THE ENDLESS NUMBER π (PI)

Greetings dear friends, this time I want to talk a little about the number π (pi), which is one of the most famous irrational numbers that appears in countless equations of physical and mathematical problems.

The relation between the length of a circle and its diameter is not exact, it is not even a rational number, but it is an irrational number, we know that number with the name of π (pi).

The fact of being an irrational number tells us that there is no fraction (with whole numbers in the numerator and denominator), that it gives us exactly its value, besides being non-periodic, that is, we can spend our whole lives discovering new decimals and We would never end. Interesting!.

Millions of decimals of π are currently known, but for example, an approximation of 10 decimal places is enough to determine the circumference of the earth with an error of less than 2 centimeters.

Generally, in most calculations we take the approximate value of 3.14, and if we need more precision, we use 3.1416.

From the number π we can only know approximate values, the Egyptians used the approximation 256/81. On the other hand the Hindus and the Chinese used 49/16 and 355/113.

But what makes the number π so special? What differentiates it from any other irrational number?

The essential difference between the number π and other irrational numbers such as √2, for example, is that π belongs to the class of irrational numbers called transcendental, which are those that can never appear as a solution to an algebraic equation.

The transcendence of π is a sample the impossibility of squaring the circle with the ruler and the compass, that is, it is impossible to construct, by using the ruler and the compass, a square whose surface is equal to that of a given circle, and one of the greatest problems of mathematics has come to an end.

There are several infinite sums whose result shows the number π, with which you can calculate approximations of their value.

The use of series allows computers to calculate approximations of π with several thousand decimal places, but these calculations do not have practical importance for measurements of specific magnitudes, the measurements of the old mathematicians are satisfactory in most cases, but with those Thousands of decimals is sought to study the presence of some regularity that allows to know better the nature of this important number.

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References:

https://www.mat.ucm.es/~rrdelrio/publica/numpi_uimp_rrodriguez.pdf

http://vviana.es/doc/El%20numero%20Pi.pdf

https://www.maeva.es/repositorio/lecturas/inicio-todos-de-fiesta-con-numero-pi.pdf