Från: Anders Tiberg Till: Ämne: Edge Datum: den 25 maj 2001 21:32 Program Edge v1.30 written by Anders Tiberg. This program 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. 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