Planes of Leibniz, Lines of Weierstrass, Varia

Walter Benz
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Walter Benz: Universität Hamburg, FB Mathematik Mathematisches Seminar

Chapter Chapter 6 in Classical Geometries in Modern Contexts, 2012, pp 265-295 from Springer

Abstract: Abstract Take two distinct points p, q of ℝ3, i.e. p, q ε ℝ3, p ≠ q, and collect all s ε ℝ3 such that the euclidean distance of p, s and that of q, s coincide. The result will be a plane of ℝ3. This simple and great idea of Gottfried Wilhelm Leibniz (1646–1716) allows us to characterize hyperplanes of euclidean, of hyperbolic geometry, of spherical geometry, the geometries of Lorentz–Minkowski and de Sitter through the (finite or infinite) dimensions ≥ 2 of X as will be shown in the present chapter.

Keywords: Product Space; Euclidean Plane; Point Invariant; Hyperbolic Geometry; Hyperbolic Case (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-0348-0420-2_6

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