6

De Mi caja de notas

🎲 the perfect number

Perfect number Cuisenaire rods 6.png

← 5 6 7 →
−1 0 1 2 3 4 5 6 7 8 9
Cardinalsix
Ordinal6th
(sixth)
Numeral systemsenary
Factorization2 × 3
Divisors1, 2, 3, 6
Greek numeralϚ´
Roman numeralVI, vi, ↅ
Greek prefixhexa-/hex-
Latin prefixsexa-/sex-
Binary1102
Ternary203
Senary106
Octal68
Duodecimal612
Hexadecimal616
Greekστ (or ΣΤ or ς)
Arabic, Kurdish, Sindhi, Urdu٦
Persian۶
Amharic
Bengali
Chinese numeral六,陸
Devanāgarī
Gujarati
Hebrewו
Khmer
Thai
Telugu
Tamil
Saraiki٦
Malayalam
ArmenianԶ
Babylonian numeral𒐚
Egyptian hieroglyph𓏿
Morse code_ ....

6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number.[1]

In mathematics

A six-sided polygon is a hexagon,[1] one of the three regular polygons capable of tiling the plane. A hexagon also has 6 edges as well as 6 internal and external angles.

6 is the second smallest composite number.[1] It is also the first number that is the sum of its proper divisors, making it the smallest perfect number.[2] 6 is the first unitary perfect number, since it is the sum of its positive proper unitary divisors, without including itself. Only five such numbers are known to exist.[3] 6 is the largest of the four all-Harshad numbers.[4]

6 is a pronic number,[5] a congruent number,[6] a harmonic divisor number, and a semiprime.[7] 6 is also the first Granville number, or

 
   
     
       
         
           S
         
       
     
   
   {\displaystyle {\mathcal {S}}}
 

-perfect number. A Golomb ruler of length 6 is a "perfect ruler".[8] 6 is a harmonic divisor number.[9]

The six exponentials theorem guarantees that under certain conditions one of a set of six exponentials is transcendental.[10] The smallest non-abelian group is the symmetric group

 
   
     
       
         
           S
           
             3
           
         
       
     
   
   {\displaystyle \mathrm {S_{3}} }
 

which has 3! = 6 elements.[1] 6 the answer to the two-dimensional kissing number problem.[11]

A regular cube, with six faces

A cube has 6 faces. A tetrahedron has 6 edges. In four dimensions, there are a total of six convex regular polytopes.

In the classification of finite simple groups, twenty of twenty-six sporadic groups in the happy family are part of three families of groups which divide the order of the friendly giant, the largest sporadic group: five first generation Mathieu groups, seven second generation subquotients of the Leech lattice, and eight third generation subgroups of the friendly giant. The remaining six sporadic groups do not divide the order of the friendly giant, which are termed the pariahs (Ly, O'N, Ru, J4, J3, and J1).[12]

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 25 50 100 1000
6 × x 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 150 300 600 6000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
6 ÷ x 6 3 2 1.5 1.2 1 0.857142 0.75 0.6 0.6 0.54 0.5 0.461538 0.428571 0.4
x ÷ 6 0.16 0.3 0.5 0.6 0.83 1 1.16 1.3 1.5 1.6 1.83 2 2.16 2.3 2.5
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
6x 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
x6 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809

Greek and Latin word parts

Hexa

Hexa is classical Greek for "six".[1] Thus:

  • "Hexadecimal" combines hexa- with the Latinate decimal to name a number base of 16[13]
  • A hexagon is a regular polygon with six sides[14]
  • A hexahedron is a polyhedron with six faces, with a cube being a special case[15]
  • Hexameter is a poetic form consisting of six feet per line
  • A "hex nut" is a nut with six sides, and a hex bolt has a six-sided head
  • The prefix "hexa-" also occurs in the systematic name of many chemical compounds, such as hexane which has 6 carbon atoms (C6H14).

The prefix sex-

Sex- is a Latin prefix meaning "six".[1] Thus:

  • Senary is the ordinal adjective meaning "sixth"[16]
  • People with sexdactyly have six fingers on each hand
  • The measuring instrument called a sextant got its name because its shape forms one-sixth of a whole circle
  • A group of six musicians is called a sextet
  • Six babies delivered in one birth are sextuplets
  • Sexy prime pairs – Prime pairs differing by six are sexy, because sex is the Latin word for six.[17][18]

The SI prefix for 10006 is exa- (E), and for its reciprocal atto- (a).

