Math 334 Assignment #2
Due: Friday, January 28
Read: Sections 1.5-1.7 of do Carmo
Submit full answers with sufficient justification to each of the following problems. Remember to
use complete sentences and proper grammar when writing a solution. Include sketches wherever
appropriate.
There are 13 problems listed below, 4 clubs (computations), 5 hearts (easier problems),
and 4 diamonds (challenges).
• Math 334 students: complete 6 problems of your choice, including at least 1 diamond
• Math 634 students: complete 9 problems of your choice, including at least 2 diamonds
Everyone is required to do problem 1♣ and 2♣. Everyone is encouraged to do problem 2♦.
All problems are from do Carmo unless otherwise noted.
Problem 1♣. [required]
1.5.1 (helix)
Problem 2♣. [required]
Shifrin 1.2.3a
Problems 3♣ and 4♣.
Shifrin 1.1.3 and Shifrin 1.2.1b (more computations)
Problem 1♥. Shifrin 1.2.4 (curvature of y = f (x))
Problems 2♥, 3♥, 4♥.
1.5.4, 1.5.6, 1.5.10
Problem 5♥.
Prove that no four points of the twisted cubic α(t) = (t, t2 , t3 ) lie in the
same plane. This is one reason why we think of the twisted cubic as being a general curve.
Problem 1♦. Shifrin 1.1.9 (deriving the shape of the catenary)
Problem 2♦. [recommended] Shifrin 1.1.10 (square-wheeled car)
Problem 3♦. Shifrin 1.2.7 (curvature bound)
Problem 4♦. Shifrin A.1.4 (this result proves why the matrix of Frenet equations is skewsymmetric)