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Communication Dans Un Congrès Année : 2023

Spatial imaginaries and spherology: Exploring the mathematical shape of space

Elizabeth de Freitas
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Résumé

We inherit from centuries of geometric thought, colonial conquest, imperial englobing of the earth, and stargazing, a tendency to imagine worlds as spheres. The sphere seems to be the very ideal of ideas and it appeals to our desire for perfect symmetry. Does this tendency in spherical thinking inhibit our ability to imagine new modes of connectivity, proximity, dependency relations, border crossing and mobility? This paper situates the embodied mathematical imagination within larger cross-cultural habits of spherical thinking, extending Peter Sloterdijk’s project of cultural spherology. I discuss the figure of the hypersphere and spherical thinking in higher dimensions. Tactics for visualizing the hypersphere are discussed - analogical thinking, boundary gluing, contracting infinity, projection, rotation, looping and smoothing. These material practices of assembling spherical forms are both mathematical and embodied, and link mathematical and cultural imaginaries.
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hal-04420759 , version 1 (26-01-2024)

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Elizabeth de Freitas. Spatial imaginaries and spherology: Exploring the mathematical shape of space. Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13), Alfréd Rényi Institute of Mathematics; Eötvös Loránd University of Budapest, Jul 2023, Budapest, Hungary. ⟨hal-04420759⟩

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