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ix ILLUSTRATIONS Figure 4.1 Euclid’s parallel as a unique limiting line. 94 Figure 4.2 Geometrical basis for Riemann’s parallel axiom. 95 Figure 4.3 All perpendiculars to a straight line meet in a point. 95 Figure 4.4 Pictorial representation of Riemann’s geometry. 96 Figure 4.5 A triangle ABC composed of geodesics. 98 Figure 4.6 A phase space with two degrees of freedom populated with vectors. 101 Figure 4.7 Phase portrait, arrived at through the integration of vectors in the vector field. 102 Figure 4.8 Phase portrait of a predator-prey system. 104 Figure 4.9 A Lorenz attractor. 109 Figures 1–4 were based on those from Kline, Mathematics in Western Culture , 464, 473, 474, and 476. Figure 5 was taken from Gray, Ideas of Space, p. 136. Figures 6 and 7 were based on those in Mainzer, Thinking in Complexity , 33. Figure 8 was based on Cohen and Stewart, The Collapse of Chaos, 205. ...

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