| ||||
---|---|---|---|---|
Cardinal | eight | |||
Ordinal | 8th (eighth) | |||
Numeral system | octal | |||
Factorization | 23 | |||
Divisors | 1, 2, 4, 8 | |||
Greek numeral | Η´ | |||
Roman numeral | VIII, viii | |||
Greek prefix | octa-/oct- | |||
Latin prefix | octo-/oct- | |||
Binary | 10002 | |||
Ternary | 223 | |||
Senary | 126 | |||
Octal | 108 | |||
Duodecimal | 812 | |||
Hexadecimal | 816 | |||
Greek | η (or Η) | |||
Arabic, Kurdish, Persian, Sindhi, Urdu | ٨ | |||
Amharic | ፰ | |||
Bengali | ৮ | |||
Chinese numeral | 八,捌 | |||
Devanāgarī | ८ | |||
Kannada | ೮ | |||
Malayalam | ൮ | |||
Telugu | ౮ | |||
Tamil | ௮ | |||
Hebrew | ח | |||
Khmer | ៨ | |||
Thai | ๘ | |||
Armenian | Ը ը | |||
Babylonian numeral | 𒐜 | |||
Egyptian hieroglyph | 𓐁 | |||
Morse code | _ _ _.. |
8 (eight) is the natural number following 7 and preceding 9.
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.
The Semitic numeral is based on a root *θmn-, whence Akkadian smn-, Arabic ṯmn-, Hebrew šmn- etc. The Chinese numeral, written 八 (Mandarin: bā; Cantonese: baat), is from Old Chinese *priāt-, ultimately from Sino-Tibetan b-r-gyat or b-g-ryat which also yielded Tibetan brgyat .
It has been argued that, as the cardinal number 7 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]
This section needs additional citations for verification .(May 2024) |
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.
8 a composite composite number. 8 is the first number which is neither prime nor semiprime. By Mihăilescu's Theorem, it is the only nonzero perfect power that is one less than another perfect power. 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 a Fibonacci number and the only nontrivial Fibonacci number that is a perfect cube. [5] Sphenic numbers always have exactly eight divisors. [6] 8 is the base of the octal number system. [7]
A polygon with eight sides is an octagon. [8] A regular octagon can fill a plane-vertex with a regular triangle and a regular icositetragon, as well as tessellate two-dimensional space alongside squares in the truncated square tiling. This tiling is one of eight Archimedean tilings that are semi-regular, or made of more than one type of regular polygon, and the only tiling that can admit a regular octagon. [9] The Ammann–Beenker tiling is a nonperiodic tesselation of prototiles that feature prominent octagonal silver eightfold symmetry, that is the two-dimensional orthographic projection of the four-dimensional 8-8 duoprism. [10]
An octahedron is a regular polyhedron with eight equilateral triangles as faces. is the dual polyhedron to the cube and one of eight convex deltahedra. [11] [12] The stella octangula, or eight-pointed star, is the only stellation with octahedral symmetry. It has eight triangular faces alongside eight vertices that forms a cubic faceting, composed of two self-dual tetrahedra that makes it the simplest of five regular compounds. The cuboctahedron, on the other hand, is a rectified cube or rectified octahedron, and one of only two convex quasiregular polyhedra. It contains eight equilateral triangular faces, whose first stellation is the cube-octahedron compound. [13] [14]
The octonions are a hypercomplex normed division algebra that are an extension of the complex numbers. They are a double cover of special orthogonal group SO(8). The special unitary group SO(3) has an eight-dimensional adjoint representation whose colors are ascribed gauge symmetries that represent the vectors of the eight gluons in the Standard Model. Clifford algebras display a periodicity of 8. [15]
The latticeΓ8 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 lattice. [16] [17] The order of the smallest non-abelian group all of whose subgroups are normal is 8.
Multiplication | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8 × x | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 | 104 | 112 | 120 |
Division | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8 ÷ x | 8 | 4 | 2.6 | 2 | 1.6 | 1.3 | 1.142857 | 1 | 0.8 | 0.8 | 0.72 | 0.6 | 0.615384 | 0.571428 | 0.53 | |
x ÷ 8 | 0.125 | 0.25 | 0.375 | 0.5 | 0.625 | 0.75 | 0.875 | 1 | 1.125 | 1.25 | 1.375 | 1.5 | 1.625 | 1.75 | 1.875 |
Exponentiation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8x | 8 | 64 | 512 | 4096 | 32768 | 262144 | 2097152 | 16777216 | 134217728 | 1073741824 | 8589934592 | 68719476736 | 549755813888 | |
x8 | 1 | 256 | 6561 | 65536 | 390625 | 1679616 | 5764801 | 16777216 | 43046721 | 100000000 | 214358881 | 429981696 | 815730721 |
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0. Some define the natural numbers as the non-negative integers0, 1, 2, 3, ..., while others define them as the positive integers1, 2, 3, .... Some authors acknowledge both definitions whenever convenient. Some texts define the whole numbers as the natural numbers together with zero, excluding zero from the natural numbers, while in other writings, the whole numbers refer to all of the integers. The counting numbers refer to the natural numbers in common language, particularly in primary school education, and are similarly ambiguous although typically exclude zero.
