3. 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?
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 cannot say that either c or d is irrational.
Therefore, the fraction is irrational. Hence, the value of is approximately equal to