Is there any way to circumference of a circle with radius but without pi?

Question

Please let me know if anybody knows how to calculate the circumference of a circle with radius but without pi?

Answer 1

It is a secret of euclidean geometry (not valid, e.g., in spherical geometry) that all figures can be linearly scaled by arbitrary real factors $\lambda>0$, whereby the lengths of all segments and curves are multiplied by $\lambda$ and the areas of nice domains are multiplied by $\lambda^2$. From this it follows that for circles there has to be a formula $${\rm circumference}=C\cdot {\rm diameter}\ ,$$ whereby $C$ is a "world constant". This is known to humanity since thousands of years. Later the constant of value slightly larger than $3$ has been denoted by $\pi$, and only in the last years of the $19^{\rm th}$ century it has been proven that this $\pi$ is very irrational, and not even expressible in terms of square roots or similar. But $\pi$ is an ordinary real number and has its "infinite precision" like every such number, e.g. $7$.