Mathematics
56 is the sum of the first six triangular numbers (making it a tetrahedral number), as well as the sum of six consecutive primes (3 + 5 + 7 + 11 + 13 + 17). It is also a tetranacci number and a pronic number. Adding up the divisors of 1 through 8 gives 56. Since 56 is twice a perfect number, it is itself a semiperfect number.
56 is a partition number - the number of distinct ways 11 can be represented as the sum of natural numbers.
Since it is possible to find sequences of 56 consecutive integers such that each inner member shares a factor with either the first or the last member, 56 is an Erdős–Woods number.
The maximum determinant in an 8 by 8 matrix of zeroes and ones is 56.
Plutarch states that the Pythagoreans associated a polygon of 56 sides with Typhon and that they associated certain polygons of smaller numbers of sides with other figures in Greek mythology. While it is impossible to construct a perfect regular 56-sided polygon using simple 'square and circle' geometry, a close approximation has recently been discovered which it is claimed might have been used at Stonehenge.
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—John Adams (1735–1826)
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