what is pi in mathematics?

Introduction :

Succinctly, pi—which is written as the Greek word for p
 or π—is the ratio of the circumference (C) of any circle to the diameter (D)  of that circle,  
Mathematically, 
                                   
                                  C/D =  π/1

Let's do cross multiplication then we get ,

                                  C=π * D
  We know  that , 
                                  D = 2 * r
                     So,

                                 C = 2 * π * r

             r  = Radius of circle

 In decimal form, the value of pi is around 3.14. But pi is an irrational number, indicating that its decimal form does not end (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666...). (To simply 16 decimal places, pi equals 3.1415926535897932.) Hence, it is useful to have a shorthand for this ratio of circumference to diameter.No matter how big your circle, the ratio of circumference to diameter is the value of Pi.
Example :

Let's we take four different types of a circle, Whose diameter 7 cm, 14 cm, 21cm, 35 cm, and circumference  is 22cm, 44cm, 66cm, 110cm
here 
          D1 = 7cm
          D2= 14cm
          D3= 21cm
          D4= 35 cm
and ,   
          C1 = 22cm.
          C2 = 44cm.
          C3 = 66cm.
          C4 = 110cm.

We know that ,
                       
                                             π = C/D

            π1 = C1/D1 =22/7 = 3.1415

            π2 =C2/D2= 44/14 =  22/7 = 3.1415

            π3 = C3/D3= 66/21 = 22/7  = 3.145

            π4 = C4/D4 = 110/35 = 22/7 = 3.1415

 "According to Petr Beckmann's A History of Pi, the Greek letter π was first used for this purpose by William Jones in 1706, probably as an abbreviation of the periphery, and became standard mathematical notation approximately 30 years later."