Frn: Anders Tiberg <anders.tiberg@telia.com>
Till: <filearchive@ticalc.org>
mne: Edge
Datum:  den 1 september 2001 18:29


         
   Programs Edge v1.40 and EFrac written by Anders Tiberg.


The program Edge gives a measurment on how hard a number is to deal
with.Irrational numbers can't be written as a fraction and so they
could be said to be "edgy".The value is concieved by the inequality:
abs(r-n/d)*d^2<=1/Ln,where Ln is a Lagrange number.(Lagrange was
the first to prove this theorem for various real numbers)The first
ones are \/5(related to tau=.5(1+\/5)),\/8(rel.to \/2), \/(221/25)
and they have the form \/(9-4/m^2),where m is a Markov number.
(Markov numbers comes from the solutions of the diofantic equation:
x^2+y^2+z^2=3xyz)   
You enter a real number and the program checks a hundred values to
pick the most favourable one with respect to the value given by the
relation above.This means that even rational numbers,if the hundred
values won't find the fraction,will appear to be "edgy". Great for
economic approximations of irrational and other numbers. 

The program EFrac features a primitive form of continued fraction
(see AFrac in this directory)You enter a real number and a tolera-
nce and the program will approximate the number as a fraction with
an error in the numerator that is smaller than or equal to the to-
lerance you give(to be used for T=.05 down to T=.001) It will also
give you the "edgyness", or the economy if you like, for that spe-
cific fraction, as will Edge.

If you're interested in numbers try to get hold on The Book of Numbers
by John H.Conway and Richard K.Guy.Copyright 1996 Springer-Verlag.N.Y.

        
       
       Questions and/or input mailto: anders.tiberg@telia.com


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