Please let me know if anybody knows how to calculate the circumference of a circle with radius but without pi?
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$\begingroup$ The circumference of a circle with radius one is $2 \pi$, what do you mean by “calculating it without pi”? – If this is meant as a serious question then you need to clarify it. $\endgroup$– Martin RCommented Mar 17, 2021 at 9:33
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2$\begingroup$ Food for thought: The diagonal of a unit square is $\sqrt 2$, also a never ending, never repeating decimal. $\endgroup$– lhfCommented Mar 17, 2021 at 10:10
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1$\begingroup$ $710/113 \ne 6.28 \ne 2\pi$. $\endgroup$– Martin RCommented Mar 17, 2021 at 11:15
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1$\begingroup$ Noted. Thanks for the information $\endgroup$– MATHEW PANICKERCommented Mar 17, 2021 at 11:26
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1$\begingroup$ Probably it is time for you to read some analysis textbooks which deal with areas of plane figures and length of plane curves in rigorous manner. $\endgroup$– Paramanand Singh ♦Commented Mar 17, 2021 at 12:11
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1 Answer
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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. $7$.
answered Mar 17, 2021 at 10:23
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$\begingroup$ Sir I have calculated the circumference using a simple formula using a fixed whole number and a decimal multiplied by the radius. I get the result 99% accuracy with the result calculated using pi. is that of any use. $\endgroup$ Commented Mar 17, 2021 at 10:40