Quadrilaterals as Geometric Loci

Yıl 2022, Cilt: 15 Sayı: 2, 321 - 333, 31.10.2022

Lorenz Halbeısen Norbert Hungerbühler Juan Läuchli

https://doi.org/10.36890/iejg.1062741

Öz

We give necessary and sufficient conditions, both algebraic and geometric, for a quadrilateral to be the level set of the sum of the distances to m ≥ 2 different lines.

Anahtar Kelimeler

Quadrilaterals, geometric locus, harmonic points

Kaynakça

• [1] Elias Abboud. Viviani’s theorem and its extension. College Math. J., 41(3):203– 211, 2010.
• [2] Henk J. M. Bos. Redefining geometrical exactness. Descartes’ transformation of the early modern concept of construction. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, 2001.
• [3] Christoph Gudermann. Grundriss der analytischen Sphärik. DuMont-Schauberg, Köln, 1830.
• [4] Lorenz Halbeisen, Norbert Hungerbühler, and Juan Läuchli. Mit harmonischen Verhältnissen zu Kegelschnitten. Perlen der klassischen Geometrie. Springer Spektrum, Berlin, 2021.
• [5] Norbert Hungerbühler and Gerhard Wanner. Ceva-triangular points of a triangle. Elem. Math., 2021, published online first.
• [6] Wei Lai and Weng Kin Ho. Graphing a quadrilateral using a single cartesian equation. In Electronic Proceedings of the 22nd Asian Technology Conference in Mathematics, Chung Yuan Christian University, Chungli, Taiwan, December 15–19 2017. Mathematics and Technology, LLC.