Mark Dominus on 26 Jan 2005 22:17:11 0000 
The topic of this talk sits on a nice part of the boundary between mathematics and computer science and may interest a lot of people. I'm doing this talk twice: once to rehearse, and once for real. The rehearsal version of my talk will occur on Wednesday, 2 February at 6PM in Levine 307 on the campus of the University of Pennsylvania. (Many thanks to the Penn chapter of Pi Mu Epsilon and the Dining Philosophers for organizing this.) The event for which I'm rehearsing is at 4:15 PM on Monday, 7 February at Haverford College. Complete details are at http://www.haverford.edu/math/colloquium/ You're welcome to attend either (or both) of these. Here's the abstract: Multiprecision arithmetic algorithms usually represent real numbers as decimals, or perhaps as their base2^n analogues. But this representation has some puzzling properties. For example, there is no exact representation of even as simple a number as onethird. Continued fractions are a practical but littleknown alternative. Continued fractions are a representation of the real numbers that are in many ways more mathematically natural than the usual decimal or binary representations. All rational numbers have simple representations, and so do many irrational numbers, such as sqrt(2) and exp(1). One reason that continued fractions are not often used, however, is that it's not clear how to involve them in basic operations like addition and multiplication. This was an unsolved problem until 1972, when Bill Gosper found practical algorithms for continued fraction arithmetic. I'll explain what continued fractions are and why they are interesting, how to represent them in computer programs, and how to calculate with them. Feel free to send me email with questions if you have any.  **Majordomo list services provided by PANIX <URL:http://www.panix.com>** **To Unsubscribe, send "unsubscribe phl" to majordomo@lists.pm.org**

