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, which even a first grader is familiar with, were previously overwhelming for the smartest people. A huge contribution to the development of this industry was made by the Egyptian number system, some of the elements of which we still use in its original form.
Brief definition
Reliable historians know that in any ancient civilization writing was mainly developed, and numerical values always stood in second place. For this reason, in the mathematics of the past millennia, there are many inaccuracies, and modern experts sometimes puzzle in such puzzles. The Egyptian number system, which, incidentally, was also non-positional, was no exception. This means that the position of a single digit in a number record does not change the total value. As an example, consider the value 15, where 1 is in the first place, and 5 is in the second. If we swap these numbers, we get a much larger number. But the ancient Egyptian number system did not suggest such changes. Even in the most significant number, all its components were recorded in random order.
Just note that the modern inhabitants of this hot country use the same Arabic numbers as we do, writing them in strict accordance with the desired order and from left to right.
What were the signs?
The Egyptians used hieroglyphs to write numbers, and there weren’t so many of them. Duplicating them according to a certain rule, it was possible to get a number of any size, however, for this it would require a large amount of papyrus. At the initial stage of its existence, the Egyptian hieroglyphic number system contained the numbers 1, 10, 100, 1000 and 10000. Later, more significant numbers appeared, which were multiples of 10. If you needed to write down one of the above indicators, we used the following hieroglyphs:
To write a number that is not a multiple of ten, this simple technique was used:
Decoding numbers
As a result of the example above, we see that in the first place we have 6 hundred, followed by two dozen and two at the end. Similarly, any other numbers are written for which thousands and tens of thousands can be used. However, this example is written from left to right, so that the modern reader can correctly understand it, only in reality the Egyptian number system was not so accurate. The same value could be written from right to left, to figure out where the beginning, and where the end, accounted for, based on the figure with the highest value. A similar reference point will also be required if the numbers are written in large numbers scattered (since the system is non-positional).
Fractions are also important.
The Egyptians had mastered mathematics before many others. For this reason, at some point, the numbers alone were not enough, and fractions were gradually introduced. Since the ancient Egyptian number system is considered hieroglyphic, symbols were also used to record numerators and denominators. For ½ there was a special and unchanging sign, and all other indicators were formed in the same way that was used for large numbers. The numerator has always featured a symbol that imitates the shape of the human eye, and the number was already indicated in the denominator.
Math operations
If there are numbers, they are added and subtracted, multiplied and divided. The Egyptian number system coped with this task perfectly, although there was a specificity. The easiest way to add and subtract. For this, the hieroglyphs of two numbers were written in a row, between them the change of digits was taken into account. It is more difficult to understand how they multiplied, since this process is little similar to the modern one. Two columns were made up, one of them began with a unit, and the other with a second factor. Then they began to double each of these numbers, writing a new result under the previous one. When it was possible to collect the missing factor from the individual numbers of the first column, the results were summed up. You can better understand this process by looking at the table. In this case, 7 times 22:
The result in the first column of 8 already exceeds 7, so doubling ends at 4. 1 + 2 + 4 = 7, and 22 + 44 + 88 = 154. This answer is correct, although obtained in such a non-standard way for us.
Subtraction and division were performed in the reverse order of addition and multiplication.
Why was the Egyptian number system formed?
The history of the appearance of hieroglyphs, replacing numbers, is as vague as the emergence of the entire Egyptian civilization. Her birth dates from the second half of the third millennium BC. It is believed that such accuracy in those days was a necessary measure. Egypt was already a full-fledged state and every year it became more powerful and vast. Temples were built, records were kept in the main governing bodies, and in order to combine all this, the authorities decided to introduce this account system. It existed for a long time - up to the 10th century AD, after which hieratics replaced it.
Egyptian number 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 were recorded on papyrus. Advantage was also considered the system of addition and multiplication of numbers. Only at first glance it seems confusing, but after understanding the essence, you will begin to quickly and easily solve such problems. The disadvantage was recognized as great confusion. Numbers could be written not only in any direction, but also randomly, so it took more time to decipher them. And the last minus, perhaps, lies in the incredibly long line of characters, because they constantly had to be duplicated.