A1. (a) Give an example of parametrised curvey: (0,1) R4 which is i. not regular; ii. regular but not unit-speed; in reg

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A1 A Give An Example Of Parametrised Curvey 0 1 R4 Which Is I Not Regular Ii Regular But Not Unit Speed In Reg 1 (20.23 KiB) Viewed 34 times

A1. (a) Give an example of parametrised curvey: (0,1) R4 which is i. not regular; ii. regular but not unit-speed; in regular and unit-speed. 3 (b) Assume that a unit-speed regular parametrised curve 3:(-7,7) + R2 with Frenet frame (TN) has constant curvature x > 0. Show that its tangent vector Tis of the form T($) = cos(ks) a + sin(ks) b, for some a, b € R. Deduce that ||a|2 = 1, |b|l2 = 1, while a - b = 0. Furthermore, prove that 3 is (part of) a circle of radius -I. 7