Egyptian number system. History, description, advantages and disadvantages, examples of the ancient Egyptian number system

Few people think that the techniques and formulas that we use to calculate simple or complex numbers have been formed over many centuries, and in different parts of the world. Modern mathematical skills, with which even a first-grader is familiar, were previously unbearable for the cleverest people. A huge contribution to the development of this industry was made by the Egyptian number system, some of which we still use in its original form.

Short definition

Historians know for certain that in any ancient civilization writing developed primarily, and numerical values always stood in second place. For this reason, there are a lot of inaccuracies in the mathematics of the past millennia, and modern experts sometimes puzzle their heads in similar puzzles. The Egyptian system of numbering was not an exception, which, incidentally, was also non-positional. This means that the position of a single digit in the number record does not change the total value. As an example, we can consider the value of 15, where 1 - in the first place, and 5 - in the second place. If we change these figures in places, we get a much larger number. But the ancient Egyptian system of calculation of such changes did not assume. Even in the most multivalued number all its components were recorded in an arbitrary order.

At once we will notice, that modern inhabitants of this hot country use the same Arabian digits, as we, writing them in strict conformity with the necessary order and from left to right.

What were the signs?

To record the numbers, the Egyptians used hieroglyphs, and there were not so many of them. Duplicating them according to a certain rule, it was possible to obtain a number of any value, however, this would require a large amount of papyrus. At the initial stage of existence the Egyptian hieroglyphic number system contained the figures 1, 10, 100, 1000 and 10,000. Later, more significant numbers appeared, multiples of 10. If one of the above indicators was to be recorded, they used such characters:

To write down a number that is not a multiple of ten, this simple technique was applied:

Decoding numbers

As a result of the example given above, we see that in the first place we have six hundred, followed by two dozen and at the end two units. Similarly, any other numbers are recorded for which thousands and tens of thousands can be used. However, this example is written from left to right, so that the modern reader could correctly understand it, only in fact the Egyptian number system was not so accurate. The same value could be written from right to left, to understand where the beginning, and where the end, had to be, drawing on the figure with the greatest value. A similar reference point will be required if the numbers in large numbers are written out randomly (since the system is non-positional).

Fractions are also important

The Egyptians had mastered mathematics before many others. For this reason, at one point only the numbers became small, and fractions were gradually introduced. Since the ancient Egyptian number system is considered hieroglyphic, symbols were also used to write numerators and denominators. For ½ there was a special and invariable sign, and all other indicators were formed in the same way that was used for large numbers. In the numerator there was always a symbol imitating the shape of the human eye, and in the denominator the number was already indicated.

Mathematical Operations

If there are numbers, they are added and subtracted, multiplied and divided. The Egyptian number system coped with this task perfectly, although it had its own specificity. The easiest way was to fold and subtract. For this, the hieroglyphs of two numbers were written in a row, and a change in the categories was taken into account. It is more difficult to understand how they multiplied, since this process is little like modern. There were two columns, one of them started with one, and the other with the second multiplier. Then they started to double each of these numbers, writing a new result under the previous one. When the individual factors of the first column were able to collect the missing multiplier, the results were summed up. More precisely, you can understand this process by looking at the table. In this case, 7 is multiplied by 22:

The result in the first column 8 already exceeds 7, so the doubling ends at 4. 1 + 2 + 4 = 7, and 22 + 44 + 88 = 154. This answer is correct, although it was received by such a non-standard way for us.

Subtraction and division were performed in the reverse order addition and multiplication.

Why was the Egyptian system formed?

The history of the appearance of the hieroglyphs that replace the numbers is just as vague as the emergence of the whole Egyptian civilization. Its birth dates back to the second half of the third millennium BC. It is generally believed that such precision was a necessary measure in those days. Egypt was already a full-fledged state and every year it became more powerful and broader. The construction of temples was carried out, records were kept in the main governing bodies, and in order to combine all this, the authorities decided to introduce this system of accounts. It existed long enough - until the X century AD, after which it replaced the hieratic.

Egyptian numeral system: advantages and disadvantages

The main achievement of the ancient Egyptians in mathematics is simplicity and accuracy. Looking at the hieroglyph, it was always possible to determine how many tens, hundreds or thousands are recorded on papyrus. The system of addition and multiplication of numbers was also considered a merit. Only at first glance, it seems confusing, but getting insightful, you will quickly and easily solve such problems. The major confusion was recognized as a flaw. Numbers could be recorded not only in any direction, but also randomly, so more time was needed to decode them. And the last negative, perhaps, is an incredibly long line of characters, because they constantly had to duplicate.