## Irrational Numbers: discovery, crisis, and resolution |

**Julius Barbanel**

Union College

January 22, 2007

4:45 pm

Bailey Hall 201

refreshments will be served in Bailey Hall 204

Pythagoras and his followers (who lived and worked about 2500 years ago) thought it obvious that any two line segments are commensurable, or, in other words, that given any two line segments, there is some third line segment that measures each. This assumption turns out to be equivalent to the statement "all real numbers are rational." Many ancient Greek geometric proofs used this assumption. When it was discovered that this assumption is false, it caused a major mathematical crisis. We shall explore the reasons why the Pythagoreans made this commensurability assumption, the discovery that it is false, the ensuing mathematical crisis, and the resolution of this crisis by Eudoxus.

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

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Sun Jul 15 18:57:41 EDT 2018 |