# 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?

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Given:

$\pi$ is defined as the ratio of the circumference (say $c$ ) of a circle to its diameter (say $d$ ). That is, $\pi=\frac{c}{d}$.

$\pi$ is irrational.

To do:

We have to resolve the above contradiction.
Solution:

When we measure the values of $c$ and $d$, we measure it to an approximate value as we cannot measure it to an absolute value using a ruler or any other device.

This implies,

We cannot be sure that $c$ and $d$ are rational.

The value of $\pi$ is equal to $3.142857…....$ and $\frac{22}{7}$ is a very good approximation to $\pi$.

Updated on 10-Oct-2022 13:38:51