Weekly Math Problem
Weekly Math Problem
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
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
i4sci Academic Moderator
 Posts : 87
Join date : 20100413
Location : under a rock
Re: Weekly Math Problem
hi dan
zangetsuosan Member
 Posts : 37
Join date : 20100423
Age : 23
Location : In your attic :D
Re: Weekly Math Problem
I m changing the questions to monday cuz my Sundays are going to be busier than i thought
Find the formula for finding the Area of an ngon with a circle inscribed in it
the only known is the radius of the inscirbed circle.
Find the formula for finding the Area of an ngon with a circle inscribed in it
the only known is the radius of the inscirbed circle.
i4sci Academic Moderator
 Posts : 87
Join date : 20100413
Location : under a rock
Re: Weekly Math Problem
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=AF
Just logic =D
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=AF
Just logic =D
_________________
"Noli confuta sine agone"
Never give up without a fight
~Ali
I am a Muslim, and proud of it!
LGBT = BAD
MUSIC = BAD
Re: Weekly Math Problem
no i need a more specific equation
btw the polygon is perfect
btw the polygon is perfect
i4sci Academic Moderator
 Posts : 87
Join date : 20100413
Location : under a rock
Re: Weekly Math Problem
nice question dan
zangetsuosan Member
 Posts : 37
Join date : 20100423
Age : 23
Location : In your attic :D
Re: Weekly Math Problem
I must admit, I am completely stumped. I have no idea.
_________________
"Noli confuta sine agone"
Never give up without a fight
~Ali
I am a Muslim, and proud of it!
LGBT = BAD
MUSIC = BAD
Re: Weekly Math Problem
Commander Ali wrote:I must admit, I am completely stumped. I have no idea.
perhaps you should noli confuta sine agonem, Commander
i4sci Academic Moderator
 Posts : 87
Join date : 20100413
Location : under a rock
Re: Weekly Math Problem
How about you give me a hint?
_________________
"Noli confuta sine agone"
Never give up without a fight
~Ali
I am a Muslim, and proud of it!
LGBT = BAD
MUSIC = BAD
i4sci Academic Moderator
 Posts : 87
Join date : 20100413
Location : under a rock
Re: Weekly Math Problem
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).
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).
i4sci Academic Moderator
 Posts : 87
Join date : 20100413
Location : under a rock
Re: Weekly Math Problem
Whats the next one?
_________________
"Noli confuta sine agone"
Never give up without a fight
~Ali
I am a Muslim, and proud of it!
LGBT = BAD
MUSIC = BAD
Re: Weekly Math Problem
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 ****)
https://i.servimg.com/u/f66/15/16/53/62/proble10.jpg
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 ****)
https://i.servimg.com/u/f66/15/16/53/62/proble10.jpg
i4sci Academic Moderator
 Posts : 87
Join date : 20100413
Location : under a rock
Re: Weekly Math Problem
Is X the whole tangent, or just a part?
_________________
"Noli confuta sine agone"
Never give up without a fight
~Ali
I am a Muslim, and proud of it!
LGBT = BAD
MUSIC = BAD
Re: Weekly Math Problem
Commander Ali wrote:Is X the whole tangent, or just a part?
Its from the point where r touches the tangent to point O
i4sci Academic Moderator
 Posts : 87
Join date : 20100413
Location : under a rock
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