Why 𝜋/5 should be included among the special angles
Abstract:
Since the earliest development of trigonometry in the days of Ptolemy and continuing up to our day special angles have been used while learning and applying the subject. These angles include 90, 60, 45 and 30 degrees or in radian measure 𝜋/2, 𝜋/3, 𝜋/4, and 𝜋/6. There are many good pedagogical and practical reasons to study the trigonometric function values of these angles. But an astute student may note that 𝜋/5 seems to be missing its rightful place in this list. Historically the special angle 𝜋/5 played an important role in applications and has beautiful and surprising geometrical implications including the golden ratio. We will look at these applications and connections in a bid to restore 𝜋/5 to its historic position as a special angle.
This presentation will be both practical and historical and should be of interest to a wide audience.
Bio:
Dr. Troy Goodsell is a professor of Mathematics at Brigham Young University-Idaho where he has taught since 2001. Previously he held positions at McMurry University in Abilene Texas, Pittsburg State University in Pittsburg Kansas, and Brigham Young University in Provo Utah. He received his PhD. from Brigham Young University and did his undergraduate work at the University of Utah. The history of mathematics is his main area of interest, and he has given a number of talks on the subject at both MAA section meetings and at the national meetings. He is deeply interested in both the teaching of a wide variety of mathematics courses and in helping the students learn the history of the subject so as to understand the culture and society and individuals that brought the science of mathematics to us. When not doing mathematics, he enjoys spending time with his children and grandchildren and enjoys camping and many other outdoor activities.