| Author | Comment |
gulyman
Goliath
Posted: 30 Jun 2009
22:03 GMT
Total Posts: 144 | At the camp I'm at, some of use are posting math problems for others to solve. Here's today's.
There are two identical circles, each with a radius of 1.
They overlap with the edge/line of one circle passing through the center of the other. This produces a sort of venn-diagram shape. What is the area that the overlapping part covers. |
haveacalc
Guardian
Posted: 2 Jul 2009
17:18 GMT
Total Posts: 1111 | If the circles are named A and B:(Length of A ∪ B) / 2 = i
Solve for x in (1 - x^2)^.5 = sine( arccosine(i) ): x = ±k
k
2 * ∫( (1 - x^2)^.5 - sine( arccosine(i) ) )dx = area of A ∪ B
-k
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-quoted directly from most movies that don't exist (and some that do). |
gulyman
Goliath
Posted: 10 Jul 2009
15:25 GMT
Total Posts: 144 | Hmmm...
I took gr.12 calculus, and I sucked at integrals, so I'll just nod and pretend that I know what that means.
Yes yes, I see exactly how the sine counters the arccosine, and that the A must be ∪ B, sheer genius, yes
*nods |
statisticool
Probe
Posted: 16 Aug 2009
13:15 GMT
Total Posts: 2 | http://mathworld.wolfram.com/Circle-CircleIntersection.html |
