University of Arizona
Institute for Mathematics and Education

The Tucson High School Math Teachers' Circle

Session September 22, 2009
Dr.Joceline Lega presented Nature's Golden Rule



Click here for a copy of the Powerpoint presentation.
Click here for GoldenNumber.Net, which is a website dedicated to phi and its applications.

Dr. Lega began her talk by providing an overview of the many programs sponsored by the Institute for Mathematics and Education. IME is the host for our Teachers' Circles. Joceline is the director of IME.
In the exploration of Nature's Golden Rule , participants created a spreadsheet to list a column of Fibonacci numbers. They then created a column of ratios of each Fibonacci number to the previous one (Fn/Fn-1). The ratios converged to a specific value called phi (φ). Participants explored methods to model the value of phi both algebraically and geometrically. The value of phi is the positive root of the quadratic equation: λ² - λ - 1




DeAnnaJoceline
DeAnna McDonald shows her "bunny model".Joceline introduces the bunny
population problem.
DeAnnaToniSteve CarolynCarolineMyrna
DeAnna McDonald, Toni Moore, and
Steve Cutler share ideas.
Carolyn Hollis, Caroline Torres, and Myrna Hahn
make sense of the population data

Photos taken by Ji Li.