# 36 (number)

 ← 35 36 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

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 is both the square of six and a triangular number, making it a square triangular number.[1] It is the smallest square triangular number other than one, and it is also the only triangular number other than one whose square root is also a triangular number.

It is the smallest number n with exactly eight solutions to the equation ${\displaystyle \phi (x)=n}$. It is the smallest number with exactly nine divisors, leading 36 to be a highly composite number.[2] Adding up some subsets of its divisors (e.g., 6, 12, and 18) gives 36; hence, it is a semiperfect number.[3]

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 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.[5]

The number of domino tilings of a 4×4 checkerboard is 36.[6]

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.[7]

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

## Measurements

• The number of inches in a yard (3 feet).[8]
• In the UK, a standard beer barrel is 36 UK gallons, about 163.7 litres.[8]

## 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.[11] The Torah commands 36 times to love, respect and protect the stranger.[11] Furthermore, in every generation there are 36 righteous people (the "Lamed Vav Tzadikim") in whose merit the world continues to exist.[11] 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).[11]
• 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.[12]
• 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.[13]

## References

1. ^ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. ^ "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
3. ^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
4. ^ Weisstein, Eric W. "36 Officer Problem". mathworld.wolfram.com. Retrieved 2020-08-21.
5. ^ Weisstein, Eric W. "Archimedean Solid". mathworld.wolfram.com. Retrieved 2020-08-21.
6. ^ Weisstein, Eric W. "Domino Tiling". mathworld.wolfram.com. Retrieved 2020-08-21.
7. ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
8. ^ a b "How Many? A Dictionary of Units of Measurement. -Y". Archived from the original on 22 September 2007. Retrieved 2007-09-15.
9. ^ "WebElements.com – Krypton". Archived from the original on 4 August 2007. Retrieved 2007-08-13.
10. ^ "36bit.org". Archived from the original on 11 September 2007. Retrieved 2007-09-15.
11. ^ a b c d Winston, Pinchas (1995). The Wonderful World of Thirty-six. Mercava Productions. ISBN 0-9698032-4-9.
12. ^ "The Creation of Man". The Coming of the Maori. Retrieved 2016-04-24.
13. ^ Betz, Hans Dieter (1996). The Greek Magical Papyri in Translation. ISBN 9780226044477.
14. ^ "Adelaide 36ers Homepage". Archived from the original on 11 August 2007. Retrieved 13 August 2007.