Sure --- but do such points constitute "centres" of the edges --- in Kimberling's sense reduced appropriately to 1-D, anyway? WFL On 11/3/11, Schroeppel, Richard <rschroe@sandia.gov> wrote:
Suppose lines are drawn from each vertex of a triangle to the opposite side. Each line divides its side into a clockwise piece and a counterclockwise piece. The three lines are concurrent iff the product of the clockwise pieces equals the product of the counterclockwise pieces. [Are we discussing the same thing? Surely WFL knows this thm.]
Rich
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Fred lunnon Sent: Thursday, November 03, 2011 5:14 PM To: math-fun Subject: Re: [math-fun] Tetrahedral Centers
The answer being? WFL
On 11/3/11, Schroeppel, Richard <rschroe@sandia.gov> wrote:
The 4-concurrent version seems a natural generalization of the corresponding plane geometry problem, which has a very pretty answer.
Rich
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Fred lunnon Sent: Thursday, November 03, 2011 1:14 PM To: math-fun Subject: Re: [math-fun] Tetrahedral Centers
A natural generalisation is to identify cases where the 4 lines lie on a quadric, rather than meeting in a point (which I imagine is probably unusual). WFL
On 11/3/11, ed pegg <ed@mathpuzzle.com> wrote:
Since this has come up, here's a long time question I've had....
Take a random tetrahedron.
For a given triangle center, connect it to the opposing corner of the tetrahedron. Repeat for each face of the tetrahedron.
For which triangle centers are the 4 lines concurrent?
If X333 had that property, I suppose Y333 would be a fine name for that Tetrahedral center. Links: http://faculty.evansville.edu/ck6/encyclopedia/ETC.htmlhttp://bernard. gibert.pagesperso-orange.fr/index.htmlhttp://mathworld.wolfram.com/Ki m berlingCenter.htmlhttp://en.wikipedia.org/wiki/Triangle_center Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun