`\pi`: The Mysterious and Fascinating Number

 Happy `pi` day to everyone.🎉🥳

Today is March 14. Today called as Pi day. Because it is a day to celebrate the mathematical constant π (pi). The date written numerically as 3/14 matches the first three digits of this never-ending number: 3.14 In this article we find some interesting facts of `pi`. Today I want to talk about one of the most famous and fascinating numbers in mathematics: pi. You probably know pi as the number 3.14, but there is much more to it than that. Let me tell you what pi is, how it was discovered, and why it is important.

What is `pi`?

Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi

- William L. Schaaf -

`Pi` is the ratio of the circumference of a circle to its diameter. That means that if you measure the distance around any circle and divide it by the distance across it, you will always get the same number: pi.

Definition of `pi`

The Pi is a mathematical constant, which is the ratio of the circumference of a circle to its diameter.

`pi=\frac{\text{circumference}}{\text{Diameter}}=\frac{\text{circumference}}{\text{2}\times \text{radius}}`

This definition was built on an unknown origin theory that the ratio between a perimeter of any circle and its diameter is constant

For example, if a circle has a circumference of 31.4 cm and a diameter of 10 cm, then its pi value is 31.4/10 = 3.14.

Pi is also an irrational number, which means that it cannot be written as a fraction of two whole numbers. Its decimal representation never ends or repeats, so we can only approximate it with finite digits. 

The Symbol

• The Greek translation of the word “circumference” - περιφέρεια - (periféreia)
• The Greek translation of the word “Perimeter” - περίμετρος - (perímetros)

William Jones
(1675 - 1749)

It is believed that the symbol of Pi was inherited from the 16th letter of the lowercase Greek alphabet from the above translations. It is the Greek letter for p. 

The symbol π  was first used by British mathematician William Jones in 1706 to represent this constant ratio.  It was later popularized by the Swiss mathematician Leonhard Euler in his works.

Pi has been calculated to trillions of digits using computers , but we only need a few digits for most practical purposes.

How was `pi` discovered?

The concept of pi dates back to ancient civilizations that needed to measure circles for various purposes, such as astronomy, architecture, and art. The Babylonians and Egyptians used simple approximations of pi based on inscribing regular polygons inside circles . Around 250 BC, the Greek mathematician Archimedes improved on this method by using polygons with more sides and calculating upper and lower bounds for pi . He showed that 223/71 < π < 22/7, which gives an average value of about 3.1418.

Over time, mathematicians from different cultures refined Archimedes’ method and computed more digits of pi using geometry and arithmetic . In the 17th century, new tools from calculus allowed for faster calculations using infinite series . For example, Isaac Newton used his binomial theorem to calculate 16 decimal places quickly . In the 20th century, Indian mathematician Srinivasa Ramanujan developed ingenious formulas that could compute thousands of digits with minimal effort .

Why is pi important?

Pi is not just a curiosity; it has many applications in mathematics and science. Pi appears in many formulas that describe shapes and motions involving circles or spheres . For example, 

• The area of a circle is πr² , where r is the radius.
• The volume of a sphere is (4/3)πr³ , where r is the radius.
• The circumference of an ellipse is approximately 2π√((a² + b²)/2), where a and b are the semi-major and semi-minor axes.
• The period of a simple pendulum is approximately 2π√(L/g), where L is the length and g is the gravitational acceleration.

Pi also shows up in other areas such as probability theory , number theory , complex analysis , Fourier analysis , cryptography , fractals , cosmology , quantum mechanics , and more Pi connects seemingly unrelated concepts and reveals hidden patterns in nature.

I hope you enjoyed learning about pi today. If you want to explore more about this amazing number, you can check out some online resources such as:

• Pi Day : A website dedicated to celebrating pi on March 14th every year.
• Pi Search : A tool that lets you search for any string of digits within the first 200 million digits of pi.
• Pi World Ranking List : A list of people who have memorized thousands or millions of digits of pi.

Later Complete  blog post of History of `pi` will be Published.
Thanks for reading my blog post! Stay tuned for more mathematical adventures!

-Ashan Jayamal-