Speaker: Keith Taylor
Title: Why is the Golden Ratio Special?
Affiliation: Dalhousie University
Date: Monday, April 14, 2008
Place and Time: Room 101, Love Building, 3:35-4:30 pm

Abstract. The golden ratio is the square root of five minus one divided by two. This remarkable number has special properties that result in it popping up in geometry (the ratio of the length of a side of a regular pentagon to the distance between two non-adjacent vertices), the growth patterns of many plants, and in solid state materials (quasi-crystals) as just a few examples. We will remind people of the definition of the golden ratio and some of the basic properties such as its relation with the Fibonacci sequence and its influence in phyllotaxis (think of the obvious spirals that stand out in the arrangement of seeds on a sunflower). Two interactive figures, mathlets, will be used to illuminate the properties in a visually striking manner. The talk has three goals: First, it attempts to spread understanding of how many patterns observed in nature are there for very fundamental, essentially mathematical, reasons. Second, it illustrates how powerful well-designed technology based learning tools can be. And, third, the golden ratio is just plain fun!