Generalizing the Steiner-Lehmus theorem using the Gröbner cover
| Autor: | Antonio Montes, Tomás Recio |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta, Universidad de Cantabria |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statement (computer science)
Discrete mathematics Numerical Analysis Polynomial General Computer Science Applied Mathematics Automatic deduction Comprehensive Gröbner system Elementary geometry Computer Science::Computational Geometry Gröbner cover System of linear equations Automatic discovery Steiner–Lehmus theorem Computational geometry Geometria computacional Theoretical Computer Science Combinatorics Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria [Àrees temàtiques de la UPC] Modeling and Simulation Cover (algebra) Mathematics Parametric statistics Elementarygeometry |
| Zdroj: | Mathematics and Computer in Simulation, Vol. 104, Pp. 67-81 Recercat. Dipósit de la Recerca de Catalunya Universitat Jaume I UCrea Repositorio Abierto de la Universidad de Cantabria Universidad de Cantabria (UC) UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | In this note we present an application of a new tool (the Gröbner cover method, to discuss parametric polynomial systems of equations) in the realm of automatic discovery of theorems in elementary geometry. Namely, we describe, through a relevant example, how the Gröbner cover algorithm is particularly well suited to obtain the missing hypotheses for a given geometric statement to hold true. We deal with the following problem: to describe the triangles that have at least two bisectors of equal length. The case of two inner bisectors is the well known, XIX century old, Steiner-Lehmus theorem, but the general case of inner and outer bisectors has been only recently addressed. We show how the Gröbner cover method automatically provides, while yielding more insight than through any other method, the conditions for a triangle to have two equal bisectors of whatever kind. |
| Databáze: | OpenAIRE |
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