Delving Deeper: N-Mids
Keyword(s):
In the study of plane geometry, certain figures and points are given considerable attention. Among these are the centroid of a triangle, and the observation that it lies one-third of the way along the median from its foot to the opposite vertex. If we take the equilateral triangle as a special case, the centroid is that point equidistant from the three points that define the triangle. The point equidistant from two points (the endpoints of a segment) lies halfway from one to the other. The simplicity of these fractions almost tells us to look further. The point equidistant from the vertices of a regular tetrahedron lies one-quarter of the way from the base to the vertex.