36 (number) - in Mathematics

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).