Thursday, March 8, 2012

Math Problem

Math Time

Recently, the following math problem was posed to me:


What that chicken scratch above shows is a problem I have not yet been able to solve.  By what formula can one determine the area of the space in between three circles of the exact same size touching each other in the arrangement shown above? 

The area in the middle isn't a straight edged triangle, it's a three sided space with each side having a curve that somehow relates to the diameter of each circle, I think.

I'm going to keep thinking about this.  If anyone has any thoughts on the subject or could point me in the right direction I would appreciate it.  



32 comments:

  1. my head is starting to hurt... :(

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  2. Maybe when I'm done with my rigorous math and physics education I might understand it more... But right now that's a real stumper..

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  3. Maths seriously melts me out mate, it's never been my subject of expertise to say the very least haha!

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  4. I've actually hard of this problem before, back in college.

    I think it had something to do with blocking it off as a square or a circle itself, then subtracting from the individual diameters or some shit like that.

    Seriously. :3

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  5. Despite how not bad I am with maths I don't think I could work that out at all.

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  6. I don't really like maths...

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  7. This comment has been removed by the author.

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  8. Form an equilateral triangle connected the centers of each circle.
    A1 =>Area of that triangle = (root 3)/4 *a^2 where a = 2r => root 3*r^2
    A2=>Area of 3 sectors = 3* (angle of sector)/360*pie*r^2 = 60/360*pie*r^2 = pie*r^2/6
    A1-A2 should give the answer = r^2(root 3 - (pie/6))

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    1. I left one 3,so final answer maybe r ^2*(root 3-(pie/2)).

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    2. I got (r*sqr(3))-((Pi*(r^2))/2)
      if the radius of a circle is 1 then the area inside 3 similar tangent circles is sqr(3)-(pi/2) or about 0.2
      https://dl.dropbox.com/u/57605393/2012-07-10%2014.22.15.jpg

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  9. The area of a triangle connecting the centers of the circles minus three times 1/6th of the area of one circle.

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    1. that makes sense to me, as 60 degrees of each of the triangle's corners is 1/6th of a circle's 360... Doesn't seem hard looking back. I had started thinking of something much less elegant. No fun in that direction now, i guess. hehe

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    2. damn that's what I was going to say lol

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    3. Looks like not just the nerds are ignored but their version of answers too? ;-)

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  10. I am lost. That will surprise no one at all.

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  11. I have no idea. Why would you ask me this? ;)

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  12. Oh, I have no clue!!! But now I'm going to be puzzling it out all weekend...darn it! haha

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  13. Matt Damon isn't busy, he can solve anything

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  14. My brain has been lying dormant so long as I waste my life slaving for the most evil corporation on earth, that for a second there I even forgot the difference between "area" and "perimeter." But then I tried to make myself feel better by remembering Albert Einstein didn't even have his own phone number memorized. (paraphrasing) "Why would I use space to keep something up here (his mind), that I could just look up," he explained. Well, I guess today Albert wouldn't have even bothered to remember his own name since he could look that up on the internet too. Anyway, I don't know the answer to your math problem, but what you could do is take a hammer and pound out the sides of the circle until they are straight, and then you would have a straight edged triangle in the middle. Problem solved.

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  15. I was never good at maths...

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  16. Hmm.. Seems like just use the diameters of the circle to calculate the length of the sides of an imaginary box. Take that area, and then subtract it from the areas of all the circles, and do some extra math to subtract the other spaces too.

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  17. Ok I am def. not a math person.
    www.thoughtsofpaps.com

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  18. little brain teaster, love it :D

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  19. I've always been horrible in math. Extremely terrible, can't even do the simplest problems. I just don't get it. Good to see there are similar people here.

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