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36 (number)

January 01, 1970

36 (thirty-six) is the natural number following 35 and preceding 37.

Cardinalthirty-six
Ordinal36th
(thirty-sixth)
Factorization22 × 32
Divisors1, 2, 3, 4, 6, 9, 12, 18, 36
Greek numeralΛϚ´
Roman numeralXXXVI
Binary1001002
Ternary11003
Senary1006
Octal448
Duodecimal3012
Hexadecimal2416

In mathematics edit

 
36 depicted as a triangular number and as a square number
 
36 as the sum of the first positive cubes

36 is both the square of six, and the eighth triangular number[1] or the sum of the first eight non-zero positive integers, which makes 36 the first non-trivial square triangular number.[2] Aside from being the smallest square triangular number other than 1, it is also the only triangular number (other than 1) whose square root is also a triangular number. 36 is also the eighth refactorable number, as it has exactly nine positive divisors, and 9 is one of them;[3] in fact, it is the smallest number with exactly nine divisors, which leads 36 to be the 7th highly composite number.[4] It is the sum of the fourth pair of twin-primes (17 + 19),[5] and the 18th Harshad number in decimal, as it is divisible by the sum of its digits (9).[6]

It is the smallest number   with exactly eight solutions (37, 57, 63, 74, 76, 108, 114, 126) to the Euler totient function  . Adding up some subsets of its divisors (e.g., 6, 12, and 18) gives 36; hence, it is also the eighth semiperfect number.[7]

This number is the sum of the cubes of the first three positive integers and also the product of the squares of the first three positive integers.

36 is the number of degrees in the interior angle of each tip of a regular pentagram.

The thirty-six officers problem is a mathematical puzzle with no solution.[8]

The number of possible outcomes (not summed) in the roll of two distinct dice.

36 is the largest numeric base that some computer systems support because it exhausts the numerals, 0–9, and the letters, A-Z. See Base 36.

The truncated cube and the truncated octahedron are Archimedean solids with 36 edges.[9]

The number of domino tilings of a 4×4 checkerboard is 36.[10]

Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number.[11]

The sum of the integers from 1 to 36 is 666 (see number of the beast).

36 is also a Tridecagonal number.[12]

Measurements edit

  • The number of inches in a yard (3 feet).[13]
  • In the UK, a standard beer barrel is 36 UK gallons, about 163.7 litres.[13]
  • 3 dozen, or a quarter of a gross.

In science edit

In religion edit

  • Jewish tradition holds that the number 36 has had special significance since the beginning of time: According to the Midrash, the light created by God on the first day of creation shone for exactly 36 hours; it was replaced by the light of the Sun that was created on the Fourth Day.[16] The Torah commands 36 times to love, respect and protect the stranger.[16] Furthermore, in every generation there are 36 righteous people (the "Lamed Vav Tzadikim") in whose merit the world continues to exist.[16] In the modern celebration of Hanukkah, 36 candles are kindled in the menorah over the eight days of that holiday (not including the shamash candle).[16]
  • In one Māori legend, concerning the creation of mankind by the god Tāne, 36 gods took active part in assembling the various parts of the first human before Tāne breathed life into her.[17]
  • In Shaivism (s.a. Kaśmir Śaivism), The 36 tattvas describe the Absolute, its internal aspects and the creation including living beings, down to the physical reality.
  • In Egyptian religion, the 36 decans are a series of gods presiding over the degrees of the zodiac and the fixed stars.[18]
  • Traditional Hindu marriage bases compatibility on a set of 36 astrological qualities or Gunas, 18 of which must be shared if the union is to be considered auspicious.

In the arts, culture, and philosophy edit

In sports edit

In other fields edit

See also edit

References edit

  1. ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  2. ^ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  4. ^ "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A001097 (Twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  7. ^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  8. ^ Weisstein, Eric W. "36 Officer Problem". mathworld.wolfram.com. Retrieved 2020-08-21.
  9. ^ Weisstein, Eric W. "Archimedean Solid". mathworld.wolfram.com. Retrieved 2020-08-21.
  10. ^ Weisstein, Eric W. "Domino Tiling". mathworld.wolfram.com. Retrieved 2020-08-21.
  11. ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A051865 (13-gonal (or tridecagonal) numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ a b "How Many? A Dictionary of Units of Measurement. -Y". from the original on 22 September 2007. Retrieved 2007-09-15.
  14. ^ "WebElements.com – Krypton". from the original on 4 August 2007. Retrieved 2007-08-13.
  15. ^ "36bit.org". from the original on 11 September 2007. Retrieved 2007-09-15.
  16. ^ a b c d Winston, Pinchas (1995). The Wonderful World of Thirty-six. Mercava Productions. ISBN 0-9698032-4-9.
  17. ^ "The Creation of Man". The Coming of the Maori. Retrieved 2016-04-24.
  18. ^ Betz, Hans Dieter (1996). The Greek Magical Papyri in Translation. University of Chicago Press. ISBN 9780226044477.
  19. ^ . Archived from the original on 11 August 2007. Retrieved 13 August 2007.

