Departments of Knowledge with a New Atlas of the World. 1906. p. 1384. ...are radially symmetrical, and swim by means of eight meridional ciliated bands, ...
43. ^ Parrish, Fred K. (1975). Keys to Water Quality Indicative Organisms of the Southeastern United States. Environmental Protection Agency, Office of Research and Development, Environmental Monitoring and Support Laboratory, Biological Methods Branch, Aquatics Biology Section. p. 11. ... the ascospores, are borne in sac like structures termed asci. The ascus usually contains eight as cospores,...
44. ISBN 978-0-8273-6685-5
    . ...In each quadrant of the permanent set of teeth (dentition), there are eight teeth
45. ^ Quain, Jones (1909). Quain's Elements of Anatomy. Longmans, Green, & Company. p. 52. These eight pairs are usually reckoned as eight cervical nerves ...
46. ISBN 978-1-317-41366-0
    . Linda Berens used the term 'cognitive processes' (1999) to refer to the eight types of consciousness that Jung discovered.
47. ^ "Definition of byte | Dictionary.com". www.dictionary.com. Retrieved 8 August 2020.
48. ISBN 978-1-136-05322-1
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117. ISBN 978-0-87021-062-4
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External links

• The Octonions, John C. Baez