Recall, \pi is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, \pi= c/d. This seems to contradict the fact that \pi is irrational…

Question

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

Answer 1

Yes, it is true that π = c / d . However, note here that c or the circumference is known by the equation c = 2πr. In finding the circumference, we take value of pi approximately, and hence there is no contradiction. However, even if the circumference is accurate, it will be an irrational number. Recall that an irrational number operated in any way results again into an irrational number. 

Answer 2

Though
`\pi` =
`(c)/(d)`, it is an approximate value. As we get an approximate value and not a fixed one, there is no contradiction. Mathematically,

`(c)/(d)`=
`(2 \pi r)/(2r)`=
`\pi`.
Hence, no contradiction.