Glasnik Matematicki, Vol. 55, No. 2 (2020), 337-349.

TANGENTIALS IN CUBIC STRUCTURES

Vladimir Volenec, Zdenka Kolar-Begović and Ružica Kolar-Šuper

Department of Mathematics, University of Zagreb, Bijenička cesta 30, HR-10 000 Zagreb, Croatia
e-mail: volenec@math.hr

Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR-31 000 Osijek, Croatia
e-mail: zkolar@mathos.hr

Faculty of Education, University of Osijek, Cara Hadrijana 10, HR-31 000 Osijek, Croatia
e-mail: rkolar@foozos.hr

Abstract.   In this paper we study geometric concepts in a general cubic structure. The well-known relationships on the cubic curve motivate us to introduce new concepts into a general cubic structure. We will define the concept of the tangential of a point in a general cubic structure and we will study tangentials of higher-order. The characterization of this concept will be also given by means of the associated totally symmetric quasigroup. We will introduce the concept of associated and corresponding points in a cubic structure, and discuss the number of mutually different corresponding points. The properties of the introduced geometric concepts will be investigated in a general cubic structure.

2010 Mathematics Subject Classification.   20N05

Key words and phrases.   Cubic structure, TSM-quasigroup, corresponding points, associated points, tangential of a point

Full text (PDF) (free access)

https://doi.org/10.3336/gm.55.2.10

References:

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  4. C. Maclaurin, De linearum geometricarum proprietatibus, London, 1720.

  5. V. Volenec, Z. Kolar-Begović and R. Kolar-Šuper, Cubic structure, Glas. Mat. Ser. III 52(72) (2017), 247-256.
    MathSciNet     CrossRef
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