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The sphere by itself: can we distribute points on it evenly?

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Abstract

As we shall see throughout this chapter, the geometry of the “ordinary sphere” S2 – two dimensional in a space of three dimensions – harbors many pitfalls. It’s much more subtle than we might think, given the nice roundness and all the symmetries of the object. Its geometry is indeed not made easier – at least for certain questions – by its being round, compact, and bounded , in contrast to the Euclidean plane. Sect. III.3 will be the most representative in this regard; but, much simpler and more fundamental, we encounter the “impossible” problem of maps of Earth, which we will scarcely mention, except in Sect. III.3; see also 18.1 of [B]. One of the reasons for the difficulties the sphere poses is that its group of isometries is not at all commutative, whereas the Euclidean plane admits a commutative group of translations.

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  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). The sphere by itself: can we distribute points on it evenly?. In: Geometry Revealed. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70997-8_3

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