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Fibonacci numbers
1. Fibonacci sequence and golden ratio
The Fibonacci sequence is as follows.
1 1 2 3 5 8 13 21 34 55 ...
The sequence starts with two
1's.
Each following term is the sum of the previous two terms.
Fibonacci sequence:
1 1 2 3 5 8 13 21 34 ...
The Fibonacci sequence is related to the golden ratio, golden rectangles, etc.
2. Golden rectangle animation
What is happening here?
3. Golden rectangle areas
4. Golden ratio
5. Sunflowers
Many plants, such as sunflowers, grow in a pattern that matches the Fibonacci sequence.
6. Fibonacci in nature
The perfect rectangle is related to the nautilus shell.
This sequence appears often in nature, must be precisely tuned, and has many implication for a created universe.
7. Pentagram
The pentagram is filled with golden ratios in an endless descent.
The Fibonacci sequence goes as follows.
Fib(0) = 0
Fib(1) = 1
Fib(i) = Fib(i-1) + Fib(i-2)
The first few terms are as follows.
0 1 1 2 3 5 8 13 21 34 55 89 ...
Fibonacci sequences appear often in nature (e.g., fractal), in mathematics, and in the analysis of computer algorithms.
If the first Fibonacci term is 1 and the second Fibonacci term is 1, what is the eighth Fibonacci term? Show your work and clearly identify the answer.
Try writing a short Python program to calculate and print the first 30 Fibonacci numbers. Details to be available after class.
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