I'm an amateur in mathematics, being in 9th grade. I have been trying to derive $\pi$. During this I reached a limit to find the value of $\pi$. $$\lim_{x \to 0} \frac{180\sin x}{x}$$ Where $x$ is in degree measure. Isn't this better than the other complex derivations of $\pi$? We just need to set a very small value for x and derive it.
2026-03-30 10:34:56.1774866896
Simpler derivation to $\pi$
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You are right, this limit will yield $\pi$ but take a look at $\sin$. It's "degree" version is defined as
$$\sin_d(x)=\sin\left(\frac{\pi}{180}x\right)$$
Since you can approximate $\sin$ using Taylor series as $$\sin(x)=\sum_{n=0}^\infty \frac{(-1)^nx^{2n+1}}{(2n+1)!}$$
There is no simple way to calculate $\sin_d$, as in calculations you have to use value of $\pi$.