Euler lines and the RGB additive scheme: dynamic constructions in GeoGebra

Authors

  • João Paulo Martins dos Santos USP
  • Alessandro Firmiano de Jesus Academia de Força Aérea - AFA
  • Juan Lopez Juan Lopez Linares USP https://orcid.org/0000-0002-8059-0631

DOI:

https://doi.org/10.23925/2237-9657.2021.v10i2p026-039

Keywords:

Euler line, Neuberg parameter, RGB scheme

Abstract

Dynamic colors in rectangular regions can be obtained from basic concepts of Euclidean geometry. In GeoGebra, interesting images are revealed through the display of tracks added in an RGB additive system. In order to relate Euler lines in a composition of color maps, this article presents a specific and dependent scheme of the cartesian position of the vertices of a given  quadrilateral. The results of the geometric constructions and the dynamic illustrations obtained reinforce the playful and attractive character of GeoGebra. Thus, supported by a rigorous presentation of geometric concepts, it was possible to reveal figures with intriguing patterns that were not visible in a direct observation of mathematical formulas.

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References

BARBOSA, S. M. O software Geogebra e as possibilidades do trabalho com animação, Revista do Instituto GeoGebra de São Paulo, v.2 n.1, pp.22-32, 2013.

HALL, J., LINGEFJÄRD, T. Mathematical Modeling: Applications with GeoGebra, New Jersey: John Wiley & Sons, 2017.

LAGO R. C., NÓS, R. L., Investigando teoremas de geometria plana com o GeoGebra, Revista do Instituto GeoGebra de São Paulo, v. 9, n. 3, p. 15-29, 2020.

LINARES, J. L., Geometria: Soluções detalhadas para 20 problemas de Olimpíadas Internacionais de Matemática, Pirassununga: FZEA – Universidade de São Paulo, 2020.

PINHEIRO, P. R. O Círculo dos Nove Pontos. Revista do Professor de Matemática, n 14, SBM, 1989. Disponível em: https://www.rpm.org.br/cdrpm/14/12.htm. Acesso em: 10 dez. 2020.

NETO, A. C. M. Geometria, Coleção ProfMat, SBM, 1ª Edição, 2013.

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Published

2021-12-27

How to Cite

Martins dos Santos, J. P. ., de Jesus, A. F., & Juan Lopez Linares, J. L. (2021). Euler lines and the RGB additive scheme: dynamic constructions in GeoGebra. Revista Do Instituto GeoGebra Internacional De São Paulo, 10(2), 026–039. https://doi.org/10.23925/2237-9657.2021.v10i2p026-039

Issue

Vol. 10 No. 2 (2021)

Section

Artigos

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