Pi is perhaps the most important mathematical constant. He appears in various formulas in mathematics and science in areas as diverse as physics, statistics and sociology. Although pi is defined in terms of the geometry of a circle, most applications of this number are not directly related to circles.
Since ancient times, people have been fascinated by pi. This is hardly a surprise, since the circle is one of the most basic, but still fascinating, geometric shapes. Pi is defined as the ratio of the circumference to the diameter of the circle. (Any circle will work, since all circles are similar.) With rounding to 10 decimal places, its value is 3.1415926536.
Part of what makes pi fascinating is that it appears in several other formulas, including circles or spheres. For example, the area of a circle is pi times the square of its radius. In addition, the surface area of the ball is 4 pi times the square of its radius, and its volume is 4/3 pi multiplied by the cube of its radius. In fact, the formulas for containing all higher dimensional analogues of the sphere also include pi.
As already mentioned, pi also appears in many formulas that are not directly related to circles or spheres. For example, the periods of all trigonometric functions are pi or 2 pi. Although trigger functions can be defined in terms of a circle, they are usually used in contexts that are not directly related to circles. Another place pi is widely used in the normal distribution, which is commonly used in statistics, whose formula includes the square root of pi.
Calculating pi has a long and fascinating history. Some of the most complex mathematical methods have been used in the development of various formulas for pi. By the end of the XIX century, its value was calculated manually by several hundred decimal places. From the very beginning of the computer age in the middle of the 20th century, the number of calculated numbers pi increased dramatically. Since 2002, its value has been known to more than trillions of decimal places - enough to fill a large library!
One of the reasons why some mathematicians are keen on calculating so many pi digits is to look for patterns in its digits. Until now, no obvious ones have been found. It has been suggested that pi is a normal number, which means that each final sample of numbers in each database occurs infinitely often in pi with the same frequency that one would expect if the numbers were random.
In 1995, an amazing formula was found for pi, which allows you to calculate hexadecimal (base 16) digits of pi without having to calculate any previous digits. This formula was used in 2000 to calculate the quadrillion (10 ^ 15th) hexadecimal number pi, which turned out to be 0. Since then, several similar formulas have been discovered, some of the other bases, but none of the bases 10 yet not found.
