For earlyBrahmi 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, theCham andKhmer 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 inhandwriting in the Western world but which is almost never used incomputer fonts. This horizontal stroke is, however, important to distinguish the glyph for seven from the glyph forone 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.
Onseven-segment displays, 7 is the digit with the most common graphic variation (1, 6 and 9 also have variant glyphs). Most devices use three line segments, but devices made by some Japanese companies such asSharp andCasio, as well as in the Koreas and Taiwan, 7 is written with four line segments because in those countries, 7 is written with a "hook" on the left, as ① in the following illustration. Further segments can give further variation. For example,Schindler elevators in the United States and Canada installed or modernized from the late 1990s onwards usually use a sixteen segment display and show the digit 7 in a manner more similar to that of handwriting.
While the shape of the character for the digit 7 has anascender in most moderntypefaces, in typefaces withtext figures the character usually has adescender, as, for example, in.
Most people in Continental Europe,[3] Indonesia,[citation needed] and some in Britain, Ireland, Israel, Canada, and 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 that digit from the digitone, as they can appear similar when written in certain styles of handwriting. This form is used in official handwriting rules forprimary 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]
A seven-sided shape is aheptagon.[17] Theregularn-gons forn ⩽ 6 can be constructed bycompass and straightedge alone, which makes the heptagon the first regular polygon that cannot be directly constructed with these simple tools.[18]
7 is the only numberD for which the equation2n −D =x2 has more than two solutions forn andxnatural. In particular, the equation2n − 7 =x2 is known as theRamanujan–Nagell equation. 7 is one of seven numbers in the positivedefinite quadraticinteger matrix representative of allodd numbers: {1, 3, 5, 7, 11, 15, 33}.[19][20]
A heptagon inEuclidean space is unable to generateuniform tilings alongside other polygons, like the regularpentagon. However, it is one of fourteen polygons that can fill aplane-vertex tiling, in its case only alongside a regulartriangle and a 42-sided polygon (3.7.42).[24][25] Otherwise, for any regularn-sided polygon, the maximum number of intersecting diagonals (other than through its center) is at most 7.[26]
In two dimensions, there are precisely seven7-uniformKrotenheerdt tilings, with no other suchk-uniform tilings fork > 7, and it is also the onlyk for which the count ofKrotenheerdt tilings agrees withk.[27][28]
Inhyperbolic space, 7 is the highest dimension for non-simplexhypercompactVinberg polytopes of rankn + 4 mirrors, where there is one unique figure with elevenfacets. On the other hand, such figures with rankn + 3 mirrors exist in dimensions 4, 5, 6 and 8;not in 7.[35]
When rolling two standard six-sideddice, seven has a 1 in 6 probability of being rolled, the greatest of any number.[37] The opposite sides of a standard six-sided die always add to 7.
999,999 divided by 7 is exactly142,857. Therefore, when avulgar fraction with 7 in thedenominator is converted to adecimal 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.[40] Indecimal representation, thereciprocal of 7 repeats sixdigits (as 0.142857),[41][42] whose sum whencycling back to1 is equal to 28.
ThePythagoreans 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 (number4) with the spiritual (number3).[46] In Pythagoreannumerology the number 7 means spirituality.
The number seven had mystical and religious significance in Mesopotamian culture by the 22nd century BCE at the latest. This was likely because in the Sumeriansexagesimal number system, dividing by seven was the first division which resulted in infinitelyrepeating fractions.[47]
^Carl B. Boyer,A History of Mathematics (1968) p.52, 2nd edn.
^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. 24.67
^"Μαθηματικά Α' Δημοτικού" [Mathematics for the First Grade](PDF) (in Greek). Ministry of Education, Research, and Religions. p. 33. RetrievedMay 7, 2018.
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