General two-dimensional hypercomplex numbers

Francesco Catoni, Dino Boccaletti, Roberto Cannata, Vincenzo Catoni, Enrico Nichelatti, Paolo Zampetti

Research output: Contribution to journalArticle


In this chapter we study the Euclidean and pseudo-Euclidean geometries associated with the general two-dimensional hypercomplex variable, i.e., the algebraic ring (see Section 2.2) {z = x + u y; u2= α + uβ x α β ∈ R; u ∉ R}, 6.0.1 and we show that in geometries generated by these numbers, ellipses and general hyperbolas play the role which circles and equilateral hyperbolas play in Euclidean and in pseudo-Euclidean planes, respectively. © 2008 Birkhäuser Verlag AG.
Original languageEnglish
Pages (from-to)73 - 86
Number of pages14
JournalFrontiers in Mathematics
Publication statusPublished - 2008
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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