Eratosthenes Meets the GPS

Multiple representations of a problem encourage students to make and strengthen connections across mathematics. This article presents three solution methods that students can use to estimate the Earth's circumference. All solution methods involve proportional reasoning, require physical measurements, and draw upon basic concepts of geography, notably longitude and latitude. They range from a geometric representation first proposed by ancient Eratosthenes using simple measuring devices of meter sticks and protractors (with and without use of trigonometry) to the use of modern Global Positioning System (GPS) units