Geodesic
Phenomenology of mathematical concepts: a historical perspective on curves and tangents
Didactica Mathematicae, Tome 45 (2023), pp. 111-156.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The phenomenological perspective in the study of mathematical concepts makes it possible to describe and analyse these concepts from multiple angles, with a grasp of their various appearances and an inquiry into their essence. Mathematical concepts, however, are not isolated entities. Understanding one concept often requires a good understanding of another concept with which that one is related. For example, in most cases, when we talk about a tangent line, it is inseparably connected with some curve. Therefore, much of our understanding of the concept of tangent may rely on how we perceive the concept of curve itself. This paper provides an overview of how the concepts of curve and tangent have been conceived by mathematicians over the centuries, which is a part of what Hans Freudenthal called historical phenomenology. The paper ends with some remarks and conclusions pertaining to the practice of teaching mathematics.
DOI : 10.14708/dm.v45i0.7289
Mots-clés : phenomenological perspective in the study of mathematical concepts, historical phenomenology, a curve, a tangent 
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Barbara Barańska. Phenomenology of mathematical concepts: a historical perspective on curves and tangents. Didactica Mathematicae, Tome 45 (2023), pp.  111-156. doi : 10.14708/dm.v45i0.7289. http://geodesic.mathdoc.fr/articles/10.14708/dm.v45i0.7289/

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