
Re: Unitary (Egyptian) fractions
Posted:
Mar 20, 2000 3:25 PM


milogardner@juno.com (Milo Gardner) writes: > It is interesting that no one has taken the Egyptian position that > the first term of the series can be 2/3 or 3/4. Considering that > 732/733 is requires a large first term, I suspect that one David > Eppstein's 40 + algorithmic methods, or one of Kevin Brown 'inverse > methods' should create a series shorter or equal to the HorusEye > 5term series. YES, TO BE EGYPTIAN 5TERM OR SHORTER SERIES is a > request when converting any rational number to a finite series.
I don't think I really have 40 different methods, and they're mostly not original to me.
Using 2/3 at least would be more historically accurate if less aesthetically pleasing. However there is no 5term series for 732/733 using 2/3, it requires six, e.g.
732/733 = 2/3 + 1/5 + 1/8 + 1/145 + 1/17592 + 1/63771 = 3/4 + 1/5 + 1/24 + 1/145 + 1/17592 + 1/63771
(The requirement for six terms follows easily from the facts that 732/733 needs seven unit fractions and that 2/3 or 3/4 can be expanded into two unit fractions each.)  David Eppstein UC Irvine Dept. of Information & Computer Science eppstein@ics.uci.edu http://www.ics.uci.edu/~eppstein/

