Question

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?

Answer 1

$\pi$ is a ratio of magnitudes,$\frac{circumference}{diameter}$, but it is not a ratio of integers.

for example, $\frac{\sqrt{5}-1}{2}$ is an irrational number but it is expressed in $\frac{c}{d}$ form.

therefore $\pi$ is an irrational number. if circumference is integer then

diameter is not integer and viceversa.