On Viviani's Theorem and its Extensions

Details On Viviani's Theorem and its Extensions On Viviani's Theorem and its Extensions

2009-03-04

arxiv.org/abs/0903.0753v3

Mathematics

Metric Geometry

16 pages, 6 figures

Scientific paper

Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. We consider extensions of the theorem and show that any convex polygon can be divided into parallel segments such that the sum of the distances of the points to the sides on each segment is constant. A polygon possesses the CVS property if the sum of the distances from any inner point to its sides is constant. An amazing result, concerning the converse of Viviani's theorem is deduced; Three non-collinear points which have equal sum of distances to the sides inside a convex polygon, is sufficient for possessing the CVS property. For concave polygons the situation is quite different, while for polyhedra analogous results are deduced.

Affiliated with

Also associated with

No associations

Rating

On Viviani's Theorem and its Extensions 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 On Viviani's Theorem and its Extensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Viviani's Theorem and its Extensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-369261