Glasnik Matematicki, Vol. 54, No. 2 (2019), 409-420.

A COMPLETE SYSTEM OF THE SHAPES OF TRIANGLES

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 examine the shape of a triangle by means of a ternary operation which satisfies some properties. We prove that each system of the shapes of triangles can be obtained by means of the field with defined ternary operation. We give a geometric model of the shapes of triangles on the set of complex numbers which motivate us to introduce some geometric concepts. The concept of transfer is defined and some interesting properties are explored. By means of transfer the concept of a parallelogram is introduced.

2010 Mathematics Subject Classification.   20N05

Key words and phrases.   Shape of a triangle, ternary operation, transfer.

https://doi.org/10.3336/gm.54.2.07

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