Concurrence of tetrahedral cevians associated with triangle centers

2020 ◽  
Vol 111 (1) ◽  
Author(s):  
M. Hajja ◽  
I. Hammoudeh ◽  
M. Hayajneh ◽  
H. Martini
Keyword(s):  
Triangle Centers

scholarly journals Towards a Certified Version of the Encyclopedia of Triangle Centers

2016 ◽  
Vol 10 (1) ◽  
pp. 57-73 ◽  
Author(s):  
Julien Narboux ◽  
David Braun
Keyword(s):  
Triangle Centers

Triangle Center Technology

2020 ◽  
Vol 113 (3) ◽  
pp. 237-243
Author(s):  
Anne Quinn
Keyword(s):  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Web Based ◽  
Triangle Center ◽  
Triangle Centers

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.

scholarly journals Distance Product Cubics

KoG ◽  
2020 ◽  
pp. 29-40
Author(s):  
Boris Odehnal
Keyword(s):  
Geometric Properties ◽  
The Real ◽  
Cubic Curve ◽  
Triangle Center ◽  
Triangle Centers ◽  
Trilinear Coordinates

The locus of points that determine a constant product of their distances to the sides of a triangle is a cubic curve in the projectively closed Euclidean triangle plane. In this paper, algebraic and geometric properties of these distance product cubics shall be studied. These cubics span a pencil of cubics that contains only one rational and non-degenerate cubic curve which is known as the Bataille acnodal cubic determined by the product of the actual trilinear coordinates of the centroid of the base triangle. Each triangle center defines a distance product cubic. It turns out that only a small number of triangle centers share their distance product cubic with other centers. All distance product cubics share the real points of inflection which lie on the line at infinity. The cubics' dual curves, their Hessians, and especially those distance product cubics that are defined by particular triangle centers shall be studied.

Sign in / Sign up

Export Citation Format

Share Document