Transformations Which Render Curves Parallel
- Author(s):
- Levine, Michael V.
- Publication Year:
- 1968
- Report Number:
- RB-68-15
- Source:
- ETS Research Bulletin
- Document Type:
- Report
- Page Count:
- 69
- Subject/Key Words:
- Geometry, Mathematics
Abstract
Eight examples are given to indicate the desirability of having a general theory treating sets of curves which can be transformed into parallel curves. With this theory it is shown that a set of curves can be rendered parallel if and only if every pair of functions in the completion of a particular group associated with the curves is uncrossed. Under general conditions any two transformations rendering a set of curves parallel are related by a linear transformation. Methods for calculating transformations are proposed. Several structural properties of sets of curves which can be rendered parallel are proven.
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- http://dx.doi.org/10.1002/j.2333-8504.1968.tb00380.x