Geometry can rightly be called one of the most ancient sciences, originating in the time of Euclid.
But even more than 4000 years ago, the Egyptians made simple geometric measurements and used almost the same methods as scientists today.
The inhabitants of ancient Babylon measured the simplest geometric shapes using square units.
The square has become the standard of measurement of area since ancient times - and all thanks to the simplicity of its construction, equal angles and sides.
Although in the territory of ancient Kievan Rus this measure was not taken for a long time. An interesting fact is that the Rusich used different measures of land area, which did not express the accuracy of the measurements and were absolutely arbitrary. For example, in calculating the tax for a measure of area, they took a unit measured by labor opportunities, and it was called the “labor measure”. Grasslands were measured by haystacks - this was a “productive” measure. Naturally, all these measures were subjective and arbitrary, moreover, in different principalities sometimes did not correspond to each other, which caused considerable inconvenience. Around the end of the 14th century, in the ancient writings in Russia, the word tithe begins to appear. It got its name due to the fact that it was a tenth of the side of a square equal to one verst.
All this was only a conditional measurement of rectangles and triangles. And only the ancient Greeks knew how to find the area of a regular polygon. Although they did not use the term "area", as well as did not use numbers to determine the area of the polygon.
In The Beginnings, Euclid studied the issue of transforming various shapes into equal, taking the polygon as part of the plane bounded by a closed curve. Based on the fact that the area of the figure does not change, if it is divided into its component parts and arranged without intersection, he was able to establish that the area of the polygon can be calculated by adding the area of these figures.
The results of his work today find wide practical application, for example, among masters in tile laying. For the area of the polygon, they take a wall of complex configuration. It is enough to count the number of tiles used to clad it, and add up their area to find out the quadrature of this wall.
By quadrature is meant the area of a geometric figure. What is included in the definition of area? To put it more simply, this is a number that shows how many identical squares are in the figure. Note that this is not a definition, but only a free interpretation. A unit of area is a square with a side equal to the unit of measurement of the segment. If a meter is used for this measurement, then the area, respectively, will be calculated in square meters, a square centimeter, etc., will be similarly determined. The area of all geometric figures when measuring is expressed by a number that has a positive value.
In order to determine the area of a polygon, a certain formula is used, as well as its division into equal triangles. If the polygon has a complex shape, then you can try to divide it into equal figures and by adding their areas to calculate the area of the originally given figure. Similarly, the area of a convex polygon is calculated.
A polygon can be convex if one of the following conditions is met:
- it lies on one side of a straight line connecting its neighboring peaks;
- a polygon is the intersection of several planes.
Among other things, a convex polygon can be regular if all its sides and angles are equal. An example of this is a pentagon with equal sides.
There is only one conclusion: the space around us, if you look closely, consists of various geometric figures, and the knowledge of the laws of geometry and the ability to use them organically fit into our lives.