Evolution of the Hindu-Arabic digit

The first appearance of 6 is in the Edicts of Ashoka c. 250 BCE. These are Brahmi numerals, ancestors of Hindu-Arabic numerals.
The first known digit "6" in the number "256" in Ashoka's Minor Rock Edict No.1 in Sasaram, c. 250 BCE

The evolution of our modern digit 6 appears rather simple when compared with the other digits. The modern 6 can be traced back to the Brahmi numerals of India, which are first known from the Edicts of Ashoka c. 250 BCE.[19][20][21][22] It was written in one stroke like a cursive lowercase e rotated 90 degrees clockwise. Gradually, the upper part of the stroke (above the central squiggle) became more curved, while the lower part of the stroke (below the central squiggle) became straighter. The Arabs dropped the part of the stroke below the squiggle. From there, the European evolution to our modern 6 was very straightforward, aside from a flirtation with a glyph that looked more like an uppercase G.[23]

On the seven-segment displays of calculators and watches, 6 is usually written with six segments. Some historical calculator models use just five segments for the 6, by omitting the top horizontal bar. This glyph variant has not caught on; for calculators that can display results in hexadecimal, a 6 that looks like a "b" is not practical.

Just as in most modern typefaces, in typefaces with text figures the character for the digit 6 usually has an ascender, as, for example, in .[24]

This digit resembles an inverted 9. To disambiguate the two on objects and documents that can be inverted, the 6 has often been underlined, both in handwriting and on printed labels.

In music

A standard guitar has six strings.

In artists

In instruments

  • A standard guitar has six strings[31]
  • Most woodwind instruments have six basic holes or keys (e.g., bassoon, clarinet, pennywhistle, saxophone); these holes or keys are usually not given numbers or letters in the fingering charts

In music theory

  • There are six whole tones in an octave.[32]
  • There are six semitones in a tritone.[33]

In works

In religion

Judaism

Islam

Indeed, We created the heavens and the earth and everything in between in six Days,1 and We were not ˹even˺ touched with fatigue.2

— Surah Qaf:38

Note 1: The word day is not always used in the Quran to mean a 24-hour period. According to Surah Al-Hajj (The Pilgrimage):47, a heavenly Day is 1000 years of our time. The Day of Judgment will be 50,000 years of our time - Surah Al-Maarij (The Ascending Stairways):4. Hence, the six Days of creation refer to six eons of time, known only by Allah.

Note 2: Some Islamic scholars believe this verse comes in response to Exodus 31:17, which says, "The Lord made the heavens and the earth in six days, but on the seventh day He rested and was refreshed."

Others

In science

Astronomy

Biology

The cells of a beehive are six-sided.

Chemistry

A molecule of benzene has a ring of six carbon and six hydrogen atoms.
A molecule of benzene has a ring of six carbon and six hydrogen atoms.

Medicine

  • There are six tastes in traditional Indian medicine (Ayurveda): sweet, sour, salty, bitter, pungent, and astringent. These tastes are used to suggest a diet based on the symptoms of the body.[57]
  • Phase 6 is one of six pandemic influenza phases.[58]

Physics

In the Standard Model of particle physics, there are six types of quarks and six types of leptons.

In technology

6 as a resin identification code, used in recycling.
6 as a resin identification code, used in recycling.

