Graduate Thesis Or Dissertation
 

Tangential families of study vectors

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/37720h07m

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  • 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.
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