The Three Unsolved Problems of Ancient Greece | Research & Encyclopedia Articles

The Three Unsolved Problems of Ancient Greece

Overview

The geometry of ancient Greece, as characterized by Euclid's famous book, the Elements, has formed the basis of much of modern mathematical thought. For example, the Greek insistence on strict methods of proof has survived to this day. The methods and theorems found in the Elements were taught to schoolchildren almost unchanged until the twentieth century. Even today, school geometry is essentially the same geometry as that composed by Euclid (c. 325-c. 265 B.C.) well over two millennia ago.

It became the practice in traditional Greek mathematics to accept geometrical constructions only if they could be performed with an unmarked straightedge and a compass. This custom is derived from the first three postulates of Euclid's Elements. A postulate is a statement that is accepted as true without proof. In the Elements, Euclid gives five postulates that are the starting points for the propositions or theorems given in the body of the book. The first three of these postulates address the construction of a straight line and a circle:

1. A straight line can be drawn between any two points.
2. A finite straight line can be extended indefinitely.
3. A circle can be drawn with any center point and any line segment as a radius.

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