*Non-Euclidean (Hyperbolic) Geometry

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.