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 January 25th, 2019, 07:15 AM #1 Newbie   Joined: May 2018 From: Idaho, USA Posts: 29 Thanks: 4 Calculating Pi for fun. Hello, So, I was doing the following equation for fun: (5/2)r^2sin(72) A thought came to my mind I wanted to share. The more sides a regular polygon has, and the smaller the angles, the closer the answer gets to Pi if r=1. I thought this because, the more sides and the smaller the angles, the closer it gets to being a circle. I began to experiment as follows. (5/2)1^2sin(72)=2.377641291 (36/2)1^2sin(10)=3.12566719 (360/2)1^2sin(1)=3.14143315 (3600/2)1^2sin(0.1)=3.14159105 (36000/2)1^2sin(0.01)=3.14159263 (360000/2)1^2sin(0.001)=3.14159265 And so on. When I post this kind of stuff, I am NOT trying to be boastful or smart. I just like sharing what I learn. I just wanted to share this. I hope you enjoyed reading it. If you have anything you want to add on, feel free to do so. Happy calculating! Jared Thanks from AplanisTophet and idontknow
 January 25th, 2019, 07:37 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra Well done. That's the way Pythagoras (I think) worked out his value for $\pi$. You are in good company.
January 25th, 2019, 08:13 AM   #3
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Quote:
 Originally Posted by v8archie Well done. That's the way Pythagoras (I think) worked out his value for $\pi$. You are in good company.
I think you mean Archimedes.

EDIT:

If I remember correctly, he used inscribed and circumscribed polygons so that he placed upper and lower bounds on the value of pi.

Last edited by JeffM1; January 25th, 2019 at 08:15 AM.

 January 25th, 2019, 01:23 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra Close enough! Thanks from JeffM1
January 25th, 2019, 02:58 PM   #5
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Quote:
 Originally Posted by JeffM1 I think you mean Archimedes. EDIT: If I remember correctly, he used inscribed and circumscribed polygons so that he placed upper and lower bounds on the value of pi.
Oh that's right. Pythagoras invented triangles...

-Dan

 January 25th, 2019, 03:23 PM #6 Senior Member   Joined: Dec 2015 From: somewhere Posts: 514 Thanks: 80 Pi is everywhere , i doubt that it hides a lot . Last edited by idontknow; January 25th, 2019 at 03:26 PM.

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