Tangential families of study vectors Public Deposited

http://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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  • File scanned at 300 ppi using ScandAll PRO 1.8.1 on a Fi-6670 in PDF format. CVista PdfCompressor 5.0 was used for pdf compression and textual OCR.
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  • description.provenance : Approved for entry into archive by Katy Davis(kdscannerosu@gmail.com) on 2014-05-06T15:05:07Z (GMT) No. of bitstreams: 1 JohnsonRobertC1966_Redacted.pdf: 933232 bytes, checksum: 51225f06cc41b797278ed515e34fe6c9 (MD5)
  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2014-05-06T13:34:48Z (GMT) No. of bitstreams: 1 JohnsonRobertC1966_Redacted.pdf: 933232 bytes, checksum: 51225f06cc41b797278ed515e34fe6c9 (MD5)
  • description.provenance : Submitted by Katy Davis (kdscannerosu@gmail.com) on 2014-05-05T23:43:01Z No. of bitstreams: 1 JohnsonRobertC1966_Redacted.pdf: 933232 bytes, checksum: 51225f06cc41b797278ed515e34fe6c9 (MD5)
  • description.provenance : Made available in DSpace on 2014-05-06T15:05:07Z (GMT). No. of bitstreams: 1 JohnsonRobertC1966_Redacted.pdf: 933232 bytes, checksum: 51225f06cc41b797278ed515e34fe6c9 (MD5) Previous issue date: 1966-02-10

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