    Stemfractions  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.

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.
However there were some exceptions:
 2 3
and
 3 4
, using special symbols.

So
 2 3
was called “the two parts”.
The addition to 1 is “the third part”.

Each fraction may be written as the sum of different stemfractions.
 8 11
=
 1 2
+
 1 5
+
 1 37
+
 1 4070

But this result is not unique:
 2 19
=
 1 10
+
 1 190
, but also
 2 19
=
 1 11
+
 1 70
+
 1 14630

However, if we subtract the biggest possible stemfraction, the split up is unique.
This is the procedure for stemfraction splitting.

Take
 5 11
.
Because 2 <
 11 5
< 3
we have
 1 3
<
 5 11
<
 1 2

So
 1 3
is the biggest stemfraction that is smaller than
 5 11
.
Decrease
 5 11
by
 1 3

This yields
 5 11
−
 1 3
=
 4 33
.
Because 8 <
 33 4
< 9
we get
 1 9
<
 4 33
<
 1 8
.
So
 1 9
the biggest stemfraction smaller than
 4 33
.
Decrease
 4 33
by
 1 9
.
This yields
 4 33
−
 1 9
=
 1 99
.
And we found
 5 11
=
 1 3
+
 1 9
+
 1 99
.

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 Delphi-7 project.   