## Doubling the Cube: How it was done by the ancient Greeks |

**Julius Barbanel**

Union College

February 25, 2008

4:15 pm

Bailey Hall 207

Refreshments will be served in Bailey 204 at 4 pm

According to legend, the people in the Greek city of Delos were suffering from a terrible plague. Relief was sought from the oracle at Delphi. Delos had a cubical altar that was used in religious ceremonies. The oracle told the people of Delos that they could rid themselves of the plague if they constructed a new cubical altar having double the volume. How would one do this? ("Double the length of a side" is certainly the wrong answer!) Some of the most brilliant ancient Greek mathematicians worked on this problem. We present two solutions. One is a mechanical procedure by Eratosthenes (276-194BC) involving moving triangles. The other is by Archytas (428-350BC) and involves a three-dimensional construction in which a certain point is determined as the intersection of three surfaces of revolution.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

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