The medians define the center of gravity, which is computed through the average of the three points.

You can, however, try and use the center of the smallest enclosing circle to get something more towards the middle - although it can happen it''s outside of the triangle.

ToohrVyk

The average of the vertices is called a centroid and is the centre (sorry for my non-American spelling) of gravity and is easiest to calculate. There are a couple of other ways of calculating centres (like the intersection of the lines perpindicular from each edge to the opposite vertex or the intersection of the lines that go from the centre of each edge to the opposite vertex), but to calculate those, it would be much more complicated to calculate and would in involve finding the formula of the lines that need to be intersected and then actually calculating the intersection (which is hard enough on paper, never mind solving for the general case and coding it). In short, listen to everyone else if you don''t mind using any definition of a centre of a triangle.

quote:Original post by clum
or the intersection of the lines that go from the centre of each edge to the opposite vertex

This is precisely the centroid. It''s easy to prove that the intersection of these three lines is actually the average of the vertices (using barycentric relationships).

ToohrVyk

quote:Original post by ToohrVyk

quote:Original post by clum
or the intersection of the lines that go from the centre of each edge to the opposite vertex

This is precisely the centroid. It''s easy to prove that the intersection of these three lines is actually the average of the vertices (using barycentric relationships).

ToohrVyk

You''re right. I meant the intersection of the lines that start from the centre of each each and are perpendicular (and don''t hit the opposite vertex).