Natural number
Natural number
6 (six ) is thenatural number following5 and preceding7 . It is acomposite number and the smallestperfect number .[ 1]
In mathematics A six-sidedpolygon is ahexagon ,[ 1] regular polygons capable oftiling the plane . A hexagon also has 6edges as well as 6internal and external angles .
6 is the second smallestcomposite number .[ 1] perfect number .[ 2] digital root of 1.[ 3] unitary perfect number , since it is the sum of its positive properunitary divisors , without including itself. Only five such numbers are known to exist.[ 4] all-Harshad numbers .[ 5]
6 is the 2ndsuperior highly composite number ,[ 6] colossally abundant number ,[ 7] triangular number ,[ 8] highly composite number ,[ 9] pronic number ,[ 10] congruent number ,[ 11] harmonic divisor number ,[ 12] semiprime .[ 13] Granville number , orS {\displaystyle {\mathcal {S}}} Golomb ruler of length 6 is a "perfect ruler".[ 14]
Thesix exponentials theorem guarantees that under certain conditions one of a set of six exponentials istranscendental .[ 15] abelian group is thesymmetric group S 3 {\displaystyle \mathrm {S_{3}} } 3! = 6 elements.[ 1] kissing number problem .[ 16]
A regularcube , with sixfaces Acube has 6faces . Atetrahedron has 6edges . Infour dimensions , there are a total of sixconvex regular polytopes .
In theclassification of finite simple groups , twenty of twenty-sixsporadic groups in thehappy family are part of three families of groups which divide the order of thefriendly giant , the largest sporadic group: fivefirst generation Mathieu groups , sevensecond generation subquotients of theLeech lattice , and eightthird generation subgroups of the friendly giant. The remainingsix sporadic groups do not divide the order of the friendly giant, which are termed thepariahs Ly O'N Ru J 4 J 3 J 1 [ 17]
6 is the smallest integer which is not an exponent of aprime number , making it the smallest integer greater than 1 for which there does not exist afinite field of that size.[ 18]
List of basic calculations 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 ÷ 60.16 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 x 6 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809
Greek and Latin word parts
Hexa Hexa Greek for "six".[ 1]
The prefixsex- Sex- Latin prefix meaning "six".[ 1]
Senary is the ordinal adjective meaning "sixth"[ 22] People withsexdactyly have six fingers on each hand The measuring instrument called asextant got its name because its shape forms one-sixth of a wholecircle A group of six musicians is called asextet Six babies delivered in one birth aresextuplets Sexy prime pairs – Prime pairs differing by six aresexy , because sex is the Latin word for six.[ 23] [ 24] TheSI prefix for 10006 isexa- (E), and for its reciprocalatto- (a).
Evolution of the Hindu-Arabic digit The first appearance of 6 is in theEdicts 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'sMinor Rock Edict No.1 inSasaram ,c. 250 BCE The evolution of the modern digit 6 appears to be more simple when compared with the other digits. The modern 6 can be traced back to theBrahmi numerals ofIndia , which are first known from theEdicts of Ashoka c. 250 BCE .[ 25] [ 26] [ 27] [ 28] [ 29]
On theseven-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 moderntypefaces , in typefaces withtext figures the character for the digit 6 usually has anascender , as, for example, in[ 30]
This digit resembles an inverted9 . 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.
The cells of abeehive are six-sided.
Chemistry
Anthropology
Buddhism Buddhism describes six realms of existence or realms into which beings can be reborn according to their deeds. They are visualised on theTibetan wheel of life and illustrate the perpetual cyclical existence insamsara . The six perfections or "six paramitas " are among the best-known Buddhist symbols of the six. InMahayana Buddhism, these are fundamental spiritual qualities on the path of thebodhisattva to achievenirvana .
