English eight, from Old English eahta, æhta,
Proto-Germanic*ahto is a direct continuation of
Proto-Indo-European*oḱtṓ(w)-, and as such cognate with Greek ὀκτώ and Latin octo-, both of which stems are reflected by the English prefix
oct(o)-, as in the ordinal adjective octaval or octavary, the distributive adjective is octonary.
The adjective octuple (Latin octu-plus) may also be used as a noun, meaning "a set of eight items"; the diminutive octuplet is mostly used to refer to eight siblings delivered in one birth.
It has been argued that, as the
cardinal number7 is the highest number of items that can universally be
cognitively processed as a single set, the etymology of the numeral eight might be the first to be considered composite, either as "twice four" or as "two short of ten", or similar.
The
Turkic words for "eight" are from a
Proto-Turkic stem *sekiz, which has been suggested as originating as a negation of eki "two", as in "without two fingers" (i.e., "two short of ten; two fingers are not being held up");[1]
this same principle is found in
Finnic*kakte-ksa, which conveys a meaning of "two before (ten)". The Proto-Indo-European reconstruction *oḱtṓ(w)- itself has been argued as representing an old dual, which would correspond to an original meaning of "twice four".
Proponents of this "quaternary hypothesis" adduce the numeral 9, which might be built on the stem new-, meaning "new" (indicating the beginning of a "new set of numerals" after having counted to eight).[2]
Evolution of the Arabic digit
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
infinity symbol ∞, described as a "sideways figure eight", is unrelated to the digit 8 in origin; it is first used (in the mathematical meaning "infinity") in the 17th century, and it may be derived from the
Roman numeral for "one thousand" CIƆ, or alternatively from the final Greek letter,
ω.
Mathematics
Eight is the third
composite number, lying between the fourth prime number (
7) and the fourth composite number (
9). 8 is the first non-unitary cube
prime of the form p3. With
proper divisors1,
2, and
4, it is the third
power of two (23). 8 is the first number which is neither
prime nor
semiprime and the only nonzero
perfect power that is one less than another perfect power, by
Mihăilescu's Theorem.
8 is the first proper
Leyland number of the form xy + yx, 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
Fibonacci number and the first even, non-prime Fibonacci number. It is also the only positive Fibonacci number aside from
1 that is a
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
semiprime10 =
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]
A
tesseract or 8-cell is the
four-dimensional analogue of the
cube. It is one of six
regular polychora, with a total of eight cubical
cells, hence its name. Its dual figure is the analogue of the
octahedron, with twice the amount of cells and simply termed the
16-cell, that is the
orthonormal basis of vectors in four dimensions. Whereas a
tesseractic honeycomb is self-dual, a
16-cell honeycomb is dual to a
24-cell honeycomb that is made of
24-cells. The 24-cell is also regular, and made purely of octahedra whose vertex arrangement represents the
ring of
Hurwitz integral quaternions. Both the tesseract and the 16-cell can fit inside a 24-cell, and in a 24-cell honeycomb, eight 24-cells meet at a vertex. Also, the
Petrie polygon of the tesseract and the 16-cell is a regular octagon.
The number 8 is involved with a number of interesting mathematical phenomena related to the notion of
Bott periodicity. If is the direct limit of the inclusions of real orthogonal groups , the following holds:
The latticeΓ8 is the smallest positive even
unimodular lattice. As a lattice, it holds the optimal structure for the densest packing of 240spheres in eight dimensions, whose lattice points also represent the
root system of
Lie groupE8. 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 lattice.[24][25] The order of the smallest non-abelian group all of whose subgroups are normal is 8.
Vertex-transitivesemiregular polytopes whose
facets are finite exist up through the 8th dimension. In the
third dimension, they include the
Archimedean solids and the infinite family of uniform
prisms and
antiprisms, while in the
fourth dimension, only the
rectified 5-cell, the
rectified 600-cell, and the
snub 24-cell are semiregular polytopes. For dimensions
five through eight, the
demipenteract and the
k21 polytopes221,
321, and
421 are the only semiregular (
Gosset) polytopes. Collectively, the k21 family of polytopes contains eight figures that are rooted in the
triangular prism, which is the simplest semiregular polytope that is made of three cubes and two equilateral triangles. It also includes one of only three semiregular
Euclidean honeycombs: the
affine521 honeycomb that represents the arrangement of vertices of the eight-dimensional
lattice, and made of 421facets. The culminating figure is the ninth-dimensional
621 honeycomb, which is the only affine semiregular
paracompacthyperbolic honeycomb with infinite facets and
vertex figures in the k21 family. There are no other finite semiregular polytopes or honeycombs in dimensions n > 8.
Sporadic groups
In the classification of sporadic groups, the
third generation consists of eight groups, four of which are
centralizers of (itself the largest group of this generation), with another three
transpositions of
Fischer group.[26]8 is the
difference between
53 and
61, which are the two smallest prime numbers that do not divide the order of any
sporadic group. The largest
supersingular prime that divides the
order of is
71, which is the eighth self-convolution of Fibonacci numbers (where
744, which is essential to
Moonshine theory, is the twelfth).[27][28] While only two sporadic groups have eight prime factors in their order (
Lyons group and Fischer group ),
Mathieu group holds a semi-presentation whose
order is equal to .[29]
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.
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.
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.
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]
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.
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).
