Question

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

Answer 1

Given

$\pi =\frac{c}{d}\approx \frac{22}{7}$

So $\frac{22}{7}$ is its approximate value not the exact value which is equal to $3.141592\dots$ which is non-terminating non-recurring decimal.

Therefore, $\pi$ is irrational.

When we measure a value with a scale, we only get an approximate value. We never obtain an exact value.

Therefore, we may not realize whether $c$ or $d$ is irrational.

Thus, the value of $\pi$ is almost equal to $\frac{22}{7}$ or $3.141592...$