1. Patterns in Nature

2. Mathematics….& patterns
We don’t know all the answers unlike in class!
Mathematics is a science which looks for patterns and structure
Language for understanding nature’s patterns

3. Studying cool patterns in nature
Astronomers model the patterns found in giant spiral galaxies
Physicists: movements of atoms
Biologists & Doctors try to understand the random patterns of growth, spread of disease .
Geologists study the meandering of rivers, tortuous coastlines, and awe-inspiring mountain landscapes.

4. Patterns in nature Many different patterns arise in nature.
Do we always know what they mean ?

5. Patterns in plants

7. Mathematics can be fun! There is mathematics at every level of life…
…you just need to look!
So let’s do just that!

8. Busy Bunnies A newly born male-female pair starts.
Can mate once they are 1 month old.
Female produces a pair 1 month after mating.
And so on…

9. Busy Bunnies

10. Busy Bunnies

11. Fibonacci Series The rule for the sequence? 1, 1, 2, 3, ?, ?, ….
The Answer :
1, 1, 2, 3, 5, 8, 13, 24, …
1+ 1 = 2
1+ 2 = 3
2+ 3 = 5
3+ 5 = 8
5+ 8 = 13
8+ 13 = 24

12. Who was Fibonacci ? Greatest European mathematician of the middle ages
Born in Pisa, Italy, the city with the famous Leaning Tower,~ 1175 AD
Major contributions in arithmetic, algebra and number theory
Decimal system

13. Nature and Fibonacci
White calla lily

14. Nature and Fibonacci
Euphorbia

15. Nature and Fibonacci
trillium

16. Nature and Fibonacci
Black eyed susan

17. More Fibonacci
Pinecones and pineapples…
Count the number of spirals.

18. Spirals in a pine cone: clockwise and anti-clockwise

19. And more

20. Spirals

21. Spirals

22. Golden Ratio Compute the ratio of Fibonacci numbers: 2 ÷ 1 = 3 ÷ 2 =
5 ÷ 3 =
8 ÷ 5 =
13 ÷ 8 =
21 ÷ 13 =

23. Another fun way to get Golden ratio
Choose any number, say x.
Find x + 1
Find 1/x (reciprocal)
Do the above two steps over and over and over…

24. Another fun way to get Golden ratio
Choose any number, say x.
Find x + 1
Find square root of result
Do the above two steps over and over and over…

25. The Golden ratio
in nature

26. In Art & Architecture..
Great Wall of China
Parthenon, Greece
The Mona Lisa

27. What we learnt today… Fibonacci numbers: Busy Bunnies
Pineapples and pinecones: # spirals
Spirals in nature
The Golden ratio