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Patterns in Nature

What patterns can we find in nature? Plants, flowers and fruits have all kinds of patterns, from petal numbers that are in the Fibonacci sequence, to symmetry, fractals and tessellation.

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Patterns in Nature

1. 1. Who IS Fibonacci? Fibonacci was an Italian mathematician. He was really named Leonardo de Pisa but his nickname was Fibonacci. About 800 years ago, in 1202, he wrote himself a Maths problem all about rabbits that went like this: "A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair breed a new pair from which the second month on becomes productive?" (Liber abbaci, pp. 283-284)
2. 2. Fibonacci’s Rabbits! Like all good mathematicians he stayed working on this problem for months and eventually came up with a solution:
3. 3. A load of…  Fibonacci’s rabbit theory turned out not to be true BUT the sequence he created IS incredibly useful…  The sequence goes: Can you work 1, 1, 2, 3, 5, 8, 13, 21, 34 …. out which numbers come next?
4. 4. Continue the sequence…  Fibonacci’s sequence is made by adding the two previous numbers together to create the next, starting with zero and one:  0+1=1 1+1=2 1+2=3 2+3=5 3+5=8 …keep going in your notebooks!
5. 5.  The sequence Fibonacci created may not have solved his rabbit reproduction problem  BUT other mathematicians looked at his numbers and started seeing them all over the place.
6. 6. Find Fibonacci!
7. 7. Other patterns in nature…  Nature may be full of Fibonacci but not EVERY plant or flower has a Fibonacci number.  There are plenty of other interesting patterns to look out for.  Can you think of any patterns?
8. 8. 1. Symmetry… SYMMETRY – You can find symmetry in leaves, flowers, insects and animals. Can you think of any examples?
9. 9. 2. Spirals… Can you count the spirals??
10. 10. A Fibonacci number?
11. 11. Check this out!  Look at what your teacher has brought in and talk about any pattern you see.
12. 12. 3. Fractals…  Some plants have fractal patterns. A fractal is a never-ending pattern that repeats itself at different scales. A fractal continually reproduces copies of itself in various sizes and/or directions.  Fractals are extremely complex, sometimes infinitely complex.
13. 13. Watch this fractal zoooom!  Watch from 3:05 for one minute:  http://www.youtube.com/watch?v=IIOQcJZlJE  Watch the same minute again and write your own definition of a fractal.
14. 14. A never-ending pattern
15. 15. Tessellation… Sometimes in nature we find tessellation. A tessellation is a repeating pattern of polygons that covers a flat surface with no gaps or overlaps.   Think about when you tile a floor. No gaps and no overlapping tiles! There are regular tessellations (all the same shape tiles) and irregular (a mix of shapes).  Can you think of any examples in nature?
16. 16. Where is THIS tessellation from?!
17. 17. Pattern hunters!  With all these patterns to search for, fifth graders will be pattern hunters on Friday!  With your clipboards, pencils and lots of curiosity, you will be searching for and sketching patterns. Good luck! 
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What patterns can we find in nature? Plants, flowers and fruits have all kinds of patterns, from petal numbers that are in the Fibonacci sequence, to symmetry, fractals and tessellation.

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