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Proof of Some Properties of the Cross Product of Three Vectors in with Mathematica

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Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12949))

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Abstract

In this paper, the definition of the cross product of three tangent vectors to at the same point is stated, based on this definition a lemma is stated in which eight properties of said product are proposed and demonstrated. In addition, four theorems and two corollaries are stated and proved. One of the theorems constitutes an extension of the Jacobi identity. In some of the proofs, programs based on the paradigms: functional, rule-based and list-based from the Wolfram language, incorporated in Mathematica, are used.

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References

  1. Bayram, E., Kasap, E.: Hypersurface family with a common isogeodesic. Ser. Math. Inform. 24(2), 5–24 (2014)

    MathSciNet  MATH  Google Scholar 

  2. Düldül, M.: On the intersection curve of three parametric hypersurfaces. Comput. Aided Geom. Des. 27, 118–127 (2010)

    Article  MathSciNet  Google Scholar 

  3. Düldül, B.U., Düldül, M.: The extension of Willmore’s method into 4-space. Math. Commun. 17, 423–431 (2012)

    MathSciNet  MATH  Google Scholar 

  4. Gray, J.W.: Mastering Mathematica: Programming Methods and Applications, 2nd edn. Academic Press, Cambridge (1997)

    Google Scholar 

  5. Maeder, R.: Programming in Mathematica, 2nd edn. Addison-Wesley, Redwood City (1991)

    MATH  Google Scholar 

  6. Williams, M.Z., Stein, F.M.: A triple product of vectors in four-space. Math. Mag. 37(4), 230–235 (1964)

    Article  MathSciNet  Google Scholar 

  7. Wolfram, S.: An Elementary Introduction to the Wolfram Language, 2nd edn. Wolfram Media, Inc. (2017)

    Google Scholar 

  8. Wolfram, S.: The Mathematica Book, 4th edn. Wolfram Media, Champaign; Cambridge University Press, Cambridge (1999)

    Google Scholar 

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Acknowledgements

The authors would like to thank to the authorities of the Universidad Nacional de Piura for the acquisition of the Mathematica 11.0 license and the reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. Universidad Tecnológica del Perú, Av. Vice Cdra 1 – Costado Real Plaza, Piura, Peru

    Judith Keren Jiménez-Vilcherrez

  2. Universidad Privada Antenor Orrego, Av. Los Tallanes Zona Los Ejidos s/n, Piura, Peru

    Josel Antonio Mechato-Durand

  3. Universidad Nacional de Piura, Urb. Miraflores s/n Castilla, Piura, Peru

    Ricardo Velezmoro-León & Robert Ipanaqué-Chero

Authors
  1. Judith Keren Jiménez-Vilcherrez
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  2. Josel Antonio Mechato-Durand
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  3. Ricardo Velezmoro-León
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  4. Robert Ipanaqué-Chero
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Corresponding author

Correspondence to Robert Ipanaqué-Chero .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Monash University, Clayton, VIC, Australia

    David Taniar

  7. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

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Jiménez-Vilcherrez, J.K., Mechato-Durand, J.A., Velezmoro-León, R., Ipanaqué-Chero, R. (2021). Proof of Some Properties of the Cross Product of Three Vectors in with Mathematica. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_18

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  • DOI: https://doi.org/10.1007/978-3-030-86653-2_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86652-5

  • Online ISBN: 978-3-030-86653-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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