What’s Pi?

Pi is the sixteenth letter of the Greek alphabet, but it is best known as the symbol used to name a mathematical relationship: the ratio of a circle’s circumference to its diameter. As such, it is a mathematical constant and has many uses. Obviously, it can be used to calculate the circumference of a circle from its diameter and vice versa. Other examples are the formulas for finding the area of ​​a circle and the volume of a sphere. It is often represented by the Greek form of the letter, , and is commonly given the value 16; however, this is only an approximation and the number has some intriguing properties.

Value

The precise value of pi cannot be stated. No fraction is exactly equivalent to it, and when expressed as a decimal, there are an infinite number of digits after the decimal point. Therefore, whenever a calculation is required, an approximation must be used. The value used depends on how precise the calculation needs to be.

For some purposes, 3.14 is acceptable, while for others a correct value may be required, for example, to eight decimal places — 3.14159265. No calculation requires a value accurate to more than 40 decimal places. Many people have used computers to perform record-breaking calculations worth ; as of 2013, it was calculated to 10 trillion decimal places. However, there is no conceivable application that requires such an accurate value.

it is used

Although pi is defined in terms of the diameter of a circle, in mathematical formulas, it is normally the radius, represented by “r”, that is used, so that the formula for the circumference of a circle is 2πr, or radius times π times twice. Other common mathematical formulas they use include the following:

the area of ​​a circle — r2
the surface area of ​​a sphere — 4πr2
the volume of a sphere — 4/3πr3

The constant is also widely used in
physics
statistics and
engineering
.

Property
Pi is an irrational number, which means it can’t be expressed as a ratio, or fraction, involving two integers, such as 2/5 or 7/3. Some fractions are close approximations, for example 355/113 gives the correct number to 6 decimal places; however, an exact value cannot be obtained this way. When irrational numbers are expressed as decimals, the digits after the decimal point form an infinite, non-repeating sequence.

It is also a transcendental number, which means that it cannot be a root, or solution, of any algebraic equation with rational coefficients. The coefficients of an equation are simply the numbers that precede the symbols; where there is no numeric prefix, the coefficient is 1. For example, in the equation 3x + y = 0, the coefficients of x and y are 3 and 1, respectively. The fact that pi is transcendental is evidence that the ancient The “squaring the circle” problem – constructing a square with the same area as a circle using only a ruler and a compass – is insoluble.
The sequence of digits after the decimal point seems random. Many attempts have been made to find models within this number, but all have failed. Randomness has not been proven but, as of 2013, the sequence, as far as it has been calculated, passes all tests for it.

History
Both the ancient Babylonians and ancient Egyptians used rough approximations of , calculating values ​​just over 3.1. Archimedes, the ancient Greek mathematician, discovered that the value was between 223/71 and 22/7. Pi was found irrational in 1770 by the German mathematician Johann Lambert and in 1882 the physicist Ferdinand Lindemann proved that it is a transcendental number. In more recent years, the value has been calculated to an ever-increasing number of decimal places, a trend that looks set to continue as computing power grows.
Interesting facts about π
If the sequence of digits after the decimal point in is random, this means, since it is also infinite, that every conceivable sequence of numbers, no matter how long or improbable, must occur somewhere in the series. In fact, each must occur an infinite number of times. Digits can be used to represent other characters, such as letters of the alphabet and punctuation marks. That way, every conceivable sequence of characters could, in theory, be found within pi by searching through enough digits. These sequences would include the complete works of Shakespeare, all known math textbooks and this article, as well as countless books that have yet to be written.

However, finding something meaningful longer than a few characters would require calculating pi to an unimaginable number of decimal places, many orders of magnitude larger than the current record. As of 2013, it is possible for anyone, using a simple online program, to search for strings of characters in the first four billion digits of π. The probability of finding a sequence of characters of a given length is easily calculated. For example, the probability of finding a given sequence of ten characters in the first four billion digits of pi is 0.0003%.
So far, nothing that appears significant has been found in pi. There is, however, a sequence of six consecutive 9s, starting with the 762nd digit. This is known as the Feynman point and is named after physicist Richard Feynman. Its probability of occurring so early in the sequence is 0.0685%; however, it is thought to be simply a freak occurrence.
Many people have managed to memorize π with a huge number of decimal places. As of 2013, the record is held to be 67,890. The date of March 14 (also spelled 3/14) has been designated “Pi Day” in the United States, with various pi-related activities going on. Music has been created based on this constant, and novels have been written in which the lengths of the words are the digits of in the correct sequence.

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