Who discovered this method of finding the number sequence of $\pi$?

Enter $\sin(0.72)$ into a pocket calculator and divide it by 4:

$$ 0.012566039/4=0.003141509\tag{1} $$

It is even better if you do $\sin(0.0072)$.

  • $\begingroup$ Why don't you provide a link to this method, which would make it more believable (to some users) that it's a method? $\endgroup$ Aug 25 '21 at 23:14
  • $\begingroup$ I discoverd it by playing around with a pocket calculater, sine 72 degrees is the length or height of the top spike of the pentagram.Phi squared devided by sine 72 is the diameter of the circle that encompasses the pentagram. Phi squared devided by sine 72, four times is 3.2,or the music interval 1.6 times 2 $\endgroup$ Aug 26 '21 at 1:38
  • $\begingroup$ So now I see why it has a net score of -3 maybe... I wasn't one of the downvoters, but you made it look (at least to me) like it was a more prominent method. $\endgroup$ Aug 26 '21 at 1:54
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    $\begingroup$ Nice! How did you find yourself entering sin(0.72) into your calculator and dividing it by 4? It might have been better for you to just ask on Mathematics.SE why you got something resembling pi when you did that on your calculator, rather than trying to ask here who discovered this. You might not have got as many downvotes :) $\endgroup$ Aug 26 '21 at 2:51
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    $\begingroup$ Well I was looking for music intervals in the the pentagram and this involved multiplying and dividing numbers by the octave 2, as for the question I think it was edited in such a way. $\endgroup$ Aug 26 '21 at 9:26

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.

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

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