Wikipedia:Reference desk/Archives/Mathematics/2008 August 24

= 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)


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

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)

mathemetician
The name of the Greek mathemetician please —Preceding unsigned comment added by 84.45.143.243 (talk) 22:22, 24 August 2008 (UTC)
 * There have been a number of Greek mathematicians, including these guys and these guys. Algebraist 22:27, 24 August 2008 (UTC)
 * Perhaps after browsing Algebraist's suggestions, this or this or even this may be of interest.  --hydnjo talk 23:30, 24 August 2008 (UTC)