Introduction

Who first determined the size of the Earth? How did they do it? These fundamental questions arise in studying early Greek, Indian and Islamic mathematical astronomy. In this article we look at the attempts of Eratosthenes, Posidonius, and al-Bīrūnī to determine the circumference of the Earth and ways to use this topic in the classroom. These calculations use only basic knowledge of geometry and trigonometry, so that instructors in many different courses can include this topic in their syllabus. It would be appropriate to discuss the problem in a high school or college geometry class, in a precalculus class, a history of mathematics class, or in a freshman mathematics survey class.

There are three primary methods for determining the circumference of the Earth: using the lengths of shadows, the elevation of stars, or the altitude of a mountain. Explaining these methods can be done in roughly two hours of class time. If an instructor wants to assign students a project to carry out one of these calculations then one or two more hours may be needed to complete the topic (assuming that the students do measurements during class time).

There are certain geographical and astronomical terms that are frequently used in this topic and should be defined for students. The position of a point on the Earth's surface is given by two coordinates, its latitude and longitude. The latitude of a point ismeasured by how far it is north or south of the equator, so that points of equal latitude form a circle parallel to the equator. Latitude is measured in degrees from the equator (0°) to the poles (90°).