*Non-Euclidean (Hyperbolic) Geometry

John Snygg ()

Chapter Chapter 8 in A New Approach to Differential Geometry using Clifford's Geometric Algebra, 2012, pp 299-331 from Springer

Abstract: Abstract You should be forewarned that a prerequisite for this chapter is a strong familiarity with the basic manipulations of complex numbers – multiplication, the polar representation, and the notion of complex conjugate. The non-Euclidean geometry of Bolyai and Lobachevsky eventually became known as hyperbolic geometry because the ordinary trigonometric functions sine and cosine that appear in formulas for the surface of a sphere are replaced by the hyperbolic functions sinhϕ and coshϕ for surfaces of constant negative Gaussian curvature.

Keywords: Unit Disk; Equilateral Triangle; Euclidean Geometry; Hyperbolic Geometry; Cross Ratio (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-0-8176-8283-5_8

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