A community for students.
Here's the question you clicked on:
 0 viewing
osanseviero
 one year ago
Calculating an approximation of pi using a square inside a circle
osanseviero
 one year ago
Calculating an approximation of pi using a square inside a circle

This Question is Closed

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441563540851:dw

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1I need to find a close approximation of pi using a square inside a circle

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw: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: \[r^2 <\text{ circle area} <R^2 \\ \text{ hmmm... circle area} \approx \frac{R^2+r^2}{2}\]

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Ok. I also know that the radius is 1. Let me calculate the areas

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well I didn't know if we were just limited to using the square inside the circle..

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Well..how would you do it with two squares?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I drew two squares above..

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, I explained myself wrong. Give me a minute, please

freckles
 one year ago
Best ResponseYou've already chosen the best response.1oops and I wrote things wrong aboe

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[(2r)^2< \text{ circle area } < (2R^2) \\ \text{ circle area } \approx \frac{(2r)^2+(2R)^2}{2}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441564320576:dwdw:1441564336095:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I used R and r as half the side lengths above

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Yep. So we know that R is 1, which should make things a little easier. How can we calculate r?

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Right now I have pi = 2r^2 + 2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441564624855:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[2(\frac{\sqrt{2}}{2})^2+2 =2(\frac{2}{4})+2=1+2=3\]

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Great! Thanks a lot. And any idea of how to do this with 1 square? (just for curiosity)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well I guess you can get a lower approximation of the circle just by consider the area of the square

freckles
 one year ago
Best ResponseYou've already chosen the best response.1area of the small square*

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Ok, thanks a lot :) Have a nice day

freckles
 one year ago
Best ResponseYou've already chosen the best response.1it kind takes me back to calculus days

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we can find the lower sum and the upper sum but I think the average of those sums gave a better approximation

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1They told me something about finding the max square that could be inside the circle

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we can find the lower sum and the upper sum but I think the average of those sums gave a better approximation

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Ok,thanks again :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.