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osanseviero
 one year ago
Get an approximation of pi using a square and triangles inside a circle.
osanseviero
 one year ago
Get an approximation of pi using a square and triangles inside a circle.

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osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441838480540:dw

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0The idea is to first calculate the area of the square and then add triangles.

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441838520139:dw

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Asquare = (2r)^2 = 2 My problem is with getting the first level of triangles, and then adding triangles to those triangles

phi
 one year ago
Best ResponseYou've already chosen the best response.1what did you pick for r ? how about starting with r= 1?

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0I'm using r for distance from center to square. The radius is 1.

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0So with that I can get a height for a triangle 1r.

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok, but using r for the length of 1/2 the side of the square is confusing (people see "r" and think radius) can I use x instead of r? diameter is 2, and this is the length of the diagonal of the square so its side is 2/sqr(2) = sqr(2) and x= 1/2 of a side = sqr(2)/2

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Ok, lets use x instead.

phi
 one year ago
Best ResponseYou've already chosen the best response.1the height of the triangle will be r x 1  \sqr(2)/2

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Ok, and base would be x*2,right?

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Ok. So that would be ((1  sqrt(2) / 2)(sqrt(2))/2. That times 4 to get total area

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Ok, I was good until here. I started to get lost when adding a new layer of triangles

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441839343074:dw

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0So I guess it will pass through the half of the half of the base of the triangle, and then half of the side of the triangle

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, but now it's not clear what the altitude of the new triangle is. the base of the new triangle is the "hypotenuse" of the old triangle, so we can find it using pythagoras

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Ok, give me a minute, I'll try to get it

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Ok. The base is pretty simple. The altitude is a little harder. First, I would calculate the distance between the center and the intersection with the square. Then add the intersection with the triangle. For the square, I did: dw:1441839701196:dw So a = sqrt((x/2)^2 + x^2)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0How to find where the line touches the hypotenuse of the second triangle? We know that the height would be the half.dw:1441839908971:dw

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Oh...that would be the previous base/2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in my mind it looks like this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441840270963:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.1this looks like a painful process

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0It is haha. I think that with this we should get a really close approximation

phi
 one year ago
Best ResponseYou've already chosen the best response.1I know archimedes found the area of triangles formed by an ngon (n sided polygon) on the inside of the circle and the outside and so the area of the circle is between those two areas. But that process seems easier than adding smaller and smaller triangles

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0It is easier, I already did that one hehe

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for the help :)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Can you just help me get that last height?

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.0Ok, then don't worry :)

phi
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441843190370:dw find "y" using pythagoras and the altitude is 1y
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