Egyptian fraction expansions

A FreeBasic program for finding Egyptian (or unit fraction) expansions.

Egypt_fr.bas returns at most six different Egyptian representations
of a given common fraction, not guaranteed to be optimal
in any sense, but sometimes quite elegant.

An Eye of Horus expansion with ro remainder is also given.

Methods

Fibonacci-Sylvester (1202/1880),
Golomb-Brown (1962/1995),
and Fibonacci-Hultsch (1895).

The third (or multiple) method reads practical numbers from file.

Results are in clutter-free format:

                       2   1   1  
for [ 3" 5  30 ] read  - + - + --  
                       3   5   30  

 

Copyright:

        (C) 2020 Djoser.j.Spacher, All rights reserved

License:

        GNU General Public License, GPL

      _____________________________________________

Dunton and Grimm, Fibonacci on Egyptian fractions (pdf)

K. Gong, Egyptian Fractions (pdf)

K. Brown, Reverse Greed for Unit Fractions

D. Eppstein, Algorithms for Egyptian Fractions

H. Vymazalová, The Wooden Tablets from Cairo

M. Gardner, Breaking the RMP 2/n Table Code