Orthocenter vs. Centroid — What's the Difference?

The point of intersection of the three altitudes of a triangle.

In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the figure. Informally, it is the point at which a cutout of the shape could be perfectly balanced on the tip of a pin.The definition extends to any object in n-dimensional space: its centroid is the mean position of all the points in all of the coordinate directions.While in geometry the word barycenter is a synonym for centroid, in astrophysics and astronomy, the barycenter is the center of mass of two or more bodies that orbit each other.

(geometry) The intersection of the three lines that can be drawn flowing from the three corners of a triangle to a point along the opposite side where each line intersects that side at a 90 degree angle; in an acute triangle, it is inside the triangle; in an obtuse triangle, it is outside the triangle.

See center of mass.

That point in which the three perpendiculars let fall from the angles of a triangle upon the opposite sides, or the sides produced, mutually intersect.

The point in a system of masses whose coordinates on each dimension are a weighted mean of the coordinates of points on that dimension, the weights being determined by the density function of the system.

The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.

The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.

(of a finite set of points) the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.

An analogue of the centre of gravity of a nonuniform body in which local density is replaced by a specified function (which can take negative values) and the place of the body's shape is taken by the function's domain.

The arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.

Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.

The center of mass, inertia, or gravity of a body or system of bodies.

The center of mass of an object of uniform density