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