Homework Notes:

• Some notes on Homework Set 3 :
  • 2.3 # 7: 'log' in this textbook means the natural logarithm, to base 'e', also written as 'ln' (log base 10 is very rarely used in mathematics...)
  • 2.3 # 21; note that rho = 1/k is the radius of curvature of the curve, not the radius of the sphere. Since at any point the Frenet vectors T, N and B form a basis of R³, any vector, including R, can be written as a linear combination of these basis vectors, with the coefficients being the projection onto the basis vectors; thus
    R = (R.T) T + (R.N) N + (R.B) B
    Essentially, the question is thus asking you to compute R.T, R.N and R.B by successive differentiation.