541 Interactive ppt Fibonacci Sequence
- 2. Who is Leonardo of Pisa? Famous for spreading the use of Arabic number system and knowledge of the Fibonacci sequence.
- 4. The Fibonacci Sequence }+ The Fibonacci Sequence a recursive arithmetic sequence. 1 1 2
- 5. The Fibonacci Sequence This pattern continues and follows the rule: xn = xn-1 + xn-2 }+ xn is term number "n" xn-1 is the previous term (n-1) xn-2 is the term before that (n-2) 1 1 2 3
- 6. }+ The Fibonacci Sequence 1 1 2 3 5 8 13 21 34 55 89 This sequence can continue on forever…
- 7. The “Magic” of Fibonacci Numbers
- 8. Fibonacci Numbers in Nature
- 10. Arcs drawn through each square connect to make a spiral
- 11. Seeing Spirals…
- 13. Count those spirals… Fibonacci Numbers!!!
- 14. Let’s do it again…
- 15. Doodling in Math Class teaches us….
- 16. Make your own Fibonacci Spiral http://chromatism.net/cfsg.htm
- 17. The Fibonacci Sequence leads us to the Golden Ratio
- 19. What is the Golden Ratio? The ratio between successive Fibonacci Numbers will eventually give you the Golden Ratio: A B B/A 1 1 1 1 2 2 2 3 1.5 3 5 1.666666666... 5 8 1.6 8 13 1.625 13 21 1.615384615... ... ... ... 144 233 1.618055556... 233 377 1.618025751...
- 20. The importance of Phi Φ If the longer segment divided by the smaller segment is also equal to the whole length divided by the longer part then you will have the golden ratio.
- 21. The Golden Rectangle Experiment with the golden ratio at http://www.mathsisfun.com/numbers/golden-ratio.html
- 22. Golden Rectangle and the Mona Lisa?
- 23. The Golden Ratio is considered to be pleasing to the eye and can be found in art, architecture and music.
- 24. The Divine Proportion of the Human Body
- 25. Math is Beautiful The Golden Ratio can be applied to the human face to determine beauty.
- 26. Math of Beauty Interactive According to the Golden Ratio, Jessica Simpson is considered beautiful! Visit this site to participate in a fun activity: http://www.intmath.com/numbers/math-ofbeauty.php
- 27. Resources Benjamin, A. (2013). The Magic of Fibonacci Numbers. Retrieved from http://www.youtube.com/watch?v=SjSHVDfXHQ4 Fibonacci Sequence. (2013). Math is Fun. Retrieved from http://www.mathsisfun.com/numbers/fibonacci-sequence.html Hart, V. (2011). Doodling in Math: Spirals, Fibonacci, and Being a Plant. Retrieved from http://www.youtube.com/watch?v=ahXIMUkSXX0 Inspiration Green (n.d.). The Fibonacci Sequence and Nature. Retrieved from http://www.inspirationgreen.com/fibonacci-sequence-in-nature.html Lamb, R. (24 June 2008). "How are Fibonacci numbers expressed in nature?“ Retrieved from http://science.howstuffworks.com/life/evolution/fibonacci-nature.htm Number Patterns. (n.d.). Retrieved from http://www.magicmathworks.org/exhibits/numberpatterns/index.html Spirals and the Golden Ratio. (August 25, 2012). Retrieved from http://www.goldennumber.net/spirals/