
This article describes how a fraction is written as the sum of stem fractions.
A stem fraction is a fraction that has 1 as numerator.
A (Windows) program is added that accomplishes the task.
Click on the download (lightning) icon at the top of this page.
There is no installation procedure, simply copy the program to a folder of choice.
In ancient Egypt people did not know fractions like we do.
Instead, stemfractions were used.
However there were some exceptions:
and
,
using special symbols.
So was called “the two parts”.
The addition to 1 is “the third part”.
Each fraction may be written as the sum of different stemfractions.
= + + +
But this result is not unique:
= +
, but also = + +
However, if we subtract the biggest possible stemfraction, the split up is unique.
This is the procedure for stemfraction splitting.
Take .
Because 2 < < 3
we have < <
So
is the biggest stemfraction that is smaller than .
Decrease
by
This yields − = .
Because 8 < < 9
we get < < .
So
the biggest stemfraction smaller than
.
Decrease
by .
This yields − = .
And we found = + + .
The same procedure is used over and over.
In this proces, the denominator may grow very large.
In the program, the denominator size may be 19 digits long, otherwise a "denominator overflow" is reported.
Fractions that produce an overflow are: 44/53 , 5/61 , 60/67....
The biggest non overflow result is the splitup of 182/193
Interested in the program?
[HERE ] is the complete Delphi7 project.

