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TranceAddict Forums > Main Forums > Chill Out Room > GEOMETRY GURUS!!! Area of an Oval - SOLVE!
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Smeagol
Senior tranceaddict



Registered: Apr 2003
Location: Lund Sweden
a geometrical solution

Think this should work:

I'm using the angle a the big circle uses to sweep from the leftmost point up to the point where the other circle takes over.

Now the width w can be determined as a function of a and known quantities:
w = 2 R1(1-cos(a)) + 2 R2(cos(a))

and thus

cos a = (w-2R1)/(2(R2-R1))

Now half of one of the large segments has an area A1:

A1 = aR1^2 / 2 - R1 R1sin(a)/2

as the sweeping area minus the triangle in the middle.
(I'm not very good at computerdrawing... would have helped )
Same for the smaler segment A2:

A2 = (pi/2-a)R2^2 / 2 - R2 R2 cos(a)/2

And the middle rectangle A3:

A3 = R1sin(a) R2cos(a)

A = 4A1 + 4A2 + 4A3 should now give the right total area.
Provided I didn't miss anything. )
Sorry for not calculating the actual value... I can not find my calculator...

Guess that this is more of a curiosity by now anyway.

**edited a factor two that i missed

Last edited by Smeagol on Nov-15-2003 at 20:56

Old Post Nov-15-2003 19:56  Sweden
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Resnick
Supreme tranceaddict



Registered: Feb 2003
Location: Toronto

ok, first off, damn u for making me think on a saturday, second i didnt read the other solutions so i dunno if someone already solved it, and third im too lazy to solve it, but ill tell u how.

all u need to do is find the equations of the circles and the rest is easy. to do this, just imagine two circles, which is the top circle and the left circle in ur graph. now let the x axis be in the middle, and the y axis be in middle as well.

(x-36.251)^2 + y^2 = 1853.91 <---big circle
x^2 + (y-a)^2 = 5.029 <---little circle

note*: a is the distance from x axis to the centre of the little circle

now at the interection point, we can equate these to get two equations, since theres 3 unknown, we derive both and set them equal (cuz slopes are same at that point) and once we solve for a, we have eations and we done.


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Old Post Nov-15-2003 23:31  Canada
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King_Mack
Professor of Pimpology



Registered: Oct 2002
Location: Toronto, Canada
Rasta

anyone confirm the actual area??


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Old Post Nov-17-2003 17:26  Canada
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MERTON
Suspended User



Registered: Oct 2003
Location: wilmer, texas

who's the lady in king macks avvy?.. and this problem sucks!


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Old Post Nov-17-2003 17:40  United States
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TranceAddict Forums > Main Forums > Chill Out Room > GEOMETRY GURUS!!! Area of an Oval - SOLVE!
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