Record Details
Tangential families of study vectors
ScholarsArchive at Oregon State University
| Field | Value |
|---|---|
| Title | Tangential families of study vectors |
| Names |
Johnson, Robert C. (Robert Carl)
(creator) |
| Date Issued | 1966-02-10 (iso8601) |
| Note | Graduation date: 1966 |
| Abstract | This paper is devoted to the study of families of tangent lines to curves in Euclidean three dimensional space by the medium of a particular representation for lines. First, a ring of elements called dual numbers is described, and a vector space over this ring, whose elements are called dual vectors, is defined. Next, a subset of the dual vectors is singled out. The members of this subset are called Study vectors. The set of Study vectors is shown to be in one-to-one correspondence with the set of all directed lines in Euclidean three dimensional space. Study vectors are used to represent the lines to which they correspond. A necessary and several sufficient conditions on a family of Study vectors are given in order that they form a family of tangents to a curve in Euclidean three dimensional space. |
| Genre | Thesis/Dissertation |
| Topic | Vector analysis |
| Identifier | http://hdl.handle.net/1957/47954 |
