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?

AcademicMathematicsNCERTClass 9

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 $\pi$.

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

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