How do mathematicians invented and introduced $\pi$ term in the case of circle? 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 > 1. How do mathematicians invented the "$\pi$" term? > > 2. How do they introduced "$\pi$" term in the case of the circle? (circumference and area of the circle) > >

The ancient Greeks (in particular, Eudoxus) proved that circles have areas that scale with the square of the radius, i.e. if the circles have radii $r_1$ and $r_2$, the ratio of the areas is $$ \frac{A_1}{A_2} = \frac{r_1^2}{r_2^2}. $$ So if I have a circle of radius $1$, it has area equal to some number, say $a$. Then I can find the area $A$ of a circle of any radius $r$ by using the formula above as $$ \frac{A}{a} = \frac{r^2}{1^2} \\\ A = ar^2. $$ In particular, we now refer to the constant $a$ by the Greek letter $\pi$.