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 36
^{2} + 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
In science
Astronomy
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 the arts, culture, and philosophy
In sports
In other fields
Thirty-six may also refer to:
Historical years
36 A.D.,
36
B.C.,
1936,
2036,
etc.
References