Orthocentric simplices and their centers

Details Orthocentric simplices and their centers Orthocentric simplices and their centers

2005-08-03

arxiv.org/abs/math/0508080v1

Mathematics

Metric Geometry

25 pages

Scientific paper

A simplex is said to be orthocentric if its altitudes intersect in a common point, called its orthocenter. In this paper it is proved that if any two of the traditional centers of an orthocentric simplex (in any dimension) coincide, then the simplex is regular. Along the way orthocentric simplices in which all facets have the same circumradius are characterized, and the possible barycentric coordinates of the orthocenter are described precisely. In particular these barycentric coordinates are used to parametrize the shapes of orthocentric simplices. The substantial, but widespread, literature on orthocentric simplices is briefly surveyed in order to place the new results in their proper context, and some of the previously known results are given new proofs from the present perspective.

Affiliated with

Also associated with

No associations

Rating

Orthocentric simplices and their centers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orthocentric simplices and their centers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orthocentric simplices and their centers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-40357