English

Two Remarkable Ortho-Homological Triangles

General Mathematics 2010-09-08 v2

Abstract

In a previous paper we have introduced the ortho-homological triangles, which are triangles that are orthological and homological simultaneously. In this article we call attention to two remarkable ortho-homological triangles (the given triangle and its first Brocard's triangle), and using the Sondat's theorem relative to orthological triangles, we emphasize on four important collinear points in the geometry of the triangle. Orthological / homological / orthohomological triangles in the 2D-space are generalized to orthological / homological / orthohomological polygons in 2D-space, and even more to orthological / homological / orthohomological triangles, polygons, and polyhedrons in 3D-space.

Keywords

Cite

@article{arxiv.1009.0789,
  title  = {Two Remarkable Ortho-Homological Triangles},
  author = {Ion Patrascu and Florentin Smarandache},
  journal= {arXiv preprint arXiv:1009.0789},
  year   = {2010}
}

Comments

11 pages, 6 geometrical figures

R2 v1 2026-06-21T16:09:23.946Z