Silver ratio(1+√2), pell numbers and there geometry


The pell numbers produce the repeating sequence:

1, 2, 5, 3, 2, 7, 7, 3, 4, 2, 8, 9, 8, 7, 4, 6, 7, 2, 2, 6, 5, 7, 1, 9

and when added up is 117 which is the 9th pentagonal number which is composed of the three triangle numbers(tetractys) 36(8)+36(8)+45(9), the 36+36 would form the 8×8=64 square and the 64 can be found in the reduced pell number sequence.


All Fibonacci numbers divisible by 5 divided by 5 is a generalization of the Pell-numbers(?): 5, 55, 610, 6765, 75025, 832040, 9227465...=1(1), 11(2), 122(5), 1353(3), 15005(2), 166408(7), 1845493(7)...


Its interesting that the Fibonacci numbers divisible by 5 produce the repeating pell number sequence which adds up to a pentagonal number.

22 views0 comments

Recent Posts

See All