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General two-dimensional hypercomplex numbers

TitleGeneral two-dimensional hypercomplex numbers
Publication TypeArticolo su Rivista peer-reviewed
Year of Publication2008
AuthorsCatoni, F., Boccaletti D., Cannata R., Catoni V., Nichelatti E., and Zampetti P.
JournalFrontiers in Mathematics
Volume2008
Pagination73-86
ISSN16608046
Abstract

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.

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URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-46949091078&doi=10.1007%2f978-3-7643-8614-6_6&partnerID=40&md5=0047155115785d257f823f154bca6253
DOI10.1007/978-3-7643-8614-6_6
Citation KeyCatoni200873