Mathematics-Fibonacci-sequence-and-Patterns.ppt
- 1. Mathematics….Fibonacci & patterns • I have worked with others to explore, and present our findings on, how mathematics impacts on the world and the important part it has played in advances and inventions. MTH 2-12a •
- 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 ? • Or if it could have been otherwise?
- 6. Mathematics can be fun! • There is mathematics at every level of life… • …you just need to look! • So let’s do just that!
- 7. 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
- 8. 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
- 9. Nature and Fibonacci White calla lily
- 12. Nature and Fibonacci Black eyed susan
- 13. More Fibonacci • Pinecones and pineapples… • Count the number of spirals.
- 14. Spirals in a pine cone: clockwise and anti-clockwise
- 15. And more
- 16. Spirals
- 17. Spirals
- 18. Golden Ratio • Compute the ratio of Fibonacci numbers: 2 ÷ 1 = 3 ÷ 2 = 5 ÷ 3 = 8 ÷ 5 = 13 ÷ 8 = 21 ÷ 13 =
- 19. Another fun way to get Golden ratio • Choose any number, say x. • Find x + 1 • Find 1/x • Do the above two steps over and over and over…
- 20. The Golden ratio in nature
- 21. Great Wall of China Parthenon, Greece In Art & Architecture.. The Mona Lisa
- 22. So why do spirals occur ? • Helps in efficient packing of seeds. • But flowers and pinecones have to deal with growing.
- 23. Finding Golden ratio • As seeds grow older they are pushed out.
- 24. What we learnt today… • Fibonacci numbers: • Pineapples and pinecones: # spirals • Spirals in nature • The Golden ratio