Research Article
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Year 2025, , 75 - 80, 31.01.2025
https://doi.org/10.54974/fcmathsci.1563443

Abstract

References

  • Bekta¸s D.B., Aghayev N., On geometric applications of quaternions, Turkish Journal of Mathematics, 44(4), 1289-1303, 2020.
  • Crasmareanu M., Quaternionic product of circles and cycles and octonionic product for pairs of circles, Iranian Journal of Mathematical Sciences and Informatics, 17(1), 227-237, 2022.
  • Crasmareanu M., The Farey sum of Pythagorean and Eisenstein triples, Mathematical Sciences and Applications E-Notes, 12(1), 28-36, 2024.
  • Crasmareanu M., Popescu M., Quaternionic product of equilateral hyperbolas and some extensions, Mathematics, 8(10), 1686, 2020.
  • Crasmareanu M., Pi¸scoran L.-I., A quaternionic product of simple ratios, Carpathian Journal of Mathematics, 41(1), 89-93, 2025.
  • Cushman R.H., Bates L.M., Global Aspects of Classical Integrable Systems, 2nd Edition, Springer, 2015.
  • Giardino S., Differential geometry using quaternions, International Electronic Journal of Geometry, 17(2), 700-711, 2024.
  • Hamilton W.R., On quaternions; or on a new system of imaginaries in algebra, The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, Supplement to Volume XXV, 1844.
  • Millman R.S., Parker G.D., Geometry. A Metric Approach With Models, 2nd Edition, Springer- Verlag, 1991.

A Quaternionic Product of Lines in the Plane E^2

Year 2025, , 75 - 80, 31.01.2025
https://doi.org/10.54974/fcmathsci.1563443

Abstract

This note introduces a product of plane lines inspired by the product of quaternions. A technical condition is necessary for the existence of this product and some examples (squares, the axes and the bisectrices of the axes) are discussed.

References

  • Bekta¸s D.B., Aghayev N., On geometric applications of quaternions, Turkish Journal of Mathematics, 44(4), 1289-1303, 2020.
  • Crasmareanu M., Quaternionic product of circles and cycles and octonionic product for pairs of circles, Iranian Journal of Mathematical Sciences and Informatics, 17(1), 227-237, 2022.
  • Crasmareanu M., The Farey sum of Pythagorean and Eisenstein triples, Mathematical Sciences and Applications E-Notes, 12(1), 28-36, 2024.
  • Crasmareanu M., Popescu M., Quaternionic product of equilateral hyperbolas and some extensions, Mathematics, 8(10), 1686, 2020.
  • Crasmareanu M., Pi¸scoran L.-I., A quaternionic product of simple ratios, Carpathian Journal of Mathematics, 41(1), 89-93, 2025.
  • Cushman R.H., Bates L.M., Global Aspects of Classical Integrable Systems, 2nd Edition, Springer, 2015.
  • Giardino S., Differential geometry using quaternions, International Electronic Journal of Geometry, 17(2), 700-711, 2024.
  • Hamilton W.R., On quaternions; or on a new system of imaginaries in algebra, The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, Supplement to Volume XXV, 1844.
  • Millman R.S., Parker G.D., Geometry. A Metric Approach With Models, 2nd Edition, Springer- Verlag, 1991.
There are 9 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Articles
Authors

Mircea Crasmareanu 0000-0002-5230-2751

Publication Date January 31, 2025
Submission Date October 8, 2024
Acceptance Date January 6, 2025
Published in Issue Year 2025

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19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.