January 01, 1970
number, thirty, natural, number, following, preceding, list, numbersintegers, cardinalthirty, sixordinal36th, thirty, sixth, factorization22, 32divisors1, 36greek, numeralΛϚ, roman, numeralxxxvibinary1001002ternary11003senary1006octal448duodecimal3012hexadecim. 36 thirty six is the natural number following 35 and preceding 37 35 36 37 30 31 32 33 34 35 36 37 38 39 List of numbersIntegers 0 10 20 30 40 50 60 70 80 90 Cardinalthirty sixOrdinal36th thirty sixth Factorization22 32Divisors1 2 3 4 6 9 12 18 36Greek numeralLϚ Roman numeralXXXVIBinary1001002Ternary11003Senary1006Octal448Duodecimal3012Hexadecimal2416 Contents 1 In mathematics 2 Measurements 3 In science 4 In religion 5 In the arts culture and philosophy 6 In sports 7 In other fields 8 See also 9 ReferencesIn mathematics edit nbsp 36 depicted as a triangular number and as a square number nbsp 36 as the sum of the first positive cubes 36 is both the square of six and the eighth triangular number 1 or the sum of the first eight non zero positive integers which makes 36 the first non trivial square triangular number 2 Aside from being the smallest square triangular number other than 1 it is also the only triangular number other than 1 whose square root is also a triangular number 36 is also the eighth refactorable number as it has exactly nine positive divisors and 9 is one of them 3 in fact it is the smallest number with exactly nine divisors which leads 36 to be the 7th highly composite number 4 It is the sum of the fourth pair of twin primes 17 19 5 and the 18th Harshad number in decimal as it is divisible by the sum of its digits 9 6 It is the smallest number n displaystyle n nbsp with exactly eight solutions 37 57 63 74 76 108 114 126 to the Euler totient function ϕ x n displaystyle phi x n nbsp Adding up some subsets of its divisors e g 6 12 and 18 gives 36 hence it is also the eighth semiperfect number 7 This number is the sum of the cubes of the first three positive integers and also the product of the squares of the first three positive integers 36 is the number of degrees in the interior angle of each tip of a regular pentagram The thirty six officers problem is a mathematical puzzle with no solution 8 The number of possible outcomes not summed in the roll of two distinct dice 36 is the largest numeric base that some computer systems support because it exhausts the numerals 0 9 and the letters A Z See Base 36 The truncated cube and the truncated octahedron are Archimedean solids with 36 edges 9 The number of domino tilings of a 4 4 checkerboard is 36 10 Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member 36 is an Erdos Woods number 11 The sum of the integers from 1 to 36 is 666 see number of the beast 36 is also a Tridecagonal number 12 Measurements editThe number of inches in a yard 3 feet 13 In the UK a standard beer barrel is 36 UK gallons about 163 7 litres 13 3 dozen or a quarter of a gross In science editThe atomic number of krypton 14 Many early computers featured a 36 bit word length 15 36 is the number of characters required to store the display name of a UUID or GUID e g 00000000 0000 0000 C000 000000000046 In religion editJewish tradition holds that the number 36 has had special significance since the beginning of time According to the Midrash the light created by God on the first day of creation shone for exactly 36 hours it was replaced by the light of the Sun that was created on the Fourth Day 16 The Torah commands 36 times to love respect and protect the stranger 16 Furthermore in every generation there are 36 righteous people the Lamed Vav Tzadikim in whose merit the world continues to exist 16 In the modern celebration of Hanukkah 36 candles are kindled in the menorah over the eight days of that holiday not including the shamash candle 16 In one Maori legend concerning the creation of mankind by the god Tane 36 gods took active part in assembling the various parts of the first human before Tane breathed life into her 17 In Shaivism s a Kasmir Saivism The 36 tattvas describe the Absolute its internal aspects and the creation including living beings down to the physical reality In Egyptian religion the 36 decans are a series of gods presiding over the degrees of the zodiac and the fixed stars 18 Traditional Hindu marriage bases compatibility