Question

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

Answer 1

ANSWER

When we measure a length with a scale or any other device, we only get an approximate rational value. 

Therefore we may not realise that c or d is irrational.

Circumference c or the perimeter of a circle is given by 2πr,

where r is the radius of the circle

π is approximated as 3.14 or 722 

Also diameter(longest chord of circle) of the circle is equal to 2r.

Hence, c=(2πr),d=2r⇒dc=π

This is analogous to the approximated value of 722 which though looks like a rational number of the form qp (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.