Math Department (Thesis/2007-08)

The Three Special Construction Problems of Ancient Greek Mathematics

Under the direction of: Julius Barbanel

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Most mathematical historians agree that abstract mathematics began with the ancient Greeks. Three problems drew the attention of many of the greatest of the ancient Greek mathematicians and came to be known as the "Special Construction Problems." These are: the trisection of any angle, the squaring of the circle (i.e., given a circle, construct a square having the same area), and doubling the cube (i.e., given a cube, construct a cube having twice the volume.) Modern methods have been used to show that none of these problems can be solved using the traditional geometric tools of straightedge and compass. The ancient Greeks did find a variety of solutions to these problems by allowing certain other types of construction methods. Among the ancient Greeks who contributed to the study of these problems are: Archimedes, Archytas, Eratosthenes, Euclid, Eudoxus, Hippias, Hippocrates, Menaechmus, Nicomedes, and Plato.

Math Department web pages Created: 25 Apr 2007 Last modified: 25 Apr 2007 Comments to: math@union.edu

Thesis Topics - J. Barbanel Thesis Topics for 2007-2008 2007-2008 Thesis Letter