osanseviero
  • osanseviero
Calculating an approximation of pi using a square inside a circle
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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osanseviero
  • osanseviero
|dw:1441563540851:dw|
osanseviero
  • osanseviero
I need to find a close approximation of pi using a square inside a circle
freckles
  • freckles
|dw:1441563708086:dw| well you could say \[\text{ small square area }<\text{ circle area } < \text{ big square area }\] |dw:1441563787054:dw| |dw:1441563837206:dw| so you have: \[r^2 <\text{ circle area}

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osanseviero
  • osanseviero
Ok. I also know that the radius is 1. Let me calculate the areas
freckles
  • freckles
well I didn't know if we were just limited to using the square inside the circle..
osanseviero
  • osanseviero
Well..how would you do it with two squares?
freckles
  • freckles
I drew two squares above..
freckles
  • freckles
what do you mean?
osanseviero
  • osanseviero
Sorry, I explained myself wrong. Give me a minute, please
freckles
  • freckles
oops and I wrote things wrong aboe
freckles
  • freckles
\[(2r)^2< \text{ circle area } < (2R^2) \\ \text{ circle area } \approx \frac{(2r)^2+(2R)^2}{2}\]
freckles
  • freckles
|dw:1441564320576:dw||dw:1441564336095:dw|
freckles
  • freckles
I used R and r as half the side lengths above
osanseviero
  • osanseviero
Yep. So we know that R is 1, which should make things a little easier. How can we calculate r?
osanseviero
  • osanseviero
Right now I have pi = 2r^2 + 2
freckles
  • freckles
|dw:1441564624855:dw|
freckles
  • freckles
r is sqrt(2)/2
freckles
  • freckles
\[2(\frac{\sqrt{2}}{2})^2+2 =2(\frac{2}{4})+2=1+2=3\]
osanseviero
  • osanseviero
Great! Thanks a lot. And any idea of how to do this with 1 square? (just for curiosity)
freckles
  • freckles
well I guess you can get a lower approximation of the circle just by consider the area of the square
freckles
  • freckles
area of the small square*
osanseviero
  • osanseviero
Ok, thanks a lot :) Have a nice day
freckles
  • freckles
you too
freckles
  • freckles
it kind takes me back to calculus days
freckles
  • freckles
we can find the lower sum and the upper sum but I think the average of those sums gave a better approximation
osanseviero
  • osanseviero
They told me something about finding the max square that could be inside the circle
freckles
  • freckles
we can find the lower sum and the upper sum but I think the average of those sums gave a better approximation
osanseviero
  • osanseviero
Ok,thanks again :)

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