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Weekly Math Problem

Post  i4sci on Mon Apr 19, 2010 5:52 pm

Weekly Math Problem
As of Saterday the 24 th of April i will be posting weekly math problems
the answers will be due by Sat 12:00 am of the following week
The answers will be PM'ed to me with explanations.
Any questions about the problem should be asked on this post so it can benifit everyone
Winners will be announced here
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Re: Weekly Math Problem

Post  zangetsuosan on Sun Apr 25, 2010 11:21 am

hi dan
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Re: Weekly Math Problem

Post  i4sci on Mon Apr 26, 2010 10:43 am

I m changing the questions to monday cuz my Sundays are going to be busier than i thought Crying or Very sad

Find the formula for finding the Area of an n-gon with a circle inscribed in it

the only known is the radius of the inscirbed circle.
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Re: Weekly Math Problem

Post  Commander Ali on Mon Apr 26, 2010 7:52 pm

OK
A is the area of the polygon+ the area of the inscribed circle.
F is the area of the circle.
C is the final area
C=A-F
Just logic =D

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Re: Weekly Math Problem

Post  i4sci on Wed Apr 28, 2010 12:11 pm

no i need a more specific equation
btw the polygon is perfect
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Re: Weekly Math Problem

Post  zangetsuosan on Thu Apr 29, 2010 8:35 am

nice question dan
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Re: Weekly Math Problem

Post  Commander Ali on Sat May 01, 2010 1:34 pm

I must admit, I am completely stumped. I have no idea.

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Re: Weekly Math Problem

Post  i4sci on Sat May 01, 2010 2:25 pm

Commander Ali wrote:I must admit, I am completely stumped. I have no idea.

perhaps you should noli confuta sine agonem, Commander
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Re: Weekly Math Problem

Post  Commander Ali on Sat May 01, 2010 2:46 pm

How about you give me a hint?

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Re: Weekly Math Problem

Post  i4sci on Sat May 01, 2010 3:27 pm

mayb you should split it up?

btw here is a pic

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Re: Weekly Math Problem

Post  i4sci on Mon May 03, 2010 5:56 pm

Ok, so the answer to my question is An = (n/2)*r^2 * sin(180/n)

so if i split up the entire polygon into n triangles, with the sides coming from the center and meeting and the vertexes, which would make them equal to r the radius of the inscribed circle. thus the area of the polygon would be n times the area of all those triangles.

The area of a triangle, as we all should hopeful know, is the base times the height all over two. To find the height and base we use simple trigonometry. The angle between the two radii would be 360/n. thus the height would be r*cos 180/n and the base would be 2r* sin 180/n. Multiplying them together will yield r^2 * cos (180/n) * sin *(180/n). Now, we must not for get our hand trigonometric identities, that help us in times such as these. It just so happens that sin x * cos x = sin 2x/2. Thus, our final equation becomes A = n/2 * r^2 * sin (360/n).
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Re: Weekly Math Problem

Post  Commander Ali on Wed May 05, 2010 7:28 am

Whats the next one?

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Re: Weekly Math Problem

Post  i4sci on Wed May 05, 2010 10:28 pm

Ok, with the unending problem that i have with the Dell Mini 12, i have problems accessing the forum. This is the reason for the delay. But anyways Here is the problem for this week ( Due Sunday 12:00 PM Eastern Time, PM me the answers And the explanations).

The known are R and r, the radii of the two circles and the angle, theta, must be found, obviously in terms of R and r. Lines AO and BO are tangent to the two circles. The two circles also touch at one point
THEY DO NOT CROSS OVER!!!!!!!!!!!!.


Diagram ( please excuse of the crudity of this, i was using paint and it sucks ****)

http://i66.servimg.com/u/f66/15/16/53/62/proble10.jpg
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Re: Weekly Math Problem

Post  Commander Ali on Wed May 12, 2010 6:35 pm

Is X the whole tangent, or just a part?

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Re: Weekly Math Problem

Post  i4sci on Thu May 13, 2010 8:30 am

Commander Ali wrote:Is X the whole tangent, or just a part?


Its from the point where r touches the tangent to point O
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