Pi and Circle

The circle is one of the most important fundamental shapes in geometry. It is being discussed since ancient time. Let we discuss how its area was derived and value of Pi.

Value of Pi was firstly derived by Archimedes 2300 year ago. That time no mathematical tools were available for him. There was no way to write the decimal value. No way to write the rational number and even zero was not found. Let discuss how did he find the value of PI.

He drew two circles of the same size and he inscribed a square inside the first circle. He drew a large square outside the other circle. 

Consider radius of circles is r. 

From the picture, it is clear that the area of the first square is lesser than the area of the circle.

But, area of the second square is greater than that of the circle.

Because both circles have the same radius, therefore, area of both the circles is equal.

From the above diagram, we can conclude that the area of the circle is greater than the area of the first square and lesser than that of the second square. So the value of the amount of area of this circle lies between the areas of these two squares.

Somehow we need to find the areas of both the square by using simple trigonometry.

Area of  first circle=2r²

Area  of second  circle=4r²

Now he did same with pentagon and more polygon.

Area of smaller pentagon =2.37r²

Area of larger pentagon    =  3.6r²

So as we are increasing the sides of the polygon the shape of the polygon is approaching to circle and empty void between circle and polygon is decreasing.

Archimedes did this for polygon having 96 sides.

A polygon with 96 sides looks like a circle and void between circle and polygon is negligible.

  To find the area of square this formula is used

For 96 sides-

Area of larger square=3.143r²

Area of smaller square=3.139r²

Average of both values is considered as the area of the circle which is 3.141r²

This value (3.14) is named as Pi (π)

Some facts about PI:

-14th of March is celebrated as Pi day because 3=3rd month of the yea 14=14th day of March

-Albert Einstein has birthday on 14th March and Stephen Hawking died on 14th March 2018

-Leonardo Euler adopted the symbol for Pi in 1937th

List of top ten scientists of all time

This is my first blog. Please comment how was this. Thank you.

Watch:Facts about Pi