FIBONACCI-MATMOD_Week 1- Lesson 1 Numbers and Patterns
- 1. FIBONACCI SEQUENCE AND THE GOLDEN RATIO
- 2. PROPONENT • European mathematician 1175-1250 • Leonardo of Pisa. • Author of Liber abaci or Book of the Abacus.
- 3. FIBONACCI SEQUENCE • Generalized sequence of first two positive integers and the next number is the sum of the previous two, i.e. 1,1,2,3,5,8,13,21,…
- 4. SIGNIFICANCE •Has intrigued mathematicians for centuries. Shows up unexpectedly in architecture, science and nature (sunflowers & pineapples).
- 5. SIGNIFICANCE Has useful applications with •computer programming, •sorting of data, •generation of random numbers, etc.
- 6. Sunflower Seed head and the Fibonacci Sequence
- 7. FIBONACCI SEQUENCE AND THE GOLDEN RATIO •A remarkable property of the sequence is that the ratio between two numbers in the sequence eventually approaches the “Golden Ratio” as a limit.
- 8. APPLICATION
- 9. APPLICATION
- 10. GOLDEN RATIO • Famous Irrational number phi— 1.61803398… • Used extensively by Ancient Greeks in architecturE
- 11. GOLDEN RATIO • bringing balance, proportion, and careful consideration
- 12. • Da Vinci studied extensively the ratio and body proportions. GOLDEN RATIO
- 13. SUMMARY • Fibonacci Sequence has been around for hundreds of years. • Golden Ratio has been used for thousands of years. • Both concepts are still in use today and continue to interest us.
- 14. REFERENCES Gardner, Martin (1979). Fibonacci and Lucas Numbers. In Mathematical Circus (pp. 152-160), New York:Alfred Knopf Gardner, Martin (1961). Phi: The Golden Ratio. In Mathematical Puzzles & Diversions (pp.89-100), New York: Simon and Schuster. Web Page “The Golden Ratio” by Steve Blacker, Jeanette Ploanski and Marc Schwach, http://www.geom.umn.edu/~demo5337/s97b/fibonacci.html