7
Integer number 7 From Wikipedia, the free encyclopedia
Integer number 7 From Wikipedia, the free encyclopedia
7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube.
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Cardinal | seven | |||
Ordinal | 7th (seventh) | |||
Numeral system | septenary | |||
Factorization | prime | |||
Prime | 4th | |||
Divisors | 1, 7 | |||
Greek numeral | Ζ´ | |||
Roman numeral | VII, vii | |||
Greek prefix | hepta-/hept- | |||
Latin prefix | septua- | |||
Binary | 1112 | |||
Ternary | 213 | |||
Senary | 116 | |||
Octal | 78 | |||
Duodecimal | 712 | |||
Hexadecimal | 716 | |||
Greek numeral | Z, ζ | |||
Amharic | ፯ | |||
Arabic, Kurdish, Persian | ٧ | |||
Sindhi, Urdu | ۷ | |||
Bengali | ৭ | |||
Chinese numeral | 七, 柒 | |||
Devanāgarī | ७ | |||
Telugu | ౭ | |||
Tamil | ௭ | |||
Hebrew | ז | |||
Khmer | ៧ | |||
Thai | ๗ | |||
Kannada | ೭ | |||
Malayalam | ൭ | |||
Armenian | Է | |||
Babylonian numeral | 𒐛 | |||
Egyptian hieroglyph | 𓐀 | |||
Morse code | _ _... |
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 the number of days in a week.[1] 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.[citation needed]
This section needs additional citations for verification. (May 2024) |
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 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 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.[2] This is analogous to the horizontal stroke through 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 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 the character usually has a descender (⁊), as, for example, in .
Most people in Continental Europe,[3] Indonesia,[citation needed] 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 the two can appear similar when written in certain styles of handwriting. This form is used in official handwriting rules for primary school in Russia, Ukraine, Bulgaria, Poland, other Slavic countries,[4] France,[5] Italy, Belgium, the Netherlands, Finland,[6] Romania, Germany, Greece,[7] and Hungary.[citation needed]
Seven, the fourth prime number, is not only a Mersenne prime (since ) but also a double Mersenne prime since the exponent, 3, is itself a Mersenne prime.[8] It is also a Newman–Shanks–Williams prime,[9] a Woodall prime,[10] a factorial prime,[11] a Harshad number, a lucky prime,[12] a happy number (happy prime),[13] a safe prime (the only Mersenne safe prime), a Leyland prime of the second kind and the fourth Heegner number.[14] 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.[15] 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.[16] Figurate numbers representing heptagons are called heptagonal numbers.[17] 7 is also a centered hexagonal number.[18]
7 is the only number D for which the equation 2n − D = x2 has more than two solutions for n and x natural. In particular, the equation 2n − 7 = x2 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}.[19][20]
There are 7 frieze groups in two dimensions, consisting of symmetries of the plane whose group of translations is isomorphic to the group of integers.[21] These are related to the 17 wallpaper groups whose transformations and isometries repeat two-dimensional patterns in the plane.[22][23]
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 a regular triangle and a 42-sided polygon (3.7.42).[24][25] This is also one of twenty-one such configurations from seventeen combinations of polygons, that features the largest and smallest polygons possible.[26][27] Otherwise, for any regular n-sided polygon, the maximum number of intersecting diagonals (other than through its center) is at most 7.[28]
In Wythoff's kaleidoscopic constructions, seven distinct generator points that lie on mirror edges of a three-sided Schwarz triangle are used to create most uniform tilings and polyhedra; an eighth point lying on all three mirrors is technically degenerate, reserved to represent snub forms only.[29]
Seven of eight semiregular tilings are Wythoffian (the only exception is the elongated triangular tiling), where there exist three tilings that are regular, all of which are Wythoffian.[30] Seven of nine uniform colorings of the square tiling are also Wythoffian.[31] In two dimensions, there are precisely seven 7-uniform Krotenheerdt tilings, with no other such k-uniform tilings for k > 7, and it is also the only k for which the count of Krotenheerdt tilings agrees with k.[32][33]
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.[34] 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 a cross product, and the number of equiangular lines possible in seven-dimensional space is anomalously large.[35][36][37]
The lowest known dimension for an exotic sphere is the seventh dimension, with a total of 28 differentiable structures; there may exist exotic smooth structures on the four-dimensional sphere.[38][39]
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.[40] 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.[41]
When rolling two standard six-sided dice, seven has a 6 in 62 (or 1/6) probability of being rolled (1–6, 6–1, 2–5, 5–2, 3–4, or 4–3), the greatest of any number.[42] 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.[43] Currently, six of the problems remain unsolved.[44]
In decimal representation, the reciprocal of 7 repeats six digits (as 0.142857),[45][46] whose sum when cycling back to 1 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.[47] For example, 1/7 = 0.142857 142857... and 2/7 = 0.285714 285714....
In fact, if one sorts the digits in the number 142,857 in ascending order, 124578, it is possible to know from which of the digits the decimal part of the number is going to begin with. The remainder of dividing any number by 7 will give the position in the sequence 124578 that the decimal part of the resulting number will start. For example, 628 ÷ 7 = 89+5/7; here 5 is the remainder, and would correspond to number 7 in the ranking of the ascending sequence. So in this case, 628 ÷ 7 = 89.714285. Another example, 5238 ÷ 7 = 748+2/7, hence the remainder is 2, and this corresponds to number 2 in the sequence. In this case, 5238 ÷ 7 = 748.285714.
The Pythagoreans invested particular numbers with unique spiritual properties. The number seven was considered to be particularly interesting because it consisted of the union of the physical (number 4) with the spiritual (number 3).[51] 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 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 the number seven in traditions from around the world include: