I think it is safe to say that everyone knows the value of PI is 3.14…….
I am sure most of us are guilty of using the value without questioning its origin.
I am sure there are various resources online that explains how the value of PI is calculated.
This is how I derive it with my own thought process as I was doing my Final Year Project as an Undergraduate.
Imagine you have a pizza with a radius(r) cut into equal slices. Each slice can be approximated as a triangle so that we can find its area.
I decided to use 36 slices as a simple example as each slice will have an angle of (360/36) = 10 degrees.
There are many ways to calculate the area(S) of a triangle. The most suitable one for this problem is: S = ½(ab)*sinC (where a & b are the 2 sides of a triangle and C is the angle between them)
The area (A) of the whole pizza is A = n*S(where n is the number of slices)
For the example given above, a=b=r, C=10,n=36
A = n*S
= 36*S
= 36*[½(r²)*sin(10)]
=(3.1256672)r²
Comparing the result with the actual formula: A = π*r²
We find that it is not really accurate as the value of PI to 36 decimal places is 3.141592653589793238462643383279502884. This is due to the number of slices. If we cut the pizza into more slices, we would get a more accurate value, as shown in the table below.
From the results, we can deduce that the PI value increases and gets more accurate when we increase the number of slices. We could increase the number of slices up to infinity and this explains why the value of PI is irrational. Currently, the value of PI is found to the millionth digit by mathematicians using the technology of computers. Also, there is such a thing called PI Day which is celebrated everyday on the 14 March because…go figure!
I hope you learn something meaningful today!
This is my first post “For the Curious Minds”
Hope to keep it going 🙂
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