Egyptian-Fraction Expansions Of REALS

[Thomas Baruchel]

On Tue, Jan 20, 2004 at 11:31:13PM -0500, Jud McCranie wrote:
> No, don't write it as 1+1+1.  For the sequence, make the first term the 
> integer part and continue with the denominators.  For one thing, the 
> Egyptians didn't do that.  Secondly, the sequence could start with a very 
> long string of 1s.  (Alternatively, skip the integer part altogether.)

Right. Besides, the initial motivation for writing 1+1+1 was not good,
because the general mind of egyptian fractions is to avoid using
twice a fraction with identical denominator: 1/3+1/3 is forbidden.
Just starting with "3+" is much better than "1+1+1" which would certainly
not be "more egyptian"...

-- 
« nous devons agir comme si la chose qui peut-être ne sera pas devait
être » (Kant, Métaphysique des moeurs, doctrine du droit, II conclusion)

  Thomas Baruchel <thomas.baruchel at laposte.net>