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Circles and spheres

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Geometry Revealed

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Abstract

If the first chapter was essentially about affine and projective geometry, we now want to enter the Euclidean realm, i.e. we will now have a metric at our disposal, a notion of distance between points, with subsidiary notions such as circles and spheres. The basic reference for circles and spheres, completely authoritative at the time of its publication, is Coolidge (1916). We have made a critical selection from the enormity of classical results; see the very beginning of Sect. II.2. But of course above all we have chosen to talk about recent results, all the more if they require a climb up the ladder.

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Authors and Affiliations

  1. Institut des Hautes Études Scientifiques, IHÉS, Bures-sur-Yvette, 35 route des Chartres, 91440, Bures-sur-Yvette, France

    Marcel Berger

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Berger, M. (2010). Circles and spheres. In: Geometry Revealed. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70997-8_2

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