median
don steward
mathematics teaching 10 ~ 16

Wednesday 14 March 2012

centred hexagonal numbers and bridge cables

a ppt is here

a quadratic generalisation

links with the difference between consecutive cubes
and this is no coincidence (see here)








this general form is also
n^3 - (n - 1)^3

summing the terms always gives a cube number

(e.g. 1 + 7 + 19 + 37 = 64 = 4^3)
 n = 4
 n = 5
 n = 6
n = 8


















centred hexagonal numbers are closely related to triangular numbers:
























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