The Mystery of Pi Raised Once Again by Mathematical Community
The number of pi (π) remains one of the most famous numbers in mathematics studied by both professionals and amateurs. Despite its simple geometric representation – through the ratio of the circumference to its diameter, the representation of pi in the form of a decimal fraction does not have symmetry. The numbers after the comma are endless and are not repeated.
A question that excites scientists: what will happen if you build pi to the extent of itself several times? Can a natural number be a result? At first glance, the idea that the construction of an irrational number to multiple degrees can lead to a whole number seems ridiculous. But examples, such as √2 to the degree of √2, show other possibilities.
In 2013, the mathematician Dan Pipony suggested on Twitter that pi, erected to the extent of itself four times, may result in a whole number four times its original value. This idea has recently attracted the attention of the mathematical community.
Let’s consider the calculations. The process of constructing pi to the extent of itself begins with calculating pi to the power of pi, which equals 36.46. Furthermore, pi raised to the power of 36.46 produces an 18-digit number: 1.34 … x 10^18. However, the calculations do not stop there, as pi to the power of this number generates almost 10^18 (billion billion) additional digits.
An important aspect is determining whether there are any digits after the decimal point in the final result, as it is claimed that the result is an integer. The Australian mathematician Matt Parker attempted to approach a solution but concluded that an exact calculation is currently impossible in the foreseeable future.
Fortunately, mathematics offers other methods to determine whether a number is whole, irrational, or even transcendental. A transcendental number is one that cannot be expressed as a solution to