THE TRIFIGURATE NUMBERS 37 and 91
These numbers are unique in that they may each be realised as a symmetrical formation of uniform counters - squares or circles in the case of 37, circles or spheres in respect of 91 - as depicted below.
But observe that these numbers are also related by the fact that they are, respectively, the difference and sum of the cubes of 4 and 3.
37 = 4^3 - 3^3
91 = 4^3 + 3^3
Vernon Jenkins MSc
2007-05-05