Rad HAZU, Matematičke znanosti, Vol. 24 (2020), 15-27.

ON TRIANGLES WITH COORDINATES OF VERTICES FROM THE TERMS OF THE SEQUENCES {Ukn} AND {Vkn}

Neşe Ömür, Gökhan Soydan, Yücel Türker Ulutaş and Yusuf Doğru

Department of Mathematics, Kocaeli University, 41380 Izmit-Kocaeli, Turkey
e-mail: neseomur@kocaeli.edu.tr

Department of Mathematics, Bursa Uludag University, 16