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Who discoverd this method of finding the number sequence of pi. Enter sine of .72 into a pocket calculater and devide it by 4= 0.012566039/4=.003141509 whereby the sine of .0072 is an even better fit.

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This is $$\lim_{x\to 0}\frac{\sin x}{x}=1 \tag{1}$$ so that is what we need to know the history of.

Explanation: $0.72=\frac{72}{100}=\frac{18}{25}$, so $$0.72\;\text{degrees}=\frac{18}{25}\cdot\frac{\pi}{180}=\frac{\pi}{250}$$ and therefore by $(1)$, $$\sin(0.72\;\text{degrees})=\sin\left(\frac{\pi}{250}\right)\approx\frac{\pi}{250}\\ \frac{\sin(0.72\;\text{degrees})}{4}\approx\frac{\pi}{1000}$$ And, as noted, for a better approximation, take $x$ closer to $0$, for example $$\frac{\sin(0.0072\;\text{degrees})}{4}\approx\frac{\pi}{100000}$$

Note: $(1)$ is one of the many reasons that, when a mathematician writes the sine function, he assumes it is computed in radians.

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  • $\begingroup$ Bah! I had 30 points and now I have only 28, what a fool I have been $\endgroup$ – John Shanahan Jul 18 '16 at 15:50

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