As sourced from the Mahabharata, there are 8 vasus who are given elemental names:[57]
Anala or Agni (fire)
Dhara or Prithvi (earth)
Anila or Vayudeva (wind)
Apa (water)
Prabhasa or Dyauh (sky)
Pratyusha
Soma
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.
In
Mahayana Buddhism, the branches of the Eightfold Path are embodied by the Eight Great Bodhisattvas: (
Manjusri,
Vajrapani,
Avalokiteśvara,
Maitreya,
Ksitigarbha, Nivaranavishkambhi,
Akasagarbha, and
Samantabhadra).[62] These are later (controversially) associated with the Eight Consciousnesses according to the
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.
Judaism
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 eight is considered to be a
lucky number in Chinese and other Asian cultures.[77] Eight (八;
accounting捌;
pinyinbā) is considered 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 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
octave, the interval between two
musical notes with the same letter name (where one has double the frequency of the other), is so called because there are eight notes between the two on a standard major or minor
diatonic scale, including the notes themselves and without chromatic deviation.[83] The ecclesiastical
modes are ascending diatonic musical scales of eight notes or tones comprising an octave.
Dream Theater's eighth album Octavarium contains many different references to the number 8, including the number of songs and various aspects of the music and cover artwork.
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]
Eight-ballpool 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.
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]
The drott-kvaett, an
Old Icelandic verse, consisted of a stanza of eight regular lines.[111]
In
Terry Pratchett's Discworld series, eight is a magical number[112] and is considered taboo. Eight is not safe to be said by wizards on the
Discworld and is the number of Bel-Shamharoth. Also, there are eight days in a Disc week and eight colours in a Disc spectrum, the eighth one being
octarine.
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
geometricshape, 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]
^Etymological Dictionary of Turkic Languages: Common Turkic and Interturkic stems starting with letters «L», «M», «N», «P», «S», Vostochnaja Literatura RAS, 2003, 241f. (
altaica.ruArchived 31 October 2007 at the
Wayback Machine)
^the hypothesis is discussed critically (and rejected as "without sufficient support") by
Werner Winter, 'Some thought about Indo-European numerals' in: Jadranka Gvozdanović (ed.),
Indo-European Numerals, Walter de Gruyter, 1992, 14f.
^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.
^Weisstein, Eric W.
"Sphenic Number". mathworld.wolfram.com. Retrieved 7 August 2020. ...then every sphenic number n=pqr has precisely eight positive divisors
^Weisstein, Eric W.
"Octagon". mathworld.wolfram.com. Retrieved 7 August 2020.
^Bicknell, Marjorie (1975). "A primer on the Pell sequence and related sequences". Fibonacci Quarterly. 13 (4): 345–349.
MR0387173.
^Weisstein, Eric W.
"Regular Octagon". mathworld.wolfram.com. Retrieved 25 June 2022.
^Katz, A (1995). "Matching rules and quasiperiodicity: the octagonal tilings". In Axel, F.; Gratias, D. (eds.). Beyond quasicrystals. Springer. pp. 141–189.
doi:
10.1007/978-3-662-03130-8_6.
ISBN978-3-540-59251-8.
^Lounesto, Pertti (3 May 2001).
Clifford Algebras and Spinors. Cambridge University Press. p. 216.
ISBN978-0-521-00551-7. ...Clifford algebras, contains or continues with two kinds of periodicities of 8...
^Thomas, Mary Ann (15 August 2004).
Oxygen. The Rosen Publishing Group, Inc. p. 12.
ISBN978-1-4042-0159-0. Knowing that oxygen has an atomic number of 8,
^Choppin, Gregory R.; Johnsen, Russell H. (1972).
Introductory chemistry. Addison-Wesley Pub. Co. p. 366.
ISBN978-0-201-01022-0. 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...
^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
^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,...
^Quain, Jones (1909).
Quain's Elements of Anatomy. Longmans, Green, & Company. p. 52. These eight pairs are usually reckoned as eight cervical nerves ...
^Fairhall, David; Peyton, Mike (17 May 2013).
Pass Your Yachtmaster. A&C Black.
ISBN978-1-4081-5627-8. Gale warnings will be given if mean wind speeds of force 8 (34–40 knots)
^Ramachandran, Nirmala (2000).
Hindu Heritage. Stamford Lake Publication. p. 72.
ISBN978-955-8733-09-7. The temple has eight monasteries, founded by Madhvacharya
^Hay, Jeff (6 March 2009).
World Religions. Greenhaven Publishing LLC. p. 61.
ISBN978-0-7377-4627-3. The focus of ordinary believers' religious life is on following a relevant version of the Eightfold Path ...
^Little, Stephen; Eichman, Shawn; Shipper, Kristofer; Ebrey, Patricia Buckley (1 January 2000).
Taoism and the Arts of China. University of California Press. p. 139.
ISBN978-0-520-22785-9. Evidence for the early use of the Eight Trigrams in a religious Taoist...
^"CT Housing Choice Voucher Program". www.cthcvp.org. Retrieved 11 August 2020. Welcome to the Housing Choice Voucher Program (also known as Section 8)
^Boys' Life. Boy Scouts of America, Inc. 1931. p. 20. lunge forward upon this skate in a left outside forward circle, in just the reverse of your right outside forward circle, until you complete a figure 8.
^Day, Cyrus Lawrence (1986).
The Art of Knotting & Splicing. Naval Institute Press. p. 231.
ISBN978-0-87021-062-4. To make a line temporarily fast by winding it, figure – eight fashion, round a cleat, a belaying pin, or a pair of bitts.