Field Trip! Go watch the Numberphile Video: http://www.numberphile.com/videos/pisano_period.html
The Fibonacci Sequence: 1, 1, 2, 3, 5, 8,
13, 21, 34, 55, 89, …
Many mathematicians have studied this
integer sequence for hundreds of years and found several interesting
patterns. One of them is a pattern
called Pisano periods.
It says that the mth Fibonacci
number (or F(m)) evenly divides the nth Fibonacci number (or F(n)) if
m evenly divides n. So the 3rd
Fibonacci number (or F(3) which equals 2) divides every 3rd
Fibonacci number ((F(6), F(9), F(12), etc.)
|
1 1
2 1
3 2
4 3
5 5 6 8 7 13 8 21 9 34 10 55 11 89 12 144 |
2 is the 3rd Fibonacci
number. Every 3rd number
after 2 is divisible by 2 (it’s and even number).
3 is the 4th Fibonacci
number. Every 4th number
after 3 is divisible by 3.
5 is the 5th Fibonacci
number. Every 5th number
after 5 is divisible by 5.
8 is the 6th Fibonacci
number. Every 6th number
after 8 is divisible by 8.
13 is the 7th Fibonacci
number. Every 7th number
after 13 is divisible by 13.
21 is the 8th Fibonacci
number. Every 8th number
after 21 is divisible by 21.
34 is the 9th Fibonacci number. Every 9th number after 34 is
divisible by 34.
55 is the 10th Fibonacci
number. Every 10th number
after 55 is divisible by 55.
89 is the 11th Fibonacci
number. Every 11th number
after 89 is divisible by 89.
144 is the 12th Fibonacci
number. Every 12th number
after 144 is divisible by 144.
Etc.
|
David
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