Set aside for a few days, it has turned "SICP" a few pages, this is caused by thinking Feibolaqi number of columns.
Defined Fib (n) = Fib (n-1) + Fib (n-2), and Fib (0) = 0, Fib (1) = 1.
Cited are: 0,1,1,2,3,5,8,13,21 ......
A book of the series satisfies Fib (n) is the closest integer, wherein
.
Easily (by the nature of the column number ) to give
another solution is less than 0, clearly do not meet the properties, it
has been verified.
But the divisor is how to generate it?
After check the information found by its general term formula (called ratio in the formula) naturally occurring on this part of the skip.
Consider again the class of non-Fib to 0 at the beginning of the number of columns, referred Fib (0) = a, Fib (1) = b, there are: a, b, a + b, a + 2b, 2a + 3b, 3a + 5b , 5a + 8b, ......
Obviously a, b respectively Fib standard growth, so it is:
Standard Fib has an interesting theorem:
And diverse and have proved simple enough evidence, such as proof of this combination of mathematics: English original , Chinese translations .