LET’S FIBONACCIBY GROUP 3.

彭旺春 , 林易宁

刘雅 , 陈惠霞

GAME TIME

What?! 64=65 ?!! What happened? Be careful… 8,5,13 Get more… 1,1,2,3,5,8,13,21,34,55,89,144… Familiar? Fibonacci Number !!!

FIBONACCI NUMBERS

Fibonacci is a mathematician and he find an famous sequence , which is we denote by {F[n]}.

F[0]=1 F[1]=1 F[n+1]=F[n]+F[n-1]

Because that sequence is very important , it has been named as the Fibonacci Sequence.

FIBONACCI TRICKgap

MATHEMATICAL INDUCTION

ANOTHER SITUATION

HOW TO GET A PERFECT RECTANGLE?

y

y

y

x

x

x

x+yx

x

FIBONACCI WITH 0.618· · ·

The golden ratio is uneasy to use. Can you draw a line with the length of

0.618· · ·

Certainly the line with a length of a fraction would be easy to draw.

So we need a good fraction to approaching the golden ratio.

The golden ratio A fraction

AN ARITHMETIC TO GET THE FRACTION

Assume the golden cut ratio = x . Then the definition of the golden ratio is :

We can get:

AN ARITHMETIC TO GET THE FRACTION

The closest integer to approach x is 1.

So we get

What if we use this To get

FIBONACCI & BOTANY

REFERENCE

Zhenkui Wu. Fibonacci Sequence Appreciation. Harbin institute of technology press.2012.

Feifei Jia. The research and the application of Fibonacci Sequence. Technology Innovation a. 2014(13).

THE END

Thanks