To introduce the fibonacci sequence using the recursive series to my Pre-Calc H class (although most of them know it), I came up with something on the fly that worked nicely. To set up the fibonacci sequence, I showed them a recursive program that calcuates the sequence in a very clear (but inefficient) way.
def fibonacci(n):
if n==1:
return 1
elif n==2:
return 1
else:
return fibonacci(n-1)+fibonacci(n-2)
for number in range(1,10):
print "fibonacci number " + str(number) + " is ",
print fibonacci(number)
This is probably the first time they’ve seen programming in person, so to make it real I gave a post-it to each student and then had them stand up in a line. I had the person at the start of the line write n=1 on their post-it, and then they continued to the end of the line, n=19. I gave the first two students in the line their fibonacci numbers 
Then I asked the person at the end of the line what his fibonacci number was (
Well this continued all the way back to the start, and then after 
…
To show the class how inefficient the above algorithm is, I calculated 
The Code:
def fibonacci(n):
if n==1:
print "Sage"
return 1
elif n==2:
print "Jessica"
return 1
else:
return fibonacci(n-1)+fibonacci(n-2)
print fibonacci(19)
The Output (Click to expand, but it’s very long. An interesting number of lines *hint*):
Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica 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Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage 4181 >>>
So that algorithm is very inefficient for calculating fibonacci numbers because it has no memory of the previous fibonacci numbers. When
Finally to cap it off, talk about the ratio of the fibonacci numbers that you’ve written on the board. These numbers tend towards the golden ratio (
Awesome.
Continue deep into math teacher land talking about phi and fibonacci numbers. Possibly share an applet like the following which shows that phi is present in seed growth in plants like sunflowers.
Seedhead.
Or show (or assign) a video about the Golden Ratio and Fibonacci like Keith Devlin’s talk where he discusses what is true and what is false about the golden ratio.
Cheers.
Dan
One Response to Fibonacci and Recursion