From the school bench, everyone remembers a certain number "pi", which is denoted by the Greek letter π and which is used in numerous geometric formulas, for example, to calculate the circumference of a circle. But where did this number come from, and why is it so popular?
The fact is that π expresses the ratio of the circumference of a circle to the length of its diameter. And for absolutely all circles in the world, this ratio is the same and is approximately equal to 3.14!
People paid attention to such an amazing property of circles in ancient times. So, it was known in ancient Babylon and Egypt. The ratio calculated by ancient scientists differs in accuracy from the value known today by only 1%! Throughout the history of scientific thought, people have not stopped trying to calculate the value of this ratio, which was not yet called the number π, in a variety of ways.
For example, Archimedes described and inscribed polygons around a circle, taking their perimeter as the upper and lower estimates of the circumference, respectively. Considering regular 96-gons, he was able to obtain a fairly accurate estimate for the number π. Ancient Chinese and Indian scientists worked on this problem, getting more and more accurate estimates and using more and more original methods.
In the Middle Ages and Modern times, with the development of mathematical analysis and, in particular, the theory of series, it was possible to calculate the number "pi" with an accuracy of up to the 16th decimal place. With the advent of computers, science has stepped far forward, and by 2011, scientists were able to calculate the value of the number pi with an accuracy of 10 trillion digits after the decimal point!
The question arises – why do we need such a colossal accuracy of calculations? Of course, in ordinary life, in construction, architecture and production, a relatively small degree of accuracy, for example, 10-15 characters, is enough. However, let’s not forget how deeply science has penetrated into distant outer space and into matter. And in these areas, much more precise estimates are needed. Another incentive is the hypothesis that some universal constants (Planck’s constant, gravitational constant, pi) can change when space is curved.
So not everything is so simple with this amazing number "pi"!