Recall, 2π is defined as the ratio of the circumference (say c) of a

1.	Recall, 2π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = \(\frac{c}{d}\). This seems to contradict the fact that n is irrational. How will you resolve this contradiction ?
Answer» There is no contradiction. When we measure a length with a scale or any other device we get quotient. Therefore we cannot judge whether c is a rational number of d is an irrational number. ∴ Value of \(\frac{c}{d}\) is irratrional number. ∴ Value of π is also irrational number.

Recall, 2π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = \(\frac{c}{d}\). This seems to contradict the fact that n is irrational. How will you resolve this contradiction ?

Answer»

There is no contradiction. When we measure a length with a scale or any other device we get quotient.

Therefore we cannot judge whether c is a rational number of d is an irrational number.

∴ Value of \(\frac{c}{d}\) is irratrional number.

∴ Value of π is also irrational number.