Area of a circle of radius 'r' = πr2. The shaded region is a square of side 'r', whose area is r2. Therefore, area of the circle is equal to π times area of the square.
In Geometry, we know that the ratio of the circumference of a circle is a mathematical constant. It is denoted by the lower case π, the 16th letter of the Greek alphabet. It is spelt as 'pi'(not to be confused with its homonym pie!). Its counterpart, the upper case Π, is used to denote the product of a sequence.
So by definition π = C/d. We can also define, the ratio of the circumference of a circle to its radius as 2π.
Pi is an
irrational number which cannot be expressed as a ratio p/q where p and q are integers. Hence it's decimal representation is never ending nor there is a regular pattern to it.
Pi to a hundred decimal places is 3.1415926535897932384626433832795028841 971693993751058209749445923078164062862089986280348253421170679........
Pi upto eight decimal places is 3.14159265. A mnemonic to remember it is the number of letters in the words of MAY I HAVE A LARGE CONTAINER OF COFFEE?
Pi corrected to hundredth place is 3.14. But in most mathematical calculations, where accuracy is not that important, it is approximated to a rational number 22/7. The actual value of 22/7 is 3.142857 142857 142857 ..... Note that after the decimal 142857 will be recurring. A mnemonic to remember it is the number of letters in the words of HOW I WISH TO PRESERVE SWEET MOMENTS! 22/7 is most often truncated to just 3.14. So 3.14 is only an approximation of both π and 22/7.
But strictly speaking, 22/7 is greater than π as it has the digit '2' in the 1/1000 place where as π has '1'.