36
Posted on Saturday, December 20, 2014
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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 asemiperfect number.
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 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.
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[edit]
- 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[edit]
- The atomic number of krypton [2]
- Many early computers featured a 36-bit word length [3]
- 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[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 ofcreation shone for exactly 36 hours; it was replaced by the light of the Sun that was created on the Fourth Day.[4] The Torah commands 36 times to love, respect and protect the stranger.[4] Furthermore, in every generation there are 36 righteous people (the "Lamed Vav Tzadikim") in whose merit the world continues to exist.[4] 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).[4]
- 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.[5]
- 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.