In calendars

Anthropology

See also

References

  1. ^ a b c d e f Weisstein, Eric W. "6". mathworld.wolfram.com. Retrieved 2020-08-03.
  2. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 11. ISBN 978-1-84800-000-1.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A002827 (Unitary perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  4. ^ Weisstein, Eric W. "Harshad Number". mathworld.wolfram.com. Retrieved 2020-08-03.
  5. ^ "Sloane's A002378: Pronic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2020-11-30.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A003273 (Congruent numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A001358 (Semiprimes (or biprimes): products of two primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-08-03.
  8. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 72
  9. ^ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
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  11. ^ Weisstein, Eric W. "Kissing Number". mathworld.wolfram.com. Retrieved 2020-08-03.
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  18. ^ Weisstein, Eric W. "Sexy Primes". mathworld.wolfram.com. Retrieved 2020-08-03.
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  24. ^ Negru, John (1988). Computer Typesetting. Van Nostrand Reinhold. p. 59. ISBN 978-0-442-26696-7. slight ascenders that rise above the cap height ( in 4 and 6 )
  25. ^ Auric, Georges; Durey, Louis; Honegger, Arthur; Milhaud, Darius; Poulenc, Francis; Tailleferre, Germaine (2014-08-20). Caramel Mou and Other Great Piano Works of "Les Six": Pieces by Auric, Durey, Honegger, Milhaud, Poulenc and Tailleferre (in French). Courier Corporation. ISBN 978-0-486-49340-4.
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  28. ^ "Sixpence None The Richer". GRAMMY.com. 2020-05-19. Retrieved 2020-08-04.
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  32. ^ D'Amante, Elvo (1994-01-01). Music Fundamentals: Pitch Structures and Rhythmic Design. Scarecrow Press. p. 194. ISBN 978-1-4616-6985-2. The division of an octave into six equal parts is referred to as the whole-tone scale
  33. ^ Horsley, Charles Edward (1876). A Text Book of Harmony: For the Use of Schools and Students. Sampson Low, Marston, Searle, & Rivington. p. 4. Like the Tritone, it contains six semitones
  34. ^ Tribble, Mimi (2004). 300 Ways to Make the Best Christmas Ever!: Decorations, Carols, Crafts & Recipes for Every Kind of Christmas Tradition. Sterling Publishing Company, Inc. p. 145. ISBN 978-1-4027-1685-0. Six geese a-laying
  35. ^ Staines, Joe (2010-05-17). The Rough Guide to Classical Music. Penguin. p. 393. ISBN 978-1-4053-8321-9. ...the six arias with variations collected under the title Hexachordum Apollinis (1699)...
  36. ^ Hegarty, Paul; Halliwell, Martin (2011-06-23). Beyond and Before: Progressive Rock since the 1960s. Bloomsbury Publishing USA. p. 169. ISBN 978-1-4411-1480-8. Six Degrees of Inner Turbulence
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  39. ^ Lauterbach, Jacob Zallel (1916). Midrash and Mishnah: A Study in the Early History of the Halakah. Bloch. p. 9. Six orders of Mishnah
  40. ^ Rosen, Ceil; Rosen, Moishe (2006-05-01). Christ in the Passover. Moody Publishers. p. 79. ISBN 978-1-57567-480-3. Six symbolic foods
  41. ^ Repcheck, Jack (2008-12-15). The Man Who Found Time: James Hutton And The Discovery Of Earth's Antiquity. Basic Books. ISBN 978-0-7867-4399-5. it actually took only six days to create the earth
  42. ^ "CHURCH FATHERS: City of God, Book XI (St. Augustine)". www.newadvent.org. Retrieved 2020-08-04. These works are recorded to have been completed in six days (the same day being six times repeated), because six is a perfect number
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  45. ^ Shapera, Paul M. (2009-08-15). Iran's Religious Leaders. The Rosen Publishing Group, Inc. p. 10. ISBN 978-1-4358-5283-9. Islam has six articles of faith
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  49. ^ Rhoads, Samuel E. (1996). The Sky Tonight: A Guided Tour of the Stars Over Hawaiʻi. Bishop Museum Press. ISBN 978-0-930897-93-2. Three Messier objects are visible in this part of the sky : M6, M7 and M8 .
  50. ^ Sedgwick, Marcus (2011-07-05). White Crow. Roaring Brook Press. p. 145. ISBN 978-1-4299-7634-3. The cells of honeycombs are six-sided because a hexagon is the most material-efficient tessellation
  51. ^ Parker, Steve (2005). Ant Lions, Wasps & Other Insects. Capstone. p. 16. ISBN 978-0-7565-1250-7. Insects have six legs each...
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  53. ^ Mader, Sylvia S. (2004). Biology. McGraw-Hill. p. 20. ISBN 978-0-07-291934-9. The acronym CHNOPS helps us remember these six elements
  54. ^ Dufour, Fritz (2018-09-19). The Realities of Reality - Part II: Making Sense of Why Modern Science Advances. Vol. 1. Fritz Dufour. p. 100. The benzene molecule has its six carbon atoms in a ring[self-published source?]
  55. ^ Starr, Cecie; Evers, Christine (2012-05-10). Biology Today and Tomorrow without Physiology. Cengage Learning. p. 25. ISBN 978-1-133-36536-5. For example, the atomic number of carbon is 6,
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  57. ^ Woo, Teri Moser; Robinson, Marylou V. (2015-08-03). Pharmacotherapeutics For Advanced Practice Nurse Prescribers. F.A. Davis. p. 145. ISBN 978-0-8036-4581-3. Ayurvedic herbology is based on the tridoshic theory that there exist six basic tastes
  58. ^ Pandemic Influenza Preparedness and Response Guidance for Healthcare Workers and Healthcare Employers. OSHA, U.S. Department of Labor. 2007. p. 8. The WHO Plan describes six phases of increasing public health risk associated with the emergence of a new influenza
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  • The Odd Number 6, JA Todd, Math. Proc. Camb. Phil. Soc. 41 (1945) 66–68
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