Eight

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]

Eight

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]

A cube is a regular polyhedron with eight vertices that also forms the cubic honeycomb, the only regular honeycomb in three-dimensional space.[12] Through various truncation operations, the cubic honeycomb generates eight other convex uniform honeycombs under the cubic group C 3 \displaystyle \tilde C_3 .[13] The octahedron, with eight equilateral triangles as faces, is the dual polyhedron to the cube and one of eight convex deltahedra.[14][15] 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.[16][17] There are also eight uniform polyhedron compounds made purely of octahedra, including the regular compound of five octahedra, and an infinite amount of polyhedron compounds made only of octahedra as triangular antiprisms (UC22 and UC23, with p = 3 and q = 1).

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.

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.

Vertex-transitive semiregular 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 polytopes 221, 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 affine 521 honeycomb that represents the arrangement of vertices of the eight-dimensional E 8 \displaystyle \mathrm E _8 lattice, and made of 421 facets. The culminating figure is the ninth-dimensional 621 honeycomb, which is the only affine semiregular paracompact hyperbolic honeycomb with infinite facets and vertex figures in the k21 family. There are no other finite semiregular polytopes or honeycombs in dimensions n > 8.

The octonions are a hypercomplex normed division algebra that are an extension of the complex numbers. They are realized in eight dimensions, where they have an isotopy group over the real numbers that is spin group Spin(8), the unique such group that exhibits a phenomenon of triality. As a double cover of special orthogonal group SO(8), Spin(8) contains the special orthogonal Lie algebra D4 as its Dynkin diagram, whose order-three outer automorphism is isomorphic to the symmetric group S3, giving rise to its triality. Over finite fields, the eight-dimensional Steinberg group 3D4(q3) is simple, and one of sixteen such groups in the classification of finite simple groups. As is Lie algebra E8, whose complex form in 248 dimensions is the largest of five exceptional Lie algebras that include E7 and E6, which are held inside E8. The smallest such algebra is G2, that is the automorphism group of the octonions. In mathematical physics, 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.

8 is the base of the octal number system, which is mostly used with computers.[21] In octal, one digit represents three bits. In modern computers, a byte is a grouping of eight bits, also called an octet.

Ocular syphilis, a manifestation of Treponema pallidum infection, can cause a variety of ocular signs and symptoms, including eye redness, blurry vision, and vision loss. Although syphilis is nationally notifiable, ocular manifestations are not reportable to CDC. Syphilis rates have increased in the United States since 2000. After ocular syphilis clusters were reported in early 2015, CDC issued a clinical advisory (1) in April 2015 and published a description of the cases in October 2015 (2). Because of concerns about an increase in ocular syphilis, eight jurisdictions (California, excluding Los Angeles and San Francisco, Florida, Indiana, Maryland, New York City, North Carolina, Texas, and Washington) reviewed syphilis surveillance and case investigation data from 2014, 2015, or both to ascertain syphilis cases with ocular manifestations. A total of 388 suspected ocular syphilis cases were identified, 157 in 2014 and 231 in 2015. Overall, among total syphilis surveillance cases in the jurisdictions evaluated, 0.53% in 2014 and 0.65% in 2015 indicated ocular symptoms. Five jurisdictions described an increase in suspected ocular syphilis cases in 2014 and 2015. The predominance of cases in men (93%), proportion of those who are men who have sex with men (MSM), and percentage who are HIV-positive (51%) are consistent with the epidemiology of syphilis in the United States. It is important for clinicians to be aware of potential visual complications related to syphilis infections. Prompt identification of potential ocular syphilis, ophthalmologic evaluation, and appropriate treatment are critical to prevent or manage visual symptoms and sequelae of ocular syphilis.

In early 2015, clusters of ocular syphilis cases were reported in Washington and California. CDC issued a clinical advisory, notifying clinical providers and health departments of a potential increase in suspected ocular syphilis cases. After this advisory, eight jurisdictions performed a review of syphilis surveillance and case investigation data to identify syphilis cases with ocular manifestations. Seven jurisdictions reviewed data from January 1, 2014 to December 31, 2015; Indiana reviewed data from 2015 only. A patient whose illness met the surveillance case definition of syphilis (3) was considered to have a suspected case of ocular syphilis if the patient had concurrent ocular signs or symptoms noted in the surveillance database from a local syphilis case investigation or reported by a local health care provider. A standard form was used to abstract de-identified information on each case, including demographic information, syphilis stage and treatment, and any information on extent of ocular involvement. Each jurisdiction also provided a total number of syphilis surveillance cases, including numbers from all stages of syphilis, as defined by the surveillance case definitions (3).

Ocular syphilis is a serious manifestation of syphilis. This report is the first evaluating suspected ocular syphilis across multiple jurisdictions in the United States. Although there is no national reporting of ocular manifestations, eight jurisdictions reviewed their syphilis surveillance data to identify cases with ocular manifestations in 2014 and 2015. Ocular manifestations were present in 0.60% of all reported syphilis cases, ranging by jurisdiction from 0.17% to 3.9%. In most jurisdictions, the percentage was similar to data from a study in England that estimated ocular syphilis affected approximately 0.6% of early syphilis cases from 2009 to 2010 (5). Five of the seven jurisdictions that reviewed cases in both years described an increase in suspected ocular syphilis cases in 2014 and 2015. In addition, after the clinical advisory, CDC was notified of suspected ocular syphilis cases from 20 states (2). The number of cases with ocular syphilis detected in 2014 and 2015 in the United States could be attributable to increased recognition of ocular manifestations in the setting of increased syphilis rates, or an actual increase in the proportion of syphilis cases with ocular disease. The predominance of cases in men and MSM, as well as the proportion also diagnosed with HIV, is consistent with the epidemiology of syphilis in the United States (6) 041b061a72