36 (number)

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.^[1] 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 circular number- a square number that ends with the same integer by itself (6×6=36).

It is also a 13-gonal number.^[2]

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.^[3] Adding up some subsets of its divisors (e.g., 6, 12 and 18) gives 36, hence 36 is a semiperfect number.^[4]

This number is the sum of a twin prime (17 + 19), 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.

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.

36 is a Harshad number in bases 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 16 (and 9 other bases).

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.^[5]

Because 36² + 1 = 1297, a prime, which is larger than 2 × 36, 36 is a Størmer number.^[6]

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

36 multiplied by any other number always produces an answer whose individual digits, in decimal, add up to a multiple of nine.

Measurements

• The number of inches in a yard (3 feet).^[7]
• In the UK, a standard beer barrel is 36 UK gallons, about 163.7 litres.^[7]

In science

• The atomic number of krypton ^[8]
• Many early computers featured a 36-bit word length ^[9]
• 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.^[10] The Torah commands 36 times to love, respect and protect the stranger.^[10] Furthermore, in every generation there are 36 righteous people (the "Lamed Vav Tzadikim") in whose merit the world continues to exist.^[10] In the modern celebration of Hanukkah, 36 candles are kindled in the menorah over the 8 days of that holiday (not including the shamash candle).^[10]
• 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.^[11]
• 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? (Thirty-Six) is a Canadian Psychedelic rock band (On Newgrounds)
• 36 is 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 playing grid 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 Degrees is a song by the band Placebo

In sports

• Most number of runs one can hit of a (non-penalised) over in cricket.
• Australian Basketball team The Adelaide 36ers^[12]
• The number of consecutive bowling strikes in a 900 series (3 consecutive perfect games)
• Retired number of former baseball players Robin Roberts^[13] of the Phillies and Gaylord Perry^[14] of the Giants.
• Retired number of former basketball player Lloyd Neal of the Portland Trail Blazers^[15]
• 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

References