**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.

my head is starting to hurt... :(

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

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

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

ReplyDeleteI 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

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

ReplyDeleteI don't really like maths...

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ReplyDeleteForm an equilateral triangle connected the centers of each circle.

ReplyDeleteA1 =>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))

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

DeleteI got (r*sqr(3))-((Pi*(r^2))/2)

Deleteif 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

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

ReplyDeletethat 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

Deletedamn that's what I was going to say lol

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

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

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

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

ReplyDeleteMatt Damon isn't busy, he can solve anything

ReplyDeleteMy 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.

ReplyDeleteWhat is this I don't even.

ReplyDeleteGOOD LORD. I have no idea!

ReplyDeleteI don't know where to start.

ReplyDeleteAHHHHHHHH MATH

ReplyDeleteah???? head hurt

ReplyDeleteI was never good at maths...

ReplyDeleteHmm.. 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.

ReplyDeleteOk I am def. not a math person.

ReplyDeletewww.thoughtsofpaps.com

little brain teaster, love it :D

ReplyDeleteI'm SO bad at math.

ReplyDeleteI totally suck at math!

ReplyDeleteum... math is not my forte.

ReplyDeleteI'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.

ReplyDelete