Spherical Geometry and GeoGebra: trigonometric approaches to solve navigation problems on the globe
DOI:
https://doi.org/10.23925/2237-9657.2024.v13i3p123-140Keywords:
GeoGebra, Non-Euclidean Geometries, Spherical TrigonometryAbstract
In this work, we present some results on spherical trigonometry and use them to solve navigation problems involving distances between points on the globe. In order to facilitate visualization and location, we developed an applet in GeoGebra 3D that simulates planet Earth, displays points on the Earth's surface by providing latitude and longitude and calculating the distance between them. We conclude that GeoGebra is an effective tool for studying spherical geometry, and can be used both in undergraduate courses and in basic education.
Downloads
Metrics
References
ARAÚJO, Cleiton. Coordenadas geográficas. Nerdprofessor, 2017. Disponível em: https://nerdprofessor.com.br/coordenadas-geograficas-localizacao/. Acesso em: 4 set. 2024.
Bearing Problems & Navigation, 2018. 1 vídeo (18min). Publicado pelo canal The Organic Chemistry Tutor. Disponível em: https://www.youtube.com/watch?v=cSKAqfGXOPI&t=981s. Acesso em 02 set. 2024.
CARMO, Manfredo Perdigão do. Differential geometry of curves and surfaces. New York: Dover Publications, 2016.
COSTA, Sueli Irene Rodrigues; SANTOS, Sandra Augusta. Geometrias Não Euclidianas. Revista Ciência Hoje, Manaus, v. 11, n. 65, p. 14-23. 1990.
CIDADE-BRASIL. Estados Brasileiros. Disponível em: https://www.cidade-brasil.com.br/. Acesso em: 4 set. 2024.
DISTÂNCIA ENTRE CIDADES. Distância entre Cidades. Disponível em: https://www.distanciasentrecidades.com/. Acesso em: 4 set. 2024.
How to Construct Earth use GeoGebra, 2022. 1 vídeo (3min). Publicado pelo canal Ramesh Jaiswal. Disponível em: https://www.youtube.com/watch?v=k1ugd0yBj6I. Acesso em 30 out. 2024.
IBGE - INSTITUTO BRASILEIRO DE GEOGRAFIA E ESTATÍSTICA. Coordenadas Geográficas. Rio de Janeiro, IBGE, 2024. Disponível em: https://atlasescolar.ibge.gov.br/cartografia/21730-coordenadas-geograficas.html. Acesso em: 4 set. 2024.
IBGE - INSTITUTO BRASILEIRO DE GEOGRAFIA E ESTATÍSTICA. Formas da Terra. Rio de Janeiro,
IBGE, 2024. Disponível em: https://atlasescolar.ibge.gov.br/cartografia/21729-formas-da-terra.html. Acesso em: 4 set. 2024.
JENNINGS, George A. Modern Geometry with Applications. New York: Springer Science+Business Media New York, 1994.
PHYSICAL GEOGRAPHY. (b)Location, Distance, and Direction on Maps. Canadá, 1999. Disponível em: http://www.physicalgeography.net/fundamentals/2b.html#google vignette. Acesso em: 4 set. 2024.
REZENDE, Eliane Quelho Frota; QUEIROZ, Maria Lúcia Bontorim de. Geometria Euclidiana Plana e construções geométricas. 2ª ed. Campinas: UNICAMP, 2008.
STROGATZ, Steven. O poder do infinito. Tradução de Paulo Afonso. 1ª ed. Rio de Janeiro: Sextante, 2022. Título original: Infinite Powers.
WOLFE, Harold Eichholz. Introduction to non euclidean geometry. New York: Holt, Rinehart and Winston, 1945.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Journal of the GeoGebra International Institute of São Paulo
This work is licensed under a Creative Commons Attribution 4.0 International License.
Submission, processing, and publication of articles sent to the journal and registration of the DOI at Crossref is free of charge.
Authors retain their copyright and grant the journal the right of first publication of their article, which is simultaneously licensed under a Creative Commons - Attribution 4.0 International license CC BY that allows others to share the article by acknowledging its authorship and initial publication by the journal.
The GeoGebra journal encourages its authors to register their work with information and communication management systems aimed at researchers, such as Academia.edu, Mendeley, ResearchGate, etc.