36 (number)

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

← 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	36 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	100100
Hexadecimal	24

1 In mathematics
- 1.1 Measurements
2 In science
- 2.1 Astronomy
3 In religion
4 In the arts, culture, and philosophy
5 In sports
6 Historical years
7 References

[edit] In mathematics

36 is the sum of 1, 2, 3, 4, 5, 6, 7, and 8.

It is the square of 6 as well as a triangular number, making it a square triangular number, and also the only triangular number whose square root is also a triangular number. It is also a 13-gonal number.

36 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 angle of all 5 tips in a perfect star.

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.

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 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 36 twice, 36 is a Størmer number.

[edit] 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]
The number of barleycorns in an English foot.^[1]

[edit] In science

The atomic number of krypton ^[2]

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

ASCII code for the symbol '$' ^[4]

[edit] 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]

[edit] In religion

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

[edit] In the arts, culture, and philosophy

The Thirty-Six Dramatic Situations are considered a useful conceptual aid in theatre.
The Thirty-Six Stratagems are a collection of Chinese proverbs illustrating useful approaches to conflict situations.

[edit] 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]