Q:

Triangular conundrum

Place any three numbers on the vertices of a triangle:

         5
        / \
       /   \
      /     \
     8-------4

Calculate their differences, going one way:

         5
        / \
   -3  /   \ -1
      /     \
     8-------4
         4

Place another number inside the triangle:

         5
        / \
   -3  /   \ -1
      / 15  \
     8-------4
         4

Add the centre number to a vertex, and multiply the total by the opposite edge. Do this for each vertex. Add them together.
$(15+5)\times4=80$
$(15+8)\times-1=-23$
$(15+4)\times-3=-57$ 
$80-23-57=0$

You got $0$. Why?

A:

 Although weird-looking in hindsight, some elementary maths clearly show why.

