(no subject)

[simont]

Mathematical curiosity of the day:

   100/9899     = 0 . 01 01 02 03 05 08 13 21 ...
  1000/998999   = 0 . 001 001 002 003 005 008 013 021 ...
 10000/99989999 = 0 . 0001 0001 0002 0003 0005 0008 0013 0021 ...

And in general, 10^n / (10^2n-10^n-1) displays the Fibonacci numbers in n-digit blocks of its decimal expansion.

Sorry, I just thought that was outstandingly cute.

Comments

[meirion.livejournal.com]

http://mathworld.wolfram.com/FibonacciNumber.html

is a worthwhile read on this and associated subjects.

-m-

[meirion.livejournal.com]

in particular look at the section on the "curious addition tree" (10/89). i'd guess that your series are going to do the same when you get to fibonacci numbers that are more than n digits long.

the bit i find fascinating about that page is the bit about generating fibonacci numbers in terms of the golden ratio and its lesser-known sibling (does (1-sqrt(5))/2 have its own name, or is it just the discarded root of 1-x-x^2 ?)

-m-

10^n / (10^2n-10^n-1)

[calligraphkatie.livejournal.com]

agreed on cuteness.
Hmm. must go noseying on that one.
Thanks!