Recall,
is defined as the ratio of the circumference (say c) of a circle to its diameter (say d).
That is,
. This seems to contradict the fact that
is irrational. How will you resolve this contradiction?
Answer:
There is no contradiction. When we measure any length with ruler or any other device, we only get an approximate rational value. We never get an exact value. So, c or d is irrational when we are actually writing approximate rational values of c and d. So, the fraction
is irrational.
pankaj says
very lucid and straight