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Joined: 07 Nov 2007
Posts: 120

Posted: 15 Dec 2008 12:29:20 pm    Post subject:


I already got pretty far in solving this question, but I'm not quite done and I still got a few questions, and also: It's an awesome question/riddle thing. ( I only tried to solve it for my own amusement actually Razz)

So, my approach was to divide the cirkle in 3 pieces with two horizontal lines (I sketched it), then divide the middle part in 4 pieces, and divide one of the four pieces in two pieces: A triangle with a 90 degree angle, and a triangle with one curving side.

The angle opposing the curving side, is called X. The surface of this triangle is (X/360)*PI R^2. The other triangle's surface is 0,5R^2 CosX SinX. Those two added, and multiplied by 4 equal 1/3 Pi R^2.

Now, I am not gonna bother writing down the whole simplification process but I got it down to this: (Pi * X)/90 + Sin(2X) = 1/3 PI

K, here's the simplification process anyways:
(x/360)*Pi*R^2 + 0,5R^2CosXSinX = 1/4*1/3*Pi*R^2
(X/180) * Pi + CosXSinx = 1/6 Pi
CosXSinX = 0,5Sin2x (correct me if I am wrong)
(x/90) * Pi + Sin2x = 1/3 Pi

Is there a way to calculate X in some kind of P/Q notation?? And was my approach allright?? I thought it was pretty fun to do Very Happy
The sketch, in case my explanation was vague
Ah! Made a mistake in my sketch, updated it. Another mistake in the sketch -.- I put 360/x instead of the other way around-.-

I also tried calculating the 90 angle triangle using Pythagoras, which resulted in an awesome Formula containing a second degree formula and a Sin^4(x)... Very Happy But it seemed pretty unsolvable

Last edited by Guest on 15 Dec 2008 03:21:06 pm; edited 1 time in total
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Puzzleman 3000

Active Member

Joined: 02 Nov 2008
Posts: 604

Posted: 15 Dec 2008 04:41:08 pm    Post subject:

mind posting the awsome formula
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Joined: 07 Nov 2007
Posts: 120

Posted: 24 Dec 2008 04:31:53 pm    Post subject:

Aww, I can't get online as much as I'd like to be, and right now I don't have the friggin' formula with me.

I actually went a step further and divided the cirkle in 9 pieces with 2 horizontal lines, and 6 vertical lines. Seriously, people should try that Very Happy
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