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Spherical Tiling with GeoGebra

New Results, Challenges and Open Problems

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Abstract

The theory of spherical tilings is an interesting and fruitful field, attracting, among other researchers, mathematicians. It is a transverse topic crossing several mathematical areas such as geometry, algebra, topology and number theory, but it is also an object of interest for other scientific fields such as chemistry, physics, art and architecture. Here, we make use of GeoGebra to establish some results, describing a class of monohedral spherical tilings and inferring some conjectures. This will highlight how the use of this software has been crucial for the construction of new knowledge in mathematics with applications in different areas of engineering.

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Suggested Reading

  1. DMY Sommerville. VI.—Division of Space by Congruent Triangles and Tetra-hedra, Proceedings of the Royal Society of Edinburgh, 43, pp.85–116, 1924.

    Google Scholar 

  2. Yukako Ueno and Yoshio Agaoka, Tilings of the 2-dimensional Sphere by Congruent Right Triangles, Memoirs of the Faculty of Integrated Arts and Sciences, Hiroshima University, IV, Science reports: Studies of Fundamental and Environmental Sciences, 22, 1996. Available online at http://ir.lib.hiroshima-u.ac.jp/files/public/0/673/20141016120323365034/KJ00000197303.pdf, pp.1–23.

    Google Scholar 

  3. János Erdos, Sphaerica: Interactive Spherical Geometry Software, Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture, Ed. by George W Hart and Reza Sarhangi. Available online at http://archive.bridgesmathart.org/2010/bridges2010-443.html. Phoenix, Arizona: Tessellations Publishing, 2010, pp.443–446. isbn: 978-0-98460-420-3.

    Google Scholar 

  4. D Austin and W Dickinson, Spherical Easel, A Spherical Drawing Program. Available online at http://merganser.math.gvsu.edu/easel/. 2009.

    Google Scholar 

  5. Robert J Mac G Dawson et al., Some New Tilings of the Sphere with Congruent Triangles, Renaissance Ban: Mathematics, Music, Art, Culture. Bridges Conference, pp.489–496, 2005.

    Google Scholar 

  6. Markus Hohenwarter and Karl Fuchs. Combination of Dynamic Geometry, Algebra and Calculus in the Software System GeoGebra, Computer Algebra Systems and Dynamic Geometry Systems in Mathematics Teaching Conference, Available online at http://archive.geogebra.org/static/publication-s/pecs_2004.pdf. 2004.

    Google Scholar 

  7. Je Brooks and John Strantzen, Spherical Triangles of Area and Isosceles Tetra-hedra, Mathematics Magazine, 78.4, pp.311–314, 2005.

    Article  Google Scholar 

  8. Gaiane Panina, Planar Pseudo-triangulations, Spherical Pseudotilings and Hyperbolic Virtual Polytopes, arXiv preprint math/0607171, 2006.

    Google Scholar 

  9. G Yu Panina, Pointed Spherical Tilings and Hyperbolic Virtual Polytopes, Journal of Mathematical Sciences, 175.5, pp.591–599, 2011; G Yu Panina, Pointed Spherical Tilings and Hyperbolic Virtual Nolytopes, Journal of Mathematical Sciences, 175.5, 2011, pp.591-599.

    Article  Google Scholar 

  10. Ana Maria d’Azevedo Breda and José Manuel Dos Santos Dos Santos, ‘A New Class of Monohedral Pentagonal Spherical Tilings with GeoGebra’, Por-tugaliae Math, 74.3, In press, pp.257–266, 2018.

    Article  Google Scholar 

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Acknowledgement

This work was supported in part by the Portuguese Foundation for Science and Technology (FCT - Fundacäo para a Ciência e a Tecnologia), through CIDMA - Centre for Research and Development in Mathematics and Applications, within project UID/-MAT/04106/2019.

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Authors and Affiliations

  1. University of Aveiro Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    Ana Breda

  2. Portuguese Institute of GeoGebra, Lisbon, Portugal

    José Dos Santos

Authors
  1. Ana Breda
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  2. José Dos Santos
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Corresponding authors

Correspondence to Ana Breda or José Dos Santos.

Additional information

Ana Breda is Associate Professor at the University of Aveiro, Portugal. She is also a member of the algebra and geometry group of the Center for Research and Development in Mathematics and Applications (CIDMA), where she is also the coordinator of the Geometrix project.

José Manuel Dos Santos, Professor of Mathematics of secondary education and teacher trainer, is interested in computational algebra and in the use of GeoGebra for teaching and learning. He coordinates the GeoGebra Institute of Portugal since 2010.

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Breda, A., Dos Santos, J. Spherical Tiling with GeoGebra. Reson 24, 861–873 (2019). https://doi.org/10.1007/s12045-019-0849-6

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  • DOI: https://doi.org/10.1007/s12045-019-0849-6

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