Good afternoon, dear guests and subscribers of my channel!
To date, open sources and education say that the mathematical operation of multiplication is depicted in the form of three signs: a cross (x), a point (⋅) or asterisks (*), in which there is no fundamental difference.
Such an operation is not difficult and for natural numbers it looks like multiple addition of the first factor by the number of times the second: X * Y = X + X + X + X +... + X (Y times).
Both arguments are called multipliers, and the result is called the product. From school times, from math lessons - we are used to putting an end to solving examples, since teachers are explained this by the fact that the cross should not be confused with the x, although in textbooks the work was always designated as "x".
If you dig a little deeper, the oldest sign is still - "x" - it was introduced by William Otred in 1631. A little later, from 1659. Johann Rahn began to use an asterisk (*), and obelus (÷) as a division.
In 1698 Leibniz began to operate with a dot in his writings. Therefore, today, we use all three characters denoting the same operation - "multiplication".
But, referring to ancient sources, among the Slavs, each mathematical sign was also used for multiplication, but each operation carried a completely different meaning.
Below are some of the Slavic mathematical signs:
If multiplication through a dot ("HA") exactly corresponds to today's multiplication operations on the flat Pythagorean table (table, which is printed on the back of the notebook), i.e. 2 on 3 = 6, 4 on 5 = 20, then the other two types of ancient multiplication do not fit into head.
There is very little information on this topic, but according to the sources found, with three-dimensional (x) and volume-time (*) multiplication, the first factor denotes not number in our usual representation, but only carries information about the image for a person - with which structure (figure) in space the operations are performed multiplication.
A structure is a regular figure in space, which is obtained from the simplest one by its multiple projection on a plane in an n-dimensional system. And, the calculation is based on the reference points (vertices) of the resulting figure.
That is, if 3on7 equals 21 (multiplying a triangle with 3 vertices by 7), then 3 times 7 = 28 ("x" or "wa" indicates a triangle in three dimensions - a tetrahedron, which has 4 anchor points) and 3y7 = 35 ("*" or "u" indicates a 4-dimensional figure, at the base of which is a triangle, and this structure in 4-dimensional space has five vertices - a simplex).
Below, I give an illustration for a rough understanding:
On the Internet you can find many old multiplication tables of various types, here are some of them:
Thus, our ancestors used images for all kinds of calculations... Today, there is practically no information about the real application of ancient mathematics, and no one can about it to tell in detail, since knowledge is scattered all over the planet and, perhaps, will no longer be collected together.
That's all, thanks for your attention! Good luck and good!
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