Math 149S. Capstone Mathematics for Teachers.
Homework 9
The goal of this activity is to mimic Archimedes's computations to find an approximation for the number π. You may use the Pythagorean theorem, coordinate geometry (e.g. the distance formula, since it easily follows from the Pythagoream theorem), and a calculator to approximate the values of square roots to save time (this can be easily done by hand, too, but is just time-consuming). However, you may NOT use trigonometry (for example, you may NOT use a calculator to find sin(22.5o) - this was not yet available at the time of Archimedes!)
Consider a circle of radius 1. Its circumference is 2π.
Remark: Archimedes used polygons with up to 96 sides.