FIBONACCI-MATMOD_Week 1- Lesson 1 Numbers and Patterns

Numbers and Pattern Introduction to Fibonacci Sequence

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