TITLE: How do mathematicians invented and introduced $\pi$ term in the case of circle?
QUESTION [5 upvotes]: This is basic question. Since childhood I am mugging the mathematical formulae  areas  of square, rectangle and circle etc.
Now,it is possible for me to understand formula of area of square I.e. square of length, area of rectangle as product of length and breadth.
But I  still don't understand formula for area of circle I.e. $A=\pi r^2$
I want to know that


How do mathematicians invented the "$\pi$" term?

How do they introduced "$\pi$" term in the case of the circle? (circumference and area of the circle)

REPLY [3 votes]: Given: The circumference of a circle is $2\pi r$
To prove: The area is $\pi r^2$

Cut the circle into lots of sectors ("pizza slices"), and rearrange into an almost-rectangle. The more slices you use, the closer you get to an actual rectangle. This rectangle has width $\dfrac C2=\pi r$ and height $r$ (why?). So the area of the circle is $\pi r\times r=\pi r^2$.