OK ... Triangles.
The in-centre is the point that's furthest from the perimeter.
The out-centre is the point that minimises the distance to the furthest extremities.
The centroid is the centre of gravity, minimising the average distance to other points in the triangle.
What is a similar description of the ortho-centre?
@ColinTheMathmo
I don't think you can have a one sentence explanation of orthocenter. Because it isn't intuitively the center when it's hanging off the side, like it can.
@ColinTheMathmo
How about two sentences?
The orthocenter is the intersection of lines drawn at a right angle to each vertice into the triangle. The intersection can be inside or outside the triangle.
@ScottSoCal Your first sentence is true and complete as it stands, and I agree that that's how to compute a point that we subsequently call the ortho-centre.
But see my original post. It assigns a meaning to each of the in-centre, out-centre, and centroid.
So what does the ortho-centre mean? Which of these can be completed:
The Ortho-Centre minimises XXX
The Ortho-Centre maximises YYY
Does that make sense?
@ColinTheMathmo
OK, I get what you're after now. But I can't think of any practical aspect to it. I tend to think in terms of design or fabrication, and orthocenter just doesn't matter that way.
@ScottSoCal What about a three sentence explanation?
Problem is, I know how to compute it, I just would like to know if there's a physical concept behind it.
It's tricky.