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Dergiler / International Electronic Journal of Geometry / 2022 / Volume: 15 Issue: 2

Quadrilaterals as Geometric Loci

Lorenz Halbeısen(ETH Zürich)0000-0001-6078-7237
Norbert Hungerbühler(ETH Zurich)0000-0001-6191-0022
Juan Läuchli(Kantonsschule Frauenfeld)0000-0001-6200-7708
Sayfa
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Yayın Tarihi
2022-10-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Quadrilaterals · geometric locus · harmonic points

Abstract

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.

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Bu Makaleye Atıf Yap

Halbeısen, L., Hungerbühler, N., Läuchli, J. (2022). Quadrilaterals as Geometric Loci. International Electronic Journal of Geometry, Volume: 15 Issue: 2. https://doi.org/10.36890/iejg.1062741

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Kaynakça (6)

  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.