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 a semiperfect number.
This number is the sum of a twin prime (17 + 19), the sum of the cubes of the first three integers, and the product of the squares 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).
Read more about this topic: 36 (number)
Famous quotes containing the word mathematics:
“It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.”
—George Bernard Shaw (1856–1950)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)