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Fibonacci sequence hidden in ordinary division problem

posted by Jason Kottke   Jul 06, 2015

If you divide 1 by 999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 (that’s 999 quattuordecillion btw), the Fibonacci sequence neatly pops out. MATH FTW!

Fibonacci division

At the end of Carl Sagan’s Contact (spoilers!), the aliens give Ellie a hint about something hidden deep in the digits of π. After a long search, a circle made from a sequence of 1s and 0s is found, providing evidence that intelligence was built into the fabric of the Universe. I don’t know if this Fibonacci division thing is on quite the same level, but it might bake your noodle if you think about it too hard. (via @stevenstrogatz)

Update: From svat at Hacker News, an explanation of the magic behind the math.

It’s actually easier to understand if you work backwards and arrive at the expression yourself, by asking yourself: “If I wanted the number that starts like 0.0…000 0…001 0…001 0…002 0…003 0…005 0…008 … (with each block being 24 digits long), how would I express that number?”

(thx, taylor)