Applying matrix diagonalisation in the classroom with GeoGebra: parametrising the intersection of a sphere and plane

• Bradley Graeme Welch ^[1] ; Juan Carlos Ponce Campuzano ^[1]
  1. [1] University of Queensland

     University of Queensland

     Australia

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 56, Nº. 2, 2025, págs. 332-348
• Idioma: inglés
• DOI: 10.1080/0020739X.2023.2233513
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• Resumen

  • In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of this problem, namely the parametrisation of the intersection of a plane and sphere. GeoGebra not only allows students to confirm their calculations, but it can also provide motivation to create connections between prior learning experiences and new knowledge.