Exercises on Space Curves from "Differential Geometry" by K L Wardle

In the attached paper, Space Curve Exercises Wardle Ch2, we provide solutions to the exercises presented after Chapter 2 in "Differential Geometry" by K L Wardle. The exercises provide practice in working with the basic aspects of the Differential Geometry of Space Curves and include several interesting results in their own right. Included (2.18*) are some results that overlap with the previous blog entry on Bertrand Curves. If any typos or errors are found, the author would welcome feedback.

Bertrand Curves -- Theorems from Exercise 14.4-27 A Survey of Geometry Vol.2 Howard Eves

In the attached paper, Bertrand Curve Theorems, we present proofs of several key results about Bertrand curves as presented in Exercise 14.4-27 (a)-(i) in Howard Eves' "A Survey of Geometry Vol 2". The proofs provide a nice introduction to Differential Geometry reasoning applied to these pairs of space curves which share a common principal normal between corresponding points. In two parts of the exercise, (c) and (d), we actually prove a variant of the theorem as stated by Eves. If any typos or errors are found, the author would welcome feedback.