What is #(32,951,280,099)/(20,365,011,074)#?

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Answer 1 · 2016-07-04T21:05:59

#32951280099/20365011074 ~~ 1.61803398874989#

We can long divide these numbers like this:

enter image source here

The significance of these two particular numbers is that they are Fibonacci numbers (specifically #F_52# and #F_51#) from the sequence:

#1, 1, 2, 3, 5, 8, 13, 21, 34,...#

where:

#F_1 = 1#

#F_2 = 1#

#F_n = F_(n-2) + F_(n-1)#

The ratio between pairs of successive Fibonacci numbers tends towards the golden ratio:

#1/2+1/2sqrt(5) ~~ 1.61803398874989484820#