56 (fifty-six) is the natural number following 55 and preceding 57. 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. 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[1] 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[2] might have been used at Stonehenge.
Posted on: Mon, 21 Jul 2014 08:20:28 +0000
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