Unit Fractions

 

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Although the modern world inherited the wonderful architectural works of the ancient Egyptians, still the most outstanding aspect of their mathematics is the way they calculated when they needed to used fractions.

It may well be that mathematics which related to their architecture was more interesting than anything we have ever seen, but no written account of it came to us, and so we are left to admire the structure of the Egyptian fractions.

The Rhind Papyrus

Most of our knowledge of Egyptian mathematics comes from two sources -- the Rhind (or Ahmes) Papyrus and the Moscow Mathematical Papyrus. Click here to find more about both of them.

Unit Fractions

The most interesting concept described in the Rhind papyrus is the treatment of fractions since, of the 87 problems it contains, all but six deal with fractions. All Egyptian Fractions are unit fractions (in the form 1/n), which is a way of working unique to that culture. There was a special symbol for 2/3.

The Egyptians mainly used two scripts; the familiar hieroglyphics and the simpler hieratic which was the handwritten form where the scribe used a reed brush and ink. So hieratic is a corrupt hieroglyphic.

Click on the link to see other Egyptian numerals.

Click here to see how Egyptian fractions (unit fractions) were written.

Now, what is so remarkable about the use of unit fractions is the fact that they are in fact used to reduce a division between two numbers to the sums of unit fractions. An example would be dividing 2 by 43:

You will notice that no fraction is allowed to appear twice, but is not known how these particular unit fractions were derived. It is evident that there are many possible solutions, but it is not so evident why some solutions would be preferential to others.

It is interesting to note that the first section of Rhind Papyrus is a table of the division of 2 by every odd integer from 3 to 101, and it may be that the Egyptian scribes realised that the result of multiplying by 2 is the same as that of dividing 2 by n .

In fact, it may be that the decomposition for fractions of the form was the only necessary decomposition since Egyptians used the dyadic multiplication. This means that, instead of using times tables (as we do), they used two operations to multiply, doubling and adding.

Click here to find out about dyadic multiplication.

 

 

   

Click on the picture below to find more about Horus

Click on the picture below to find more about Horus Eye Fractions

More topics on Egyptian mathematics

Egyptian gods and mathematics

Rhynd and Moscow Papiri

An Egyptian scribe from the Fourth Dynasty.

To learn about gods which are related to mathematics, or learning, click here.

 

 

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