on a set of 36 astrological qualities or Gunas 18 of which must be shared if the union is to be considered auspicious In the arts culture and philosophy edit36 Views of Mount Fuji a famous series of prints by Japanese ukiyo e artist Katsushika Hokusai The 36th Chamber of Shaolin is a 1978 kung fu film 36 Quai des Orfevres often referred to simply as 36 a French police film The Thirty Six Dramatic Situations are considered a useful conceptual aid in theater Thirty Six Stratagems are a collection of Chinese proverbs illustrating useful approaches to conflict situations In French speaking countries 36 is often used as a placeholder number 36 Crazyfists are a four piece metal band from Alaska 36 is the alias of ambient experimental musician Dennis Huddleston from the UK Enter The Wu Tang 36 Chambers is an album by Wu Tang Clan The 36 Lessons of Vivec is the title of a book series in the video game The Elder Scrolls III Morrowind The game of roulette has 36 numbers on the number layout and roulette wheel together with a 0 or 00 depending on whether it is a European wheel 37 or American wheel 38 The roulette based game Rollorpoker uses 36 playing cards on the wheel and playing grid instead of numbers 36 is a song by System of a Down 36 Degrees is a song by the band PlaceboIn sports editMost runs one can hit off a non penalised over in cricket See six sixes in an over citation needed The amount of races in a NASCAR Cup Series season Australian basketball team the Adelaide 36ers is named after the year in which South Australia was founded 19 The number of consecutive bowling strikes in a 900 series 3 consecutive perfect games The number of vehicles that run in each race of NASCAR s Camping World Truck Series In other fields editPerfect score on the ACT Oilfield terminology A pipe wrench 36 inches long 36 is the code for international direct dialphone calls to HungarySee also editList of highways numbered 36References edit Sloane N J A ed Sequence A000217 Triangular numbers The On Line Encyclopedia of Integer Sequences OEIS Foundation Retrieved 2023 06 15 Sloane s A001110 Square triangular numbers The On Line Encyclopedia of Integer Sequences OEIS Foundation Retrieved 2016 05 31 Sloane N J A ed Sequence A033950 Refactorable numbers number of divisors of k divides k Also known as tau numbers The On Line Encyclopedia of Integer Sequences OEIS Foundation Retrieved 2023 06 15 Sloane s A002182 Highly composite numbers The On Line Encyclopedia of Integer Sequences OEIS Foundation Retrieved 2016 05 31 Sloane N J A ed Sequence A001097 Twin primes The On Line Encyclopedia of Integer Sequences OEIS Foundation Retrieved 2023 06 15 Sloane N J A ed Sequence A005349 Niven or Harshad or harshad numbers numbers that are divisible by the sum of their digits The On Line Encyclopedia of Integer Sequences OEIS Foundation Retrieved 2023 06 15 Sloane s A005835 Pseudoperfect or semiperfect numbers The On Line Encyclopedia of Integer Sequences OEIS Foundation Retrieved 2016 05 31 Weisstein Eric W 36 Officer Problem mathworld wolfram com Retrieved 2020 08 21 Weisstein Eric W Archimedean Solid mathworld wolfram com Retrieved 2020 08 21 Weisstein Eric W Domino Tiling mathworld wolfram com Retrieved 2020 08 21 Sloane s A059756 Erdos Woods numbers The On Line Encyclopedia of Integer Sequences OEIS Foundation Retrieved 2016 05 31 Sloane N J A ed Sequence A051865 13 gonal or tridecagonal numbers The On Line Encyclopedia of Integer Sequences OEIS Foundation a b How Many A Dictionary of Units of Measurement Y Archived from the original on 22 September 2007 Retrieved 2007 09 15 WebElements com Krypton Archived from the original on 4 August 2007 Retrieved 2007 08 13 36bit org Archived from the original on 11 September 2007 Retrieved 2007 09 15 a b c d Winston Pinchas 1995 The Wonderful World of Thirty six Mercava Productions ISBN 0 9698032 4 9 The Creation of Man The Coming of the Maori Retrieved 2016 04 24 Betz Hans Dieter 1996 The Greek Magical Papyri in Translation University of Chicago Press ISBN 9780226044477 Adelaide 36ers Homepage Archived from the original on 11 August 2007 Retrieved 13 August 2007 Retrieved from https en wikipedia org w index php title 36 number amp oldid 1214366916, wikipedia, wiki, book, books, library,

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