PI as a mathematical riddle

The number PI is a mathematical constant that is the ratio of the circumference to the length of its diameter. This number in mathematics is denoted by the Greek letter π.

Число ПИ как математическая загадка

The value of PI

Still don’t know the final value of PI. In the process of its computation has been plenty of scientific methods of account. Now scientists know more than 500 billion digits after the comma that separates the decimal fraction from a whole number. In the decimal part of the constant PI no repetition, as in a simple periodic fractions, and the number of decimal places, most likely indefinitely. Infinity this constant and the absence of recurrent digits after the decimal point do not allow the circle to close, if, acting in reverse order, multiply PI to the diameter of the circle.
Mathematicians call PI recorded the numbers of chaos. In decimal this constant can be found intended any sequence of numbers: any telephone number, pin, credit card or a historical date. Moreover, if all the books to be translated into a decimal digital code, these can also be found in the number PI. There are also the yet unwritten book. Since PI is infinite, and the sequence of digits after the decimal point is not repeated, it is potentially possible to find any information about the Universe. This fact makes the constant PI «divine» and «reasonable».
In school mathematics typically use a minimally precise value of PI with two decimal places is 3,14. For practice on the Ground is enough of PI with 11 decimal places. To calculate the length of the orbit of our planet around the sun, you must use the number with 14 decimal places. Exact calculations in our galaxy is possible with use of PI with 34 decimal places.

Unsolved problems of PI

It is unknown whether the PI are algebraically independent. Also calculated is not an exact measure of irrationality of this constant, although it is known that she can’t be more 7,6063. Unknown is PI of degree n an integer, if n is any positive integer.
There is no evidence, whether PI belongs to the ring of periods. In addition, there is an unresolved question about the normality of this number. Normal call any number, if you record in n hexadecimal the counting system are formed of a contiguous group of digits occurring with the same asymptotic frequency. It is not even known which digits from 0 to 9 occur an infinite number of times in the decimal representation of PI.

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