# Math Help - Really amazing Theorem.

1. ## Really amazing Theorem.

Let XYZ be a triangle. Then the area of XYZ is given by $A=\frac{1}{2}B+I-1$, where B is the number of boundry lattice points; I is the number of interior lattice points.

2. Both B and I are the number of interior lattice points? I know virtually nothing about this theorem, but that does strike me as a bit odd.

3. Sorry, I meant that B is the number of boundry lattice points

4. Ok. Are you asking for help proving this theorem, or are you just posting it for our edification?

5. I just posted it because I thought people might find it interesting.

6. That's cool. I think it would be even more interesting if you were to outline the construction of the lattice. I've seen a result or two similar to this, I think, in number theory. If it's what I'm thinking of.

7. This is the special case (for triangles) of Pick's Theorem. See

Pick's theorem - Wikipedia, the free encyclopedia

However, you left out a condition: The vertices of the triangle (or polygon, in the general case) must lie on grid points.

I agree with you, it's a fascinating theorem.