We can see the use of Pi when we are studying mathematics and physics as well as other branches of science. Most of us don’t know about Pi or what is pi! Pi is a mathematical symbol that came from the Greek letter pi. [1] We know that it’s approximate value is 3.1416, but how far we know?  We don’t know the accurate value of the pi. From this article, you will get brief information about pi.

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Ancient Mathematics (part 1)
Mathematics is the fundamental requirement for modern science, engineering, philosophy, chemistry, and almost all complex thinking in the contemporary world.

Pi has been known for 4000 years. [2] Even we don’t know the actual value of pi. You will be surprised to know that in 21st century, computers calculated 31.4 trillion decimal place value of the pi.[3] Let’s discuss what pi actually!

What is pi?

Pi is defined by the ratio of the circumference of a circle to its diameter. The value of pi is always the same no matter how small or large a circle is and the value is approximately 3.14. [4]

Pi is an irrational number and an irrational number cannot be expressed by a simple fraction. Though as a fraction 22/7 and 355/113 are mostly used to calculate the value of pi. The value of pi is never ending, it continues. [4]

Image credit :Wikimedia

Who invented pi ?

Archimedes of Syracuse was the first person who calculated the value of pi. [6] He was the most famous mathematician and inventor in ancient Greece. In the 1700s, mathematicians began using the letter pi. [6] In 1706, William Jones first used a symbol to represent the pi.[8] Let’s discuss the history of pi!

Ancient to Modern Mathematics (Part 2)
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The Babylonian Method:

The ancient Babylonians found that the calculated value of pi is 3. There were many tablets found in Susa and one of the tablets contains a list of the mathematical constant. The constant is 24/25. On the tablet, inside a circle, a hexagon was inscribed.

They took 24/25 to be the ratio circumference of the hexagon P to the circumference of the circle C. 24/25 = P/C and the radius of the circle R.

After the calculation they got 24/25= 6R/2πR, or π = 25/8 which is approximately 3.125.

Image credit: chalkdustmagazine

The Egyptian Method :

The Egyptians calculated the value of pi as 256/81 or 3.1605 which was indicated by Rhind Papyrus. They calculated the area of a circle by approximating the circle by an octagon. [10]

The Archimedes Method :

Archimedes of Syracuse was the first person who calculated the value of pi by using Pythagorean Theorem. Archimedes approximated the area of a circle and find out areas of a polygon that inscribed in a circle and a polygon within which the circle was circumscribed. He understands that the perimeter of the inner polygon is smaller than the circumference of the circle and the outer one is larger. He calculated the perimeter of a polygon by using 12,24,48 and finally 96 sides polygon. Finally, he calculated the value of pi between 3.1408 and 3.1428, which is accurate to two decimal places. [2][11][12]

image credit:natureofmathematics 

Other approaches:

In 1706, Willian Jones first used a symbol to represent pi. D.F. Ferguson calculated the value of up to 620 decimal places [11]. Chinese mathematician Zhao Youqin estimated the cost of pi is 355/113. Egypt the great pyramids, are the example of pi. The Great Pyramid of  Giza has a perimeter of 1760 cubits and a height of 280 cubits. The ratio between the perimeter to the height approximately equals to two pi or 6.285714. This Giza suggests some ideas about pi. [11] Indian mathematician calculated the value of pi up to 5 decimal places. [4]

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[1] https://sites.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html

[2] https://www.exploratorium.edu/pi/history-of-pi#:~:text=The first calculation of π,mathematicians of the ancient world.&text=Mathematicians began using the Greek,who adopted it in 1737.

[3] https://cloud.google.com/blog/products/compute/calculating-31-4-trillion-digits-of-archimedes-constant-on-google-cloud

[4] https://en.wikipedia.org/wiki/Pi

[5] https://www.livescience.com/29197-what-is-pi.html

[6] https://www.exploratorium.edu/pi/history-of-pi#:~:text=The Egyptians calculated the area,mathematicians of the ancient world.

[7] https://www.historytoday.com/archive/feature/man-who-invented-pi

[8] https://numberwarrior.wordpress.com/2008/12/03/on-the-ancient-babylonian-value-for-pi/

[9] https://en.wikipedia.org/wiki/Approximations_of_π

[10] http://chalkdustmagazine.com/blog/the-history-of-pi/

[11] https://www.businessinsider.com/archimedes-pi-estimation-2014-3

[12] https://www.britannica.com/biography/Zhao-Youqin