Quadrilaterals as Geometric Loci
Yıl 2022,
Cilt: 15 Sayı: 2, 321 - 333, 31.10.2022
Lorenz Halbeısen
,
Norbert Hungerbühler
,
Juan Läuchli
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.
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.
Yıl 2022,
Cilt: 15 Sayı: 2, 321 - 333, 31.10.2022
Lorenz Halbeısen
,
Norbert Hungerbühler
,
Juan Läuchli
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.