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.  



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32 comments:

  1. JayMarch 8, 2012 at 11:23 PM

    my head is starting to hurt... :(

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  2. DoceanMotionMarch 9, 2012 at 1:29 AM

    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. OutcastMarch 9, 2012 at 2:54 AM

    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. Thomas Duder, Author of the ThingsMarch 9, 2012 at 2:56 AM

    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. MarkMarch 9, 2012 at 3:00 AM

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

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  6. RMarch 9, 2012 at 6:01 AM

    I don't really like maths...

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  7. mamtcMarch 9, 2012 at 7:43 AM

    This comment has been removed by the author.

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  8. mamtcMarch 9, 2012 at 8:29 AM

    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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    Replies
    1. mamtcMarch 9, 2012 at 8:36 AM

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

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    2. UnknownJuly 10, 2012 at 12:36 PM

      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

      Delete
  9. Dave NatanMarch 9, 2012 at 9:09 AM

    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. duffboiMarch 9, 2012 at 12:53 PM

      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. GMarch 10, 2012 at 3:54 PM

      damn that's what I was going to say lol

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    3. mamtcMarch 10, 2012 at 4:58 PM

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

      Delete
  10. AnonymousMarch 9, 2012 at 1:51 PM

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

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  11. Bill PliskinMarch 9, 2012 at 1:53 PM

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

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  12. JaclynMarch 9, 2012 at 6:09 PM

    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. Cranky and DifficultMarch 10, 2012 at 8:21 AM

    Matt Damon isn't busy, he can solve anything

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  14. Jimmy FungusMarch 10, 2012 at 12:02 PM

    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. AnonymousMarch 10, 2012 at 12:24 PM

    What is this I don't even.

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  16. GeojourMarch 10, 2012 at 1:19 PM

    GOOD LORD. I have no idea!

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  17. AnonymousMarch 10, 2012 at 5:07 PM

    I don't know where to start.

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  18. BaurMarch 10, 2012 at 7:05 PM

    AHHHHHHHH MATH

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  19. AguiLeon.comMarch 10, 2012 at 8:37 PM

    ah???? head hurt

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  20. ShawMarch 10, 2012 at 11:51 PM

    I was never good at maths...

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  21. OmnislashMarch 11, 2012 at 12:18 AM

    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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  22. PAPSMarch 11, 2012 at 6:08 AM

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

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  23. CErixssonMarch 11, 2012 at 6:39 AM

    little brain teaster, love it :D

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  24. Heaven.March 11, 2012 at 5:52 PM

    I'm SO bad at math.

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  25. See on TVMarch 12, 2012 at 2:59 AM

    I totally suck at math!

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  26. Lynda R Young as Elle CardyMarch 12, 2012 at 3:59 AM

    um... math is not my forte.

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  27. Steven TorresMarch 29, 2012 at 9:52 PM

    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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