Is this Pi?... I'm afraid to work out the two triangles with question marks

Jun 2019
493
262
USA
I see. You've assumed $h = b/2$. This does not, in fact, make the shaded areas equal.

If they are equal, then yes, the area of the star equals the area of the circle or radius $i$.
$\displaystyle \pi i^2 = 4-2\sqrt{2} \rightarrow i^2 = \frac{4-2\sqrt{2}}{\pi}$
$\displaystyle i~ sin G = g~ sin I \rightarrow sin^2 G = \frac{g^2}{i^2} sin^2 I = \left( \frac{\pi}{4-2\sqrt{2}} \right) \left( \frac{1}{2} \right) sin^2 \frac{\pi}{4} = \frac{\pi}{16-8\sqrt{2}} $
$\displaystyle \rightarrow G = arcsin \left( \sqrt{\frac{\pi}{16-8\sqrt{2}}} \right) \approx 2.1823327 ~rad \approx 125.03845° $ (using $\pi - Arcsin(…)$ to account for obtuse angle)

The shaded areas had very close to the same area, but not the same. Thus, the area of the circle and the area of the star were different by a little under 1 %, causing the error when you tried to back out pi.

*Apologies to my pre-algebra teacher for not putting my radicals back in the numerator.
 
Jun 2014
650
54
USA
It’s really easy to think you’ve proven something when in fact you haven’t. It’s delusional to think you’ve proven something when everyone is telling you you’re wrong, especially when it contradicts standard mathematics, in which case you shouldn’t ignore what others are telling you. Good mathematicians go on to develop the ability to research and verify for themselves where their work goes astray, but this level of skill usually takes an education I would argue because there are so many things that have already been proven you almost need some form of organized curriculum to approach them all before being able to then start narrowing your focus on certain things.

The whole point of a math forum like this, I might also argue, is for amateurs to reach for the stars and learn by making flawed posts that face scrutiny. As long as you acknowledge peoples’ efforts to help you and try to make sense of what they are saying you end up learning something. If you take peoples’ efforts to help as being mean, or merely fail to see their points even if you do find their remarks demeaning (not everyone here is nice all the time same as anywhere else), you won’t learn anything. So have fun trying to prove $\pi$ is something other than what it is (sounds like a silly thing to try and prove to me), but do at least try and figure out your mistake because you know ahead of time that there will be one if your result is other than the standard calculation. Then you can at least take something from this, which is practice at finding your own error, with the ability to ask for others’ assistance when you’re stuck.
 
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Oct 2009
937
364
It’s really easy to think you’ve proven something when in fact you haven’t. It’s delusional to think you’ve proven something when everyone is telling you you’re wrong, especially when it contradicts standard mathematics, in which case you shouldn’t ignore what others are telling you. Good mathematicians go on to develop the ability to research and verify for themselves where their work goes astray, but this level of skill usually takes an education I would argue because there are so many things that have already been proven you almost need some form of organized curriculum to approach them all before being able to then start narrowing your focus on certain things.

The whole point of a math forum like this, I might also argue, is for amateurs to reach for the stars and learn by making flawed posts that face scrutiny. As long as you acknowledge peoples’ efforts to help you and try to make sense of what they are saying you end up learning something. If you take peoples’ efforts to help as being mean, or merely fail to see their points even if you do find their remarks demeaning (not everyone here is nice all the time same as anywhere else), you won’t learn anything. So have fun trying to prove $\pi$ is something other than what it is (sounds like a silly thing to try and prove to me), but do at least try and figure out your mistake because you know ahead of time that there will be one if your result is other than the standard calculation. Then you can at least take something from this, which is practice at finding your own error, with the ability to ask for others’ assistance when you’re stuck.
Yeah, very well put. But the OP needs to realize that his attitude will largely determine the attitude of the responses. If he would have come in here with a well organized computation and a nice picture showing everything clearly, and if he then said that he found a wrong value of pi, and subsequently asked if somebody could help him find the mistake; then he would have never gotten any mean or unhelpful reply. The mistake would have been shown to him in 5 posts or less and this entire experience would not have happened.

Instead, he came barging in exclaiming he found a new value of pi and that everybody else was wrong. At least, this is how I and a lot of others interpreted his post. No wonder he got the response he got. Especially since we get crazies like this almost every week. After a while you get tired of it.
 
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