recall,π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π=c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Dear Student

When we measure a length with a scale or any other device, we only get an approximate rational value.Therefore we may not realise thatcordis irrational.
Circumferencecor the perimeter of a circle is given by2πr,
whereris the radius of the circle
πis approximated as3.14or722​
Also diameter(longest chord of circle) of the circle is equal to2r.
Hence,c=(2πr),d=2r⇒dc​=π
This is analogous to the approximated value of722​which though looks like a rational number of the formqp​(q!=0)
But when computed corresponds to a real value of ~3.14.
And real numbers consists of irrational numbers.
Hence, there is no contradiction in the equation=dc​.


Thanks