Basic Parameters of the Kimberling Center X(47)
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
In the triangle , let be the incenter, be the orthocenter, be the Schiffler point, be the -beth conjugate of (see the glossary at [1]) and be the -Ceva conjugate of . Then the center is the intersection of the lines and .
[more]
Contributed by: Minh Trinh Xuan (January 2023)
Open content licensed under CC BY-NC-SA
Snapshots
Details
A triangle center is said to be "even center" if its barycentric coordinates can be expressed as a function of three variables , , that all occur with even exponents. If the center of a triangle has barycentric coordinates as a constant, it is called a "neutral center" (The centroid is the only "neutral center".) Conversely, a triangle center is said to be "odd center" if it is neither even nor neutral.
Standard barycentric coordinates of a point with respect to a reference triangle have a sum of 1.
Classification: odd center
Reference
[1] C. Kimberling. "Encyclopedia of Triangle Centers." (Dec 13, 2022) faculty.evansville.edu/ck6/encyclopedia.
Permanent Citation