64 ( sixty-four ) is the natural number following 63 and preceding 65 .
36-435: Sixty-four is the square of 8 , the cube of 4 , and the sixth power of 2 . It is the seventeenth interprime , since it lies midway between the eighteenth and nineteenth prime numbers ( 61 , 67 ). The aliquot sum of a power of two ( 2 ) is always one less than the power of two itself, therefore the aliquot sum of 64 is 63 , within an aliquot sequence of two composite members (64, 63 , 41 , 1 , 0 ) that are rooted in
72-597: A cross product , and the number of equiangular lines possible in seven-dimensional space is anomalously large. The lowest known dimension for an exotic sphere is the seventh dimension. 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 . On the other hand, such figures with rank n + 3 mirrors exist in dimensions 4, 5, 6 and 8; not in 7. There are seven fundamental types of catastrophes . When rolling two standard six-sided dice , seven has
108-518: A "new set of numerals" after having counted to eight). 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
144-522: A 1 in 6 probability of being rolled, the greatest of any number. The opposite sides of a standard six-sided die always add to 7. The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved . In decimal representation, the reciprocal of 7 repeats six digits (as 0. 142857 ), whose sum when cycling back to 1
180-545: A periodicity of 8. The lie group E 8 is one of 5 exceptional lie groups. The order of the smallest non-abelian group whose subgroups are all normal is 8. 7 (number) 7 ( seven ) is the natural number following 6 and preceding 8 . It is the only prime number preceding a cube . As an early prime number in the series of positive integers , the number seven has greatly symbolic associations in religion , mythology , superstition and philosophy . The seven classical planets resulted in seven being
216-492: A regular triangle and a 42-sided polygon ( 3.7.42 ). This is also one of twenty-one such configurations from seventeen combinations of polygons, that features the largest and smallest polygons possible. Otherwise, for any regular n -sided polygon, the maximum number of intersecting diagonals (other than through its center) is at most 7. In two dimensions, there are precisely seven 7-uniform Krotenheerdt tilings, with no other such k -uniform tilings for k > 7, and it
252-471: Is isomorphic to the group of integers . These are related to the 17 wallpaper groups whose transformations and isometries repeat two-dimensional patterns in the plane. 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
288-455: Is a composite number and 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 x + y , where in its case x and y both equal 2. 8 is a Fibonacci number and the only nontrivial Fibonacci number that is a perfect cube . Sphenic numbers always have exactly eight divisors. 8
324-477: 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
360-466: Is also the only k for which the count of Krotenheerdt tilings agrees with k . The Fano plane , the smallest possible finite projective plane , has 7 points and 7 lines arranged such that every line contains 3 points and 3 lines cross every point. This is related to other appearances of the number seven in relation to exceptional objects , like the fact that the octonions contain seven distinct square roots of −1, seven-dimensional vectors have
396-403: Is equal to 28. 999,999 divided by 7 is exactly 142,857 . Therefore, when a vulgar fraction with 7 in the denominator is converted to a decimal expansion, the result has the same six- digit repeating sequence after the decimal point, but the sequence can start with any of those six digits. The Pythagoreans invested particular numbers with unique spiritual properties. The number seven
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#1732776661204432-456: 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
468-410: 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
504-540: Is the atomic number of gadolinium , a lanthanide . 64 is the number of codons in the RNA codon table of the genetic code . 64 is the size in bits of certain data types in some computer programming languages , where a 64-bit integer can represent values up to 2 = 18,446,744,073,709,551,616. 64 is the number of squares in a regular eight by eight chessboard . 64 is the maximum item stack size in Minecraft , where
540-508: Is the cube-octahedron compound . 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
576-419: Is the base of the octal number system. A polygon with eight sides is an octagon . 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
612-527: 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
648-536: Is used in official handwriting rules for primary school in Russia, Ukraine, Bulgaria, Poland, other Slavic countries, France, Italy, Belgium, the Netherlands, Finland, Romania, Germany, Greece, and Hungary. Seven, the fourth prime number, is not only a Mersenne prime (since 2 3 − 1 = 7 {\displaystyle 2^{3}-1=7} ) but also a double Mersenne prime since
684-520: 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"); this same principle
720-572: 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. Just as in most modern typefaces , in typefaces with text figures
