Hello /sci/, I hope everyone's doing well. Let's get an interesting thread going, shall we?
There is a set $S$ of points in the plane with the property that any triangle with vertices in $S$ has area at most 1. Prove that there exists a triangle with area 4 containing all the points in $S$.
Let's see how /sci/ solves this.
(Problem is not original)
are you allowed to make the triangle as big as you want, because then it would be easy
>>8059520
OP here.
Let me ask you something, anon. Why are you still alive? Can you not fucking read?
'has area at most 1.'
'....there exists a triangle with area 4'
I'm not going to autistically write out a rigorous proof for this.
>>8059535
What's the circle doing there, anon? The anti-complementary triangle alone was fine.
>>8059539
The circle is the smallest circle that contains every point.
>>8059527
>area at most 1
>area 4
4 is more than 1. Did you fail elementary school, retard?
>>8059545
Read the statement of the problem again. If I'd failed elementary school, I wouldn't be posting this problem.
>>8059549
>If any point is allowed to be outside A, a triangle can be made with an area larger than 1.
Not necessarily.
>>8059549
OP here.
We construct the largest triangle possible, ABC having area 1. We construct it's anti complementary triangle, whose area is 4.
Proof by contradiction would be cleaner, anon, though you're on the right track.
>>8059553
Never mind then.
