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

Marcel Berger ()
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Marcel Berger: IHÉS, Bures-sur-Yvette, Institut des Hautes Études Scientifiques

Chapter Chapter III in Geometry Revealed, 2010, pp 141-180 from Springer

Abstract: 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 subj Symmetry of the object. Its geometry is indeed not made easier – at least for certain questions – by its being round, compact, and bounded subj 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.

Keywords: Spherical Harmonic; Isoperimetric Inequality; North Pole; Golf Ball; Regular Polyhedron (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-70997-8_3

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DOI: 10.1007/978-3-540-70997-8_3

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