756-549: The aliquot tree of the thirteenth prime, 41. 64 is: Since it is possible to find sequences of 65 consecutive integers (intervals of length 64) such that each inner member shares a factor with either the first or the last member, 64 is the seventh Erdős–Woods number . In decimal , no integer added to the sum of its own digits yields 64; hence, 64 is the tenth self number . In four dimensions , there are 64 uniform polychora aside from two infinite families of duoprisms and antiprismatic prisms , and 64 Bravais lattices . 64
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#1732776661204792-578: The bottom left corner, a line that is slightly curved in some font variants. As is the case with the European digit, the Cham and Khmer digit for 7 also evolved to look like their digit 1, though in a different way, so they were also concerned with making their 7 more different. For the Khmer this often involved adding a horizontal line to the top of the digit. This is analogous to the horizontal stroke through
828-456: The character for the digit 8 usually has an ascender , as, for example, in [REDACTED] . 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
864-639: The character usually has a descender (⁊), as, for example, in [REDACTED] . Most people in Continental Europe, Indonesia, and some in Britain, Ireland, and Canada, as well as Latin America, write 7 with a line through 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 they can appear similar when written in certain styles of handwriting. This form
900-543: The cube and one of eight convex deltahedra . 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
936-590: 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. The digits as used in Al-Andalus by
972-497: The equation 2 − D = x has more than two solutions for n and x natural . In particular, the equation 2 − 7 = x is known as the Ramanujan–Nagell equation . 7 is one of seven numbers in the positive definite quadratic integer matrix representative of all odd numbers: {1, 3, 5, 7, 11, 15, 33}. There are 7 frieze groups in two dimensions, consisting of symmetries of the plane whose group of translations
1008-443: The exponent, 3, is itself a Mersenne prime. It is also a Newman–Shanks–Williams prime , a Woodall prime , a factorial prime , a Harshad number , a lucky prime , a happy number (happy prime), a safe prime (the only Mersenne safe prime ), a Leyland number of the second kind and Leyland prime of the second kind ( 2 5 − 5 2 {\displaystyle 2^{5}-5^{2}} ), and
1044-417: The fourth Heegner number . Seven is the lowest natural number that cannot be represented as the sum of the squares of three integers. A seven-sided shape is a heptagon . The regular n -gons for n ⩽ 6 can be constructed by compass and straightedge alone, which makes the heptagon the first regular polygon that cannot be directly constructed with these simple tools. 7 is the only number D for which
1080-506: The middle that is sometimes used in handwriting in the Western world but which is almost never used in computer fonts . This horizontal stroke is, however, important to distinguish the glyph for seven from the glyph for one in writing that uses a long upstroke in the glyph for 1. In some Greek dialects of the early 12th century the longer line diagonal was drawn in a rather semicircular transverse line. On seven-segment displays , 7
1116-492: The number is called a 'stack'. The 1996 Nintendo console is also called the Nintendo 64. The number of hexagrams in the I Ching (that is also the maximum number of strokes in any Chinese character ). Song When I'm Sixty-Four by The Beatles 8 (number) 8 ( eight ) is the natural number following 7 and preceding 9 . English eight , from Old English eahta , æhta , Proto-Germanic *ahto
64 (number) - Misplaced Pages Continue
1152-532: The number of days in a week. 7 is often considered lucky in Western culture and is often seen as highly symbolic. Unlike Western culture, in Vietnamese culture , the number seven is sometimes considered unlucky. For early Brahmi numerals , 7 was written more or less in one stroke as a curve that looks like an uppercase ⟨J⟩ vertically inverted (ᒉ). The western Arab peoples' main contribution
1188-400: The only tiling that can admit a regular octagon. 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 . An octahedron is a regular polyhedron with eight equilateral triangles as faces . is the dual polyhedron to
1224-784: The tradition of the Hebrew Bible , the New Testament likewise uses the number seven as part of a typological pattern: References to the number seven in Christian knowledge and practice include: References to the number seven in Islamic knowledge and practice include: References to the number seven in Hindu knowledge and practice include: Other references to the number seven in Eastern traditions include: Other references to
1260-560: Was considered to be particularly interesting because it consisted of the union of the physical (number 4 ) with the spiritual (number 3 ). In Pythagorean numerology the number 7 means spirituality. References from classical antiquity to the number seven include: The number seven forms a widespread typological pattern within Hebrew scripture , including: References to the number seven in Jewish knowledge and practice include: Following
1296-414: Was to make the longer line diagonal rather than straight, though they showed some tendencies to making the digit more rectilinear. The eastern Arab peoples developed the digit from a form that looked something like 6 to one that looked like an uppercase V. Both modern Arab forms influenced the European form, a two-stroke form consisting of a horizontal upper stroke joined at its right to a stroke going down to
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