7 (number)

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0 1 2 3 4 5 6 7 8 9

List of numbers — Integers

0 10 20 30 40 50 60 70 80 90

Cardinal 7
seven
Ordinal 7th
seventh
Numeral system septenary
Factorization prime
Divisors 1, 7
Roman numeral VII
Roman numeral (Unicode) Ⅶ, ⅶ
Arabic ٧
Bengali
Chinese numeral
Devanāgarī
Hebrew ז (Zayin)
Khmer
prefixes hepta-/hept-
Binary 111
Octal 7
Duodecimal 7
Hexadecimal 7
Seven Days of Creation - 1765 book, title page

7 (seven) is the natural number following 6 and preceding 8.

Contents

  • 1 In mathematics
    • 1.1 In numeral systems
    • 1.2 List of basic calculations
  • 2 Evolution of the glyph
  • 3 In science
    • 3.1 Chemistry
    • 3.2 Astronomy
  • 4 In technology
  • 5 In the classical world
  • 6 In religion
  • 7 In mythology
  • 8 In psychology
  • 9 In music
  • 10 In television
  • 11 In film
  • 12 In literature
  • 13 In video games
  • 14 In sports
  • 15 In other fields
    • 15.1 Names and titles
  • 16 Notes
  • 17 See also
  • 18 References
  • 19 External links

[edit] In mathematics

  1. Remove the last digit,
  2. Double it, and
  3. Subtract it from the remaining digits.
  4. If the result is negative and there are 2 or more digits, drop the negative sign.
  5. Repeat until you end up with a result that is a multiple of seven (7). (i.e. -7, 0, or +7)
For example, the number 1358 is evenly divisible by seven, since:
135 - (8*2) = 119
11 - (9*2) = -7
Using Number Theory the proof is rather simple, once the number n is rewritten in the form:
n = 10a + b
Where:
a is the remaining digits, and
b is the last digit.
Then:
10a + b = 0 (mod 7)
5 * (10a + b) = 0 (mod 7)
49a + a + 5b = 0 (mod 7)
a + 5b - 7b = 0 (mod 7)
a - 2b = 0 (mod 7)

A second divisibility rule was formulated in 2006 in India, by Himanish Ganjoo, a Class 8 student in St. Columba's School Delhi:

  1. Remove the last two digits
  2. Divide the remaining number by 7
  3. Multiply the remainder by 2
  4. Add the product to the last two digits
  5. If the sum is divisible by 7, the number is also divisible

On March 25, 2007, Ganjoo formulated another variant form of this test, now separating the last 3 digits (in step 1), and multiplying the remainder by 6 (step 3), and then adding the sum to the last 3 digits (originally separated).

For example, 1568 is divisible by 7,
  1. 15/7 Remainder = 1
  2. Product 1*2 = 2
  3. 68 + 2 = 70 (which is divisible by 7)

Hence, 1568 is divisible by 7

[edit] In numeral systems

Base Numeral system
2 binary 111
3 ternary 21
4 quaternary 13
5 quinary 12
6 senary 11
7 septenary 10
over 7 (octal, decimal, etc) 7

In quaternary, 7 is the smallest prime with a composite sum of digits.

[edit] List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
7 \times x 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 350 700 7000
Division 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15
7 \div x 7 3.5 2.\overline{3} 1.75 1.4 1.1\overline{6} 1 0.875 0.\overline{7} 0.7
0.\overline{6}\overline{3} 0.58\overline{3} 0.\overline{5}3846\overline{1} 0.5 0.4\overline{6}
x \div 7 0.\overline{1}4285\overline{7} 0.\overline{2}8571\overline{4} 0.\overline{4}2857\overline{1} 0.\overline{5}7142\overline{8} 0.\overline{7}1428\overline{5} 0.\overline{8}5714\overline{2} 1 1.\overline{1}4285\overline{7} 1.\overline{2}8571\overline{4} 1.\overline{4}2857\overline{1}
1.\overline{5}7142\overline{8} 1.\overline{7}1428\overline{5} 1.\overline{8}5714\overline{2} 2 2.\overline{1}4285\overline{7}
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
7 ^ x\, 7 49 343 2401 16807 117649 823543 5764801 40353607 282475249 1977326743 13841287201 96889010407
x ^ 7\, 1 128 2187 16384 78125 279936 823543 2097152 4782969 10000000 19487171 35831808 62748517
Radix 1 5 10 15 20 25 30 40 50 60 70 80 90 100
110 120 130 140 150 200 250 500 1000 10000 100000 1000000
x_{7} \ 1 5 13_{7} \ 21_{7} \ 26_{7} \ 34_{7} \ 42_{7} \ 55_{7} \ 101_{7} \ 114_{7} \ 130_{7} \ 143_{7} \ 156_{7} \ 202_{7} \
215_{7} \ 231_{7} \ 244_{7} \ 260_{7} \ 303_{7} \ 404_{7} \ 505_{7} \ 1313_{7} \ 2626_{7} \ 41104_{7} \ 564355_{7} \ 11333311_{7} \

[edit] Evolution of the glyph

In the beginning, various Hindus wrote 7 more or less in one stroke as a curve that looks like an uppercase J upside down. The western Ghubar Arabs' main contribution was to make the longer line diagonal rather than straight, though they showed some tendencies to making the character more rectilinear. The eastern Arabs developed the character from a 6-look-alike into an uppercase V-look-alike. Both modern Arab forms influenced the European form, a two-stroke character consisting of a horizontal upper line joined at its right to a line going down to the bottom left corner, a line that is slightly curved in some font variants. As is the case with the European glyph, the Cham and Khmer glyph for 7 also evolved to look like their glyph for 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 above the glyph. 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 writings that use a long upstroke in the glyph for one.

On the seven-segment displays of pocket calculators and digital watches, 7 is the number with the most common glyph variation (0, 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. The reason is that in Japan & Korea 7 is written as ① in the illustration to the right.

While the shape of the 7 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in .

[edit] In science

[edit] Chemistry

[edit] Astronomy

[edit] In technology

[edit] In the classical world

In classical antiquity:

[edit] In religion

[edit] In mythology

[edit] In psychology

[edit] In music

[edit] In television

[edit] In film

[edit] In literature

[edit] In video games

[edit] In sports

[edit] In other fields

International maritime signal flag for 7
7 playing cards of all four suits

Seven is also:

[edit] Names and titles