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# Continued Fractions and Baseball Statistics

by

Susan Niefield
Union College

November 2, 2009
4:30 pm
Bailey Hall 201

Refreshments will be served at 4:15 in Bailey 204

## Abstract:

In honor of the Yankees' trip to the World Series this year, we consider the following application of number theory.

Suppose you know a player's batting average and the number of games the team has played. What are the possible batting records for that player?

For example, A-Rod batted $.429$ in the 6 games of the ALCS this year, but his record was obviously not 429 for 1000. (It was 9 for 21.)

We will show how finite continued fractions $$a_0+ {1\over{\displaystyle a_1 + {1\over{\displaystyle \ddots + {1\over {a_{n-1}+\displaystyle {1\over a_n}}}}}}}$$ can be used to find all batting records that lead to a given batting average knowing only the number of games that were played. The algorithm we describe was part of the Senior Thesis written last fall by Mike Topka '09.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.
Up: Student Seminars for 2009
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