Mathematics Problem

>>296430
It's obvious that the vertexes of the triangle have to be on the edge of the circle.
Now, if you pick any 2 random points on the edge of the circle, the triangle will have the largest area if the 3rd vertex is on the other side of the circle, directly in the middle between the other 2 vertexes. This means that the triangle you are looking for is an isosceles triangle.

Can you figure out the rest? You have to use calculus and stuff, can't prove this geometrically alone (I think).

>>296435
Thanks. I will try figure out the rest on my own.

File: improvement.png (13KB, 617x555px) Image search: [Google]

13KB, 617x555px

>>296435
I'm pretty sure the triangle must be equilateral. Otherwise its area can again be improved. Pic related
So no calculus is needed. Just find the maximal equilateral triangle.

>>296450
Of course the answer is equilateral triangle (it can have only 1 area for a given circle).
The problem is, you have to prove that you will end up with such triangle through series of improvements. Obviously, you can argue that the answer is equilateral since it can't be improved in such way.

It's just that I strongly oppose solving problems by proving that our guessed solution is correct (I also hate induction).

OP here, I think I got it. You have to maximize f(x,y)=0.5xy subject to x^2+y^2=1 using the Lagrangian function F(x,y,lambda) = f(x,y)+(lamda)g(x,y)

File: circle.png (20KB, 1152x648px) Image search: [Google]

20KB, 1152x648px

>>296469
Well, I thought you would come up with something along pic related instead.