Advances in Applied Clifford Algebras

, Volume 25, Issue 3, pp 657–672 | Cite as

Best Pair of Two Skew Lines over the Octonions

  • P. Saraiva
  • P. D. Beites
  • J. Fernandes
  • C. Costa
  • José Vitória
Article
  • 99 Downloads

Abstract

This is a work on an application of octonions to Analytic Geometry. In the octonionic context, the orthogonal projection of a point onto a straight line is presented. Further, the best approximation pair of points of two skew lines over the octonions is studied.

Keywords

Octonion equation of a line orthogonal projection inner product of octonions parallel and perpendicular octonions double vector cross product in \({\mathbb{R}^{7}}\) best approximation pair 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • P. Saraiva
    • 1
  • P. D. Beites
    • 2
  • J. Fernandes
    • 3
  • C. Costa
    • 4
  • José Vitória
    • 5
    • 6
  1. 1.Mathematics Group of the Faculty of Economics and CMUC, Centre for MathematicsUniversity of CoimbraCoimbraPortugal
  2. 2.Department of Mathematics and CMA-UBI, Centre for Mathematics and ApplicationsUniversity of Beira InteriorCovilhãPortugal
  3. 3.CGUC – Geophysical Institute, Department of Mathematics and Astronomical ObservatoryUniversity of CoimbraCoimbraPortugal
  4. 4.Universidade de Trás-os-Montes e Alto Douro, UTAD and CIDTFF – Centro de Investigação “Didática e Tecnologia na Formação de Formadores” – Laboratório de Didática de Ciências e Tecnologia (UTAD)Vila RealPortugal
  5. 5.Department of MathematicsUniversity of CoimbraCoimbraPortugal
  6. 6.CIDMA – Center for Research and Development in Mathematics and ApplicationsUniversity of AveiroAveiroPortugal

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