See also
References ^a b c d e f Weisstein, Eric W."6" .mathworld.wolfram.com . Retrieved2020-08-03 . ^ Higgins, Peter (2008).Number Story: From Counting to Cryptography 11 .ISBN 978-1-84800-000-1 ^ Weisstein, Eric W."Perfect Number" .mathworld.wolfram.com . Retrieved2025-03-20 . ^ Sloane, N. J. A. (ed.)."Sequence A002827 (Unitary perfect numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2016-06-01 .^ Weisstein, Eric W."Harshad Number" .mathworld.wolfram.com . Retrieved2020-08-03 . ^ "A002201 - OEIS" .oeis.org . Retrieved2024-11-28 .^ "A004490 - OEIS" .oeis.org . Retrieved2024-11-28 .^ "A000217 - OEIS" .oeis.org . Retrieved2024-11-28 .^ "A002182 - OEIS" .oeis.org . Retrieved2024-11-28 .^ "Sloane's A002378: Pronic numbers" .The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2020-11-30 .^ Sloane, N. J. A. (ed.)."Sequence A003273 (Congruent numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2016-06-01 .^ "A001599 - OEIS" .oeis.org . Retrieved2024-11-28 .^ Sloane, N. J. A. (ed.)."Sequence A001358 (Semiprimes (or biprimes): products of two primes.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2023-08-03 .^ Bryan Bunch,The Kingdom of Infinite Number . New York: W. H. Freeman & Company (2000): 72 ^ Weisstein, Eric W."Six Exponentials Theorem" .mathworld.wolfram.com . Retrieved2020-08-03 . ^ Weisstein, Eric W."Kissing Number" .mathworld.wolfram.com . Retrieved2020-08-03 . ^ Griess, Jr., Robert L. (1982)."The Friendly Giant" (PDF) .Inventiones Mathematicae 69 :91– 96.Bibcode :1982InMat..69....1G .doi :10.1007/BF01389186 .hdl :2027.42/46608 .MR 0671653 .S2CID 123597150 .Zbl 0498.20013 . ^ Dummit, David S.; Foote, Richard M. (2009).Abstract algebra (3. ed., [Nachdr.] ed.). New York: Wiley.ISBN 978-0-471-43334-7 ^ Weisstein, Eric W."Hexadecimal" .mathworld.wolfram.com . Retrieved2020-08-03 . ^ Weisstein, Eric W."Hexagon" .mathworld.wolfram.com . Retrieved2020-08-03 . ^ Weisstein, Eric W."Hexahedron" .mathworld.wolfram.com . Retrieved2020-08-03 . ^ Weisstein, Eric W."Base" .mathworld.wolfram.com . Retrieved2020-08-03 . ^ Chris K. Caldwell; G. L. Honaker Jr. (2009).Prime Curios!: The Dictionary of Prime Number Trivia ISBN 978-1-4486-5170-2 ^ Weisstein, Eric W."Sexy Primes" .mathworld.wolfram.com . Retrieved2020-08-03 . ^ Hollingdale, Stuart (2014).Makers of Mathematics 95– 96.ISBN 978-0-486-17450-1 ^ Publishing, Britannica Educational (2009).The Britannica Guide to Theories and Ideas That Changed the Modern World ISBN 978-1-61530-063-1 ^ Katz, Victor J.; Parshall, Karen Hunger (2014).Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century ISBN 978-1-4008-5052-5 ^ Pillis, John de (2002).777 Mathematical Conversation Starters ISBN 978-0-88385-540-9 ^ 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. 24.66 ^ Negru, John (1988).Computer Typesetting ISBN 978-0-442-26696-7 slight ascenders that rise above the cap height ( in 4 and 6 ) ^ Webb, Stephen; Webb, Professor of Australian Studies Stephen (2004-05-25).Out of this World: Colliding Universes, Branes, Strings, and Other Wild Ideas of Modern Physics ISBN 978-0-387-02930-6 snowflake, with its familiar sixfold rotational symmetry ^ Rimes, Wendy (2016-04-01)."The Reason Why The Dead Are Buried Six Feet Below The Ground" .Elite Readers . Retrieved2020-08-06 . ^ "Chinese Numbers 1 to 10 | maayot".maayot • Bite-size daily Chinese stories . 2021-11-22. Retrieved 2025-01-17. ^ Smith, Michael (2011-10-31).Six: The Real James Bonds 1909-1939 ISBN 978-1-84954-264-7
External links Look up
six in Wiktionary, the free dictionary.
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