The Noble Eightfold Path or Eight Right Paths is an early summary of the path of Buddhist practices leading to liberation from samsara, the painful cycle of rebirth, in the form of nirvana.
In geometry, rhombicuboctahedron is an Archimedean solid with 26 faces, consisting of 8 equilateral triangles and 18 squares. It is named by Johannes Kepler in his 1618 Harmonices Mundi, being short for truncated cuboctahedral rhombus, with cuboctahedral rhombus being his name for a rhombic dodecahedron.
0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division by zero has no meaning in arithmetic.
13 (thirteen) is the natural number following 12 and preceding 14.
Lakshmi, also known as Shri, is one of the principal goddesses in Hinduism. She is the goddess of wealth, fortune, prosperity, beauty, fertility, royal power and abundance. Lakshmi is the supreme goddess in Vaishnavism. She along with Parvati and Saraswati, forms the Tridevi.
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For example, −4, 0, and 82 are even numbers, while −3, 5, 7, and 21 are odd numbers.
In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate numbers.
A numerical digit or numeral is a single symbol used alone or in combinations, to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal digits.
In geometry, an octagon is an eight-sided polygon or 8-gon.
23 (twenty-three) is the natural number following 22 and preceding 24.
25 (twenty-five) is the natural number following 24 and preceding 26.
26 (twenty-six) is the natural number following 25 and preceding 27.
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The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold. However, quasicrystals can occur with other diffraction pattern symmetries, such as 5-fold; these were not discovered until 1982 by Dan Shechtman.
In geometry, an octagram is an eight-angled star polygon.
In geometry, an Ammann–Beenker tiling is a nonperiodic tiling which can be generated either by an aperiodic set of prototiles as done by Robert Ammann in the 1970s, or by the cut-and-project method as done independently by F. P. M. Beenker. They are one of the five sets of tilings discovered by Ammann and described in Tilings and patterns.
The vigilante film is a film genre in which the protagonist or protagonists engage in vigilante behavior, taking the law into their own hands. Vigilante films are usually revenge films in which the legal system fails protagonists, leading them to become vigilantes. The vigilante film has in recent years often crossed over with the superhero genre, due to character origin stories frequently involving an injustice having been committed against them.
...then every sphenic number n=pqr has precisely eight positive divisors
...Clifford algebras, contains or continues with two kinds of periodicities of 8...
Knowing that oxygen has an atomic number of 8,
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...
The chemical structure of lycopene consists of a long chain of eight isoprene units joined head to tail
Arachnids have eight legs
Araneids have eight eyes
Polyps with eight branched tentacles and eight septa
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
...are radially symmetrical, and swim by means of eight meridional ciliated bands, ...
... the ascospores, are borne in sac like structures termed asci. The ascus usually contains eight as cospores,...
...In each quadrant of the permanent set of teeth (dentition), there are eight teeth
These eight pairs are usually reckoned as eight cervical nerves ...
Linda Berens used the term 'cognitive processes' (1999) to refer to the eight types of consciousness that Jung discovered.
There used to be two 8 mm formats: standard 8 mm and Super-8 mm.
Betacam SX 8 mm Hi8, Digital8, Video8 DVD-Video";
First is a stopper knot, the figure of eight, ...
Gale warnings will be given if mean wind speeds of force 8 (34–40 knots)
a group manifestation of eight forms
He is one of the eight guardians of the world
The temple has eight monasteries, founded by Madhvacharya
The dharmachakra is typically depicted with eight spokes,
The focus of ordinary believers' religious life is on following a relevant version of the Eightfold Path ...
Brit Milah is observed on a boy's eighth day of life
Hanukkah is an eight-day Jewish holiday
Shemini Atzeret—literally, "the eighth day of assembly"
These eight souls in Noah's ark were the survivors...
... at the last, eight Angels will carry the Throne...
Evidence for the early use of the Eight Trigrams in a religious Taoist...
...famous Eight Immortals of China...
There are eight Sabbats
...of the gods of the Ogdoad, or the eight deities of the Egyptian creation...
...eight being a lucky number in Japanese.
a tone or note that is eight steps above or below another note or tone
a company of eight singers or musicians.
a musical composition for eight voices or instruments.
Welcome to the Housing Choice Voucher Program (also known as Section 8)
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.
To make a line temporarily fast by winding it, figure – eight fashion, round a cleat, a belaying pin, or a pair of bitts.