The Tales of Pi ( π )

This is not about the life story of the fictional character Pi in the movie. This is about how the pi(π) was derived by our great mathematicians long time ago.

Pi has been known as early as 250 B.C. The first method of finding the value of π was made by Archimedes of Syracuse, Italy. He first draw a circle with an inscribed regular hexagon like as shown in the figure.

pie pix project

 

The radius of the circle is 1. Therefore, the length of each side of the hexagon is also 1. He approximated the value of π by the following formula,

\pi=\displaystyle\frac{Perimeter Of Hexagon}{Radius Of Circle}

\pi=\displaystyle\frac{6(1)}{2} = 3    , this was the first approximation of the value of π.

After doing the calculation he doubled the number of sides. He draw a regular dodecagon and calculated again the value of pi using the same formula.

pi2

 

He didn’t stop there, he continued the process up to 96 sides. You might be asking yourselves now why he used this technique. Remember that the value of π is the ratio of the circumference of a circle to diameter. As the number of sides of a polygon increases the polygon approaches to the shape of the circle and the perimeter of the polygon approaches the circumference of the circle. Take a look of the 24-sided polygon inscribed in a circle below.

pi3

 

The polygon in red colored side is the 24-gon. Just imagine a 96-sided polygon plotted inside the circle. We cannot even distinguish it from a circle. According to studies, the value of pi we used today is equal to the approximate value if we draw 25,165,824-sided polygon inside this circle.

The method of finding the value of pi revolutionized on 16th -17th century in the existence of infinite series. Today, we are celebrating annually March 14 as the Pi day.

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1 Response

  1. Sebastian says:

    Nice!

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