Consider the path
where a, b, and ω are positive constants and a > b.
T (a) Use a computer to plot this path when
i. a = 3, b = 1, and ω = 15.
ii. a = 5, b = 1, and ω = 15.
iii. a = 5, b = 1, and ω = 25.
Comment on how the values of a, b, and ω affect the shapes of the image curves.
(b) Show that the image curve lies on the torus
(A torus is the surface of a doughnut.)
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