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August 24

Math question

There's a quarter-circle ABC with centre O and radius unit 1. There is a point D which is the midpoint of OC and DB is parallel to OA. Ive tried to draw it roughly using characters cos i wasnt bothered to draw and upload a proper picture but it should give you a good idea of it.

 A |\\\
   |    \\  B
   |      / \\
   |    /     |
   |   /      | \\
   |  /       |    \\
   | /        |      \\
   |____________________
   O          D       C

I have been asked to "BY considering separately the triangle OBD and the sector OAB, show that the area of the shaded region OABD is 1/24(2π + 3 sqrt(3) )" I get sqrt(3)/8 for OBD and 1/12π for OAB. And cant get to the required answer. What am I doing wrong? By the way, this is not homework, Im just doing questions as part of my revision for my resits. --212.120.246.239 (talk) 17:19, 24 August 2008 (UTC)[reply]

Your answer is equal to the given answer. What's the problem? Algebraist 17:25, 24 August 2008 (UTC)[reply]

OK, let's try it:

{1 \over 24}\left(2\pi +3{\sqrt {3}}\right)=\left({1 \over 24}\cdot 2\pi \right)+\left({1 \over 24}\cdot 3{\sqrt {3}}\right)={2\pi  \over 2\cdot 12}+{3{\sqrt {3}} \over 3\cdot 8}

In the first fraction the "2"s cancel and in the second fraction the "3"s cancel. You get

{\pi  \over 12}+{{\sqrt {3}} \over 8},

the same thing you say you got. Michael Hardy (talk) 17:55, 24 August 2008 (UTC)[reply]

mathemetician

The name of the Greek mathemetician please —Preceding unsigned comment added by 84.45.143.243 (talk) 22:22, 24 August 2008 (UTC)[reply]

There have been a number of Greek mathematicians, including these guys and these guys. Algebraist 22:27, 24 August 2008 (UTC)[reply]

Perhaps after browsing Algebraist's suggestions, this or this or even this may be of interest. --hydnjo talk 23:30, 24 August 2008 (UTC)[reply]