Upcoming talks on "Arithmetic with continued fractions"

[mjd-perl-pm@plover.com (Mark Dominus)]

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 base-2^n
        analogues. But this representation has some puzzling
        properties. For example, there is no exact representation of
        even as simple a number as one-third. Continued fractions are
        a practical but little-known 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.
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