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This paper presents a didactic strategy for teaching the concept of curves in three-dimensional Euclidean space, supported by symbolic and graphical tools from Wolfram Mathematica. Based on the formal mathematical definition, a collaborative activity was designed where students were challenged to propose subsets of \(\mathbb {E}^3\) and determine whether they qualify as curves according to the criteria of smooth parametrization and regularity. Selected examples are analyzed and visualized, demonstrating how this active, technology-assisted methodology fosters conceptual understanding and engagement.

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Recognition and Visualization of Curves in  \(\mathbb {E}^3\) : A Didactic Proposal with Computational Support and Student-Constructed Examples

  • 会议论文

  • 发表日期：

    2026年

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  • Robert Ipanaqué-Chero,
  • Jhoselin N. Purizaca-Pazo,
  • Alexia T. Tume-Chunga,
  • Jadhira K. Correa-Hunter,
  • Jhilson H. Ipanaqué-Juárez,
  • Tommy Suárez-Carreño

摘要

This paper presents a didactic strategy for teaching the concept of curves in three-dimensional Euclidean space, supported by symbolic and graphical tools from Wolfram Mathematica. Based on the formal mathematical definition, a collaborative activity was designed where students were challenged to propose subsets of \(\mathbb {E}^3\) and determine whether they qualify as curves according to the criteria of smooth parametrization and regularity. Selected examples are analyzed and visualized, demonstrating how this active, technology-assisted methodology fosters conceptual understanding and engagement.