Question

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

Answer 1

There is no contradiction. When we measure a length with scale or any other instrument,

we only obtain an approximate rational value. We never obtain an exact value.

For this reason, we may not realise that either c or d is irrational.

Therefore, the $\frac{ c}{d}$ fraction is irrational.

Hence, π is irrational.