999,999,999,998,999,999,999,999 is an
interesting number. I could tell you
about some of the reasons it is interesting, but I really only want to focus on
one at a time. There is one interesting
property that you would not believe unless I showed you – so that is the one I
am going to talk (write) about.
If you turn this number into a unit
fraction (1/999,999,999,998,999,999,999,999), and then find its decimal
expansion you first get a big funny look on your face – “I can’t get this number to fit into
my calculator???"
I’ve got your back. Go to the Wolfram Alpha website: www.wolframalpha.com. At that site you can input the fraction shown
above and it will perform this calculation for you. It will show you that the answer is:
1.000000000001000000000002000000000003000000000005000000...
× 10^24
Convert from scientific notation to regular
decimal notation and you get:
0.000000000000000000000001000000000001000000000002000000000003
000000000005000000...
000000000005000000...
Some of you may already notice the sequence
1, 1, 2, 3, 5 already – shhhh, don’t give it away yet.
If you request the “more digits” (several
times) and you arrange the answer into 12 digit chunks, you will see the it is
producing a famous sequence known as the Fibonacci sequence;
1/999999999998999999999999
= 0.
000000000000
000000000001
000000000001
000000000002
000000000003
000000000005
000000000008
000000000013
000000000021
000000000034
000000000055
000000000089
000000000144
000000000233
000000000377
000000000610
000000000987
000000001597
000000002584
000000004181
000000006765
000000010946
000000017711
000000028657
000000046368
000000075025
000000121393
000000196418
000000317811
000000514229
000000832040
000001346269
000002178309
000003524578
000005702887
000009227465
000014930352
000024157817
000039088169
000063245986
000102334155
000165580141
000267914296
000433494437
000701408733
001134903170
001836311903
002971215073
004807526976
007778742049
012586269025
020365011074
032951280099
053316291173
086267571272
139583862445
225851433717

Fibonacci Sequence
0
1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
2584
4181
6765
10946
17711
28657
46368
75025
121393
196418
317811
514229
832040
1346269
2178309
3524578
5702887
9227465
14930352
24157817
39088169
63245986
102334155
165580141
267914296
433494437
701408733
1134903170
1836311903
2971215073
4807526976
7778742049
12586269025
20365011074
32951280099
53316291173
86267571272
139583862445
225851433717

The Fibonacci sequence is produced by
starting with a 0, and a 1 (or a 1 and another 1), after that each new term is
the sum of the two terms before it.
This fraction produces the first 56 terms
of the Fibonacci sequence before the terms get too large to fit into a 12 digit
format. I think that is amazing. I know there is a simple (or maybe not so
simple) mathematical explanation about why this works out this way. I also know that the stars in the night sky
are really just giant ball of hydrogen gas undergoing nuclear fusion – but they
are still amazing to look at.
Just one more thing: Take a piece of paper and write down your current
age, then write down the name of an animal that lives in Africa, then add 5 to
your age, then write down the name of a swimming bird that lives in
Antarctica. The last number you wrote
down is how old you will be in 5 years!
Amazing!
Don’t forget – Fibonacci day is 11/23/2014
(1, 1, 2, 3, …),
David
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