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

In mathematics

36 the square of 6 as well as a triangular number, making it a square triangular number, the smallest square triangular number other than 1 and also the only triangular number 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), and the sum of the cubes 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).

In science

• ASCII code for the symbol '\$'

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

• 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.

In other fields

Thirty-six may also refer to:

Historical years

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

References

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