Finger curves Consider the curve r = f 1u2 = cos au - 1.5,
Chapter 10, Problem 108(choose chapter or problem)
Finger curves Consider the curve r = f 1u2 = cos au - 1.5, where a = 11 + 12p21>12p2 _ 1.78933 (see figure). a. Show that f 102 = f 12p2 and find the point on the curve that corresponds to u = 0 and u = 2p. b. Is the same curve produced over the intervals 3-p, p4 and 30, 2p4? c. Let f 1u2 = cos au - b, where a = 11 + 2kp21>12p2, k is an integer, and b is a real number. Show that f 102 = f 12p2 and that the curve closes on itself. d. Plot the curve with various values of k. How many fingers can you produce? 10
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