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Filename egyptian1.zip (Download)
Description AEGYPT2: This program decomposes fractions into sums of unit fractions: Egyptian fractions. The ancient Egyptians did not write 5/8, but 1/2+1/8, because they didn't have a system for the compact notation m/n, hence the name. They are presented, in general, in descending order, i.e. the denominators get smaller and smaller. The method in this program is to subtract the second biggest, or sometimes the third, or smaller, biggest unit fraction from the number that results in the remainder getting a smaller denominator. This makes it likely, but not necessary, that the next such unit fraction to subtract is bigger than the previous. This is repeated until the remainder itself is a unit fraction. With this method the unit fractions does not become so small as with Fibonnaci's method. When finished, the program pauses a list with the unit fractions, and then shows a list with their denominators. AEGYPT3: This program is different, but works in principle the same way. However it gives the same answers. At least for the numbers I've checked. AEGYPT4: This program is a modification of Fibonnaci's method. It gives pretty much the same answers as the other programs. But here the unit fractions become smaller and smaller in general. AEGYPT0: This program uses Fibonnaci's method. It is submitted for comparison. There is a link to a page on the subject in the text file.
Author Anders Tiberg (anders.tiberg@telia.com)
Category TI-83/84 Plus BASIC Math Programs (Arithmetic)
File Size 2,764 bytes
File Date and Time Sun Aug 5 18:09:30 2012
Documentation Included? Yes



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Archive Contents
Name Size
AEGYPT0.8xp   222
AEGYPT2,3,4&0.rtf   2173
AEGYPT2.8xp   467
AEGYPT3.8xp   510
AEGYPT4.8xp   395

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