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7 (number) - Wikipedia, the free encyclopedia

7 (number)

From Wikipedia, the free encyclopedia

0 1 2 3 4 5 6 7 8 9

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

Seven (7) is the sixth successor of one (1).

Contents

[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 easy, once we rewrite the number n 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

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} \ 48_{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

Image:SevenGlyph.svg

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.

In fonts with text figures, 7 usually has a descender, for example, Image:TextFigs078.svg.

[edit] In science

  • The number of spots on a common ladybug.
  • With very few exceptions, all mammals' necks have seven bones.

[edit] Chemistry

[edit] Astronomy

[edit] In technology

[edit] In the Classical world

[edit] In religion

  • In Islam:
    • The number of ayat in surat al-Fatiha.
    • The number of heavens in Islamic tradition.
    • The number of Earths in Islamic tradition.
    • The numbers 7, 70, 70,000, etc. are used in Islamic traditions to denote an infinite or high number. In Arabic, 70, 70,000, etc. are used to mean infinite. This is because 1 is the smallest number, 2 is just after 1, 5 and 10 are exact, 4 and 6 are just before and after 5, and 9 is just before 10. This leaves 3, 7, and 8. Eight is closer to the end although it is larger. Eight is also an even number, so divisible by 2. Between 3 and 7, 3 is smaller, so 7 is chosen to represent infinite.
  • In Judaism:
    • A highly symbolic number in the Torah, alluding to the infusion of spirituality and Godliness into the Creation. For example:
    1. God rested on and sanctified the seventh day (Shabbat).
    2. A seven-day purification period is required for one who has become tamei to become tahor.
    3. The Shemittah (Sabbatical) year arrives every seventh year.
    4. The Jubilee (Yovel) year comes after 7 times 7 years.
    5. The Counting of the Omer leading up to the Giving of the Torah is expressed as "7 times 7 weeks."
    • The weekly Torah portion is divided into seven aliyahs, and seven men or boys over the age of 13 are called up for the reading of these aliyahs during Shabbat morning services.
    • Seven blessings are recited under the chuppah during a Jewish wedding ceremony.
    • David was the seventh son of Jesse.
    • A Jewish bride and groom are feted with seven days of festive meals after their wedding, known as Sheva Berachot ("Seven Blessings").
    • The number of Ushpizzin (also known as the "Seven Shepherds") who visit the sukkah during the holiday of Sukkot: Abraham, Isaac, Jacob, Joseph, Moses, Aaron, and David.
    • The number of nations God told the Israelites they would displace when they entered the land of Israel (Deut. 7:1): the Hittite, the Girgashite, the Amorite, the Canaanite, the Perizzite, the Hivite, and the Jebusite.
    • In Breslov tradition, the seven orifices of the face (2 eyes, 2 nostrils, 2 ears, and the mouth) are called "The Seven Candles."
    • The menorah (Hebrew: מנורה), is a seven branched candelabrum lit by olive oil in the Tabernacle and the Temple in Jerusalem. The menorah is one of the oldest symbols of the Jewish people. It is said to symbolize the burning bush as seen by Moses on Mount Sinai (Exodus 25).
  • Others:
    • The number of Archangels according to some systems.
    • The minor symbol number of yang from the Taoist yin-yang.
    • The number of palms in an Egyptian Sacred Cubit.
    • The number of ranks in Mithraism.
    • The number seven is of particular significance within Cherokee cosmology.
    • In Buddhism, Buddha walked 7 steps at his birth.

[edit] In mythology

  • In Khasi mythology, the seven divine women who were left behind on earth and became the ancestresses of all humankind.
  • The number of gateways traversed by Inanna during her descent into the underworld.
  • The number of sleeping men in the Christian myth of the "Seven Sleepers."
  • The number of sages in Hindu mythology; their wives are the goddesses referred to as the "Seven Mothers."
  • The number of main islands of mythological Atlantis.
  • In Guaraní mythology, the number of prominent legendary monsters.
  • Seven Lucky Gods exist in Japanese mythology.
  • In British Folk lore, every 7 years the Farie Queen pays a tithe to Hell (or possably Hel) in the tale of Tam Lin.
  • In the British Folk tale of Thomas the Rhymer, he went to live in the farie kingdom for 7 years.

[edit] In psychology

[edit] In music

[edit] Albums

[edit] Songs

[edit] In television

  • The name of one of the monsters in the cartoon television show Seven Little Monsters.
  • Seven, an episodic character from the sitcom Married... with Children.
  • In Star Trek: Voyager, Seven of Nine (also called Seven for short) is one of the crewmembers.
  • In an episode of Seinfeld entitled "The Seven," the name George Costanza desired to give his first-born (with Susan Ross) is "Seven;" he later falsely claimed that he had promised this to the widow of baseball great Mickey Mantle, whose uniform number was 7.
  • The name of a television show 7th Heaven.
  • Seven Network, a television network in Australia.
  • The number of currently identified biological Cylon models, out of a possible 12, in the television show, Battlestar Galactica.
  • Maximum number of VHF broadcast channels available in any TV market in the United States of America; they are channels 2, 4, 5, 7, 9, 11, and 13 in the Greater New York City and Los Angeles-Long Beach SMSAs.
  • In Stargate SG-1 and Stargate Atlantis, most gate addresses use 7 chevrons on the gate.
  • Ultra Seven, a television series aired in 1967, and the superhero of the same name.

[edit] In film

[edit] In Video Games

  • 7 is a number used many times by Bungie Studios in their Halo and Marathon games. 7 appears in a variety of different contexts, from the stories of the games to the raw game coding. One obvious example is the fact that there are seven Halo rings strewn throughout the galaxy.
  • Final Fantasy VII has many instances of seven throughout the game and was even released (in North America) on the seventh day of September in 1997.

[edit] In sports

[edit] In other fields

7 playing cards of all four suits
7 playing cards of all four suits

Seven is also:

[edit] Names and titles

Seven or 7 is all or part of a number of names and titles of people, artworks, or organizations, including:

[edit] Notes

  1. ^ "21 Then Peter came to Jesus and asked, 'Lord, how many times shall I forgive my brother when he sins against me? Up to seven times?' 22 Jesus answered, 'I tell you, not seven times, but seventy times seven.'". [1]

Interestingly enough, the value of 490 suggested by Jesus has been the source of much debate among scholars. For example, did he actually mean to impose a limit at 490, or did he only mean that the number of times (one should be forgiven) is to be ongoing? Most conclude the latter.

Alternatively, it may be that the New Testament's mention of seventy "times" seven is a mistranslation of the original Hebrew based on the statement of Lemech (Genesis 4:24) that "If Cain shall be avenged sevenfold, then for Lemech it shall be seventy-seven fold."

[edit] See also

[edit] External link

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