36 (number)

← 35 37 → 36
← 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	$2^2 \cdot 3^2$
Divisors	1, 2, 3, 4, 6, 9, 12, 18, 36
Roman numeral	XXXVI
Binary	1001002
Octal	448
Duodecimal	3012
Hexadecimal	2416

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

In mathematics

36 is both the square of 6 and a triangular number, making it a square triangular number. It is the smallest square triangular number other than 1, and it is also the only triangular number other than 1 whose square root is also a triangular number.

It is also a 13-gonal number.

It is the smallest number n with exactly 8 solutions to the equation φ(x) = n. Being the smallest number with exactly 9 divisors, 36 is a highly composite number. Adding up some subsets of its divisors (e.g., 6, 12 and 18) gives 36, hence 36 is a semiperfect number.

This number is the sum of a twin prime (17 + 19), the sum of the cubes of the first three integers, and the product of the squares of the first three 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.

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.

In base 10, it is a Harshad number.

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

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.

Because 36² + 1 = 1297, a prime, which is obviously more than 2 × 36, 36 is a Størmer number.

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

Measurements

• The number of inches in a yard.^[1]
• In the UK, a standard beer barrel is 36 UK gallons, about 163.7 litres.^[1]

In science

• The atomic number of krypton ^[2]

• Many early computers featured a 36-bit word length ^[3]

• ASCII code for the symbol '$' ^[4]

Astronomy

• Messier object M36, a magnitude 6.5 open cluster in the constellation Auriga ^[5]

• The New General Catalogue object NGC 36, a spiral galaxy in the constellation Pisces ^[6]

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.^[7] The Torah commands 36 times to love, respect and protect the stranger.^[7] Furthermore, in every generation there are 36 righteous people (the "Lamed Vav Tzadikim") in whose merit the world continues to exist.^[7] In the modern celebration of Hannukah, 36 candles are kindled in the menorah over the 8 days of that holiday (not including the shamash candle).^[7]

• 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.^[8]

• 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 the arts, culture, and philosophy

• The 36 Views of Mount Fuji, a famous series of prints by Japanese ukiyo-e artist Katsushika Hokusai
• The The 36 view of the Eiffel Tower, a famous series of prints from Henri Riviere inspired 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.
• The 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 an ambient musician from the UK.
• 36 is a song on Steal This Album! by System of a Down.
• 36 is a movie releasing in 2010, directed by Martin Campbell.
• 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 playing grid and roulette wheel (together with a '0' or '00' depending on whether it is a European wheel '37' or American wheel '38')

In sports

• Australian Basketball team The Adelaide 36ers^[9]
• Retired number of former baseball players Robin Roberts^[10] of the Phillies and Gaylord Perry^[11] of the Giants.
• Retired number of former basketball player Lloyd Neal of the Portland Trail Blazers^[12]
• The number of vehicles that run in each race of NASCAR's Camping World Truck Series.

In other fields

Thirty-six may also refer to:

• IBM System/36, a minicomputer
• The number of the French department Indre
• Perfect score on the ACT.
• (Oilfield terminology): A pipe wrench 36 inches long

Historical years

36 A.D., 36 B.C., 1936, 2036, etc.

References

1. ^ ^{a b} "How Many? A Dictionary of Units of Measurement. -Y". http://www.unc.edu/~rowlett/units/dictY.html. Retrieved 2007-09-15. 
2. ^ "WebElements.com – Krypton". http://www.webelements.com/webelements/elements/text/Kr/index.html. Retrieved 2007-08-13. 
3. ^ "36bit.org". http://www.36bit.org/. Retrieved 2007-09-15. 
4. ^ "ASCII.com - ASCII Table and description.". http://www.asciitable.com/. Retrieved 2007-09-15. 
5. ^ "Messier 36, SEDS Messier pages". http://www.seds.org/messier/m/m036.html. Retrieved 2007-09-15. 
6. ^ "The NGC/IC Project". http://www.ngcic.org/dss/dss_n0001.asp. Retrieved 2007-09-15. 
7. ^ ^{a b c d} Pinchas Winston (1995). The Wonderful World of Thirty-six. Mercava Productions. ISBN 0-9698032-4-9. http://www.neveh.org/winston/wonder36/default.html. 
8. ^ "Self Guided Tour Map". Wairakei Terraces: Maori Cultural Experience. http://www.wairakeiterraces.co.nz/self_guided_tour_map.htm. Retrieved 2007-08-12. 
9. ^ "Adelaide 36ers Homepage". http://www.adelaide36ers.com/36ers/. Retrieved 2007-08-13. 
10. ^ "Robin Roberts player Profile Chronology". Baseballlibrary.com. http://www.baseballlibrary.com/ballplayers/player.php?name=Robin_Roberts_1926&page=chronology. Retrieved 2007-08-13. 
11. ^ "Giants Retire Perry's Number 36". MLB.com's Giants homepage. http://sanfrancisco.giants.mlb.com/news/article.jsp?ymd=20050723&content_id=1142533&vkey=news_sf&fext=.jsp&c_id=sf. Retrieved 2007-08-13. 
12. ^ "Learn More About Lloyd Neal". http://www.nba.com/blazers/history/Learn_More_About_Lloyd_Neal-64032-41.html. Retrieved 2008-12-29.