The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: unitary (Egyptian) fractions
Replies: 17   Last Post: Mar 31, 2000 6:38 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 128
Registered: 12/8/04
Re: Unitary (Egyptian) fractions
Posted: Mar 20, 2000 3:25 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply (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 Horus-Eye
> 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 5-term 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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.