36 (number)

← 35 36 37 →
← 30 31 32 33 34 35 36 37 38 39 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	thirty-six
Ordinal	36th (thirty-sixth)
Factorization	22 × 32
Divisors	1, 2, 3, 4, 6, 9, 12, 18, 36
Greek numeral	ΛϚ´
Roman numeral	XXXVI
Binary	1001002
Ternary	11003
Senary	1006
Octal	448
Duodecimal	3012
Hexadecimal	2416

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

In mathematics

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 ${\displaystyle n}$ with exactly eight solutions (37, 57, 63, 74, 76, 108, 114, 126) to the Euler totient function ${\displaystyle \phi (x)=n}$. 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

• 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

• The 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

• 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

• 36 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 Orfèvres , 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 Placebo

In sports

• Most 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

• Perfect score on the ACT.
• (Oilfield terminology): A pipe wrench 36 inches long
• +36 is the code for international direct-dialphone calls to Hungary

See also

• List of highways numbered 36

References

1. Sloane, N. J. A. (ed.). "SequenceA000217(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.). "SequenceA033950(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.). "SequenceA001097(Twin primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-06-15.
6. Sloane, N. J. A. (ed.). "SequenceA005349(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.). "SequenceA051865(13-gonal (or tridecagonal) numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
13. "How Many? A Dictionary of Units of Measurement. -Y". Archived from the original on 22 September 2007. Retrieved 2007-09-15.
14. "WebElements.com – Krypton". Archived from the original on 4 August 2007. Retrieved 2007-08-13.
15. "36bit.org". Archived from the original on 11 September 2007. Retrieved 2007-09-15.
16. 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. "Adelaide 36ers Homepage". Archived from the original on 11 August 2007. Retrieved 13 August 2007.