From lines and circles to hyperspheres: a problem and its generalization.

• Autores: Gareth Wilkes, Martin Griffiths
• Localización: Teaching mathematics and its applications, ISSN 0268-3679, Vol. 32, Nº. 4, 2013, págs. 214-222
• Idioma: inglés
• DOI: 10.1093/teamat/hrt015
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• Resumen

  • In this article we illustrate, by way of a particular example, that simple problems in two or three dimensions may possess elegant generalizations to higher dimensions. Such problems provide a natural setting for undergraduates in which to consider n- dimensional generalizations of familiar low-dimensional objects, and to develop the advanced mathematical ideas and techniques necessary to work in dimensions lying beyond the realm of everyday experience. Exact and asymptotic results are derived, and educational aspects are discussed.