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Extra resources for A Geometrical Study of the Elementary Catastrophes
Sections w i t h A and E negative and B either zero or + 4 shows m o v e m e n t of one cusp relative to the other. similar sections w i t h E positive. (Fig. 18). Figure 19 shows Sections in w h i c h A is p o s i t i v e or zero and B and E are also zero are typically cuspoid (Figs. 20 and 21). However, w i t h E n e g a t i v e the single Cusp b r e a k s up into two component Cusps; w i t h E p o s i t i v e the s u r f a c e b e c o m e s two n o n c o n n e c t i n g sheets (Figs. 20 and 21).
0 A = - 8 . 5 C ' + I 0 . 0 A ' - 8 . 0 A ' - 8 . 0 Fig. 30 50 A = - 8 . 0 B=+2. 0 A = - 8 . 0 A : - 8 . O A = -8. 0 A = - 8 . 0 B = - I . 0 C =+15,0 D : 0 . 0 D - 0 . O A : - 8 . 0 B : - 2 . 0 Fig. 0 A : - 8 . 0 D =0,0 Fig. 0 B A = -8. -I. 0 B = -I. 0 C =+20. 0 B : - I . 0 D : - 2 . 0 B = - I . O Fig. 0 B = - I . ed Surface Projections of Wigwam Sections of the Star 8 Catastrophe V = ~ on the p l ~ e Ax 6 Bx 5 + --~- + -~-- Cx 4 Dx 3 + -~- + -~-+ Ex 2 -~- + Fx. (D,E) A negative, B and F zero and C running from +20 to zero (Fig.
0 Fig. 0 A : - 8 . 0 D =0,0 Fig. 0 B A = -8. -I. 0 B = -I. 0 C =+20. 0 B : - I . 0 D : - 2 . 0 B = - I . O Fig. 0 B = - I . ed Surface Projections of Wigwam Sections of the Star 8 Catastrophe V = ~ on the p l ~ e Ax 6 Bx 5 + --~- + -~-- Cx 4 Dx 3 + -~- + -~-+ Ex 2 -~- + Fx. (D,E) A negative, B and F zero and C running from +20 to zero (Fig. 34) produces a series of sections typical of the Wigwam Catastrophe for example Fig. 13). (See, As before, it is possible to elucidate the structure of the cuspoids by unfolding along a moving slice of the higher order catastrophes.