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

Answers (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 cannot say that either c or d is irrational.
Therefore, the fraction  \frac{c}{d}  is irrational. Hence, the value of \pi is approximately equal to \frac{22}{7} = 3.142857....   

Therefore, \pi is irrational.

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