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heinsbergrelatzz
Post  Post subject: Mathematics problem.... stuck  |  Posted: Wed Dec 26, 2012 4:43 am
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Joined: Mon Oct 15, 2012 11:16 am
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In one mathes lecture this week, a professor suddenly threw out a random high school geometry question on our quiz for a bonus (the topic test was on central limit theorem), and i had no idea it was coming i dont know if my solution is correct, but this is the problem (if i remember correctly):

If $ \displaystyle A_1,A_2...A_n$are the vertices of a regular plane polygon with n sides and O is its centre, show that:

$ \displaystyle \displaystyle\sum\limits_{i=1}^{n-1} (OA_i \times OA_{i+1}) = (1-n)(OA_2 \times OA_1)$


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Nehushtan
Post  Post subject: Re: Mathematics problem … stuck  |  Posted: Mon Mar 11, 2013 7:01 pm
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Joined: Mon Mar 11, 2013 6:51 pm
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Umm … doesn’t this follow from the fact that $ \displaystyle \mathrm{OA_1=OA_2=\cdots=OA_n}$ for a regular polygon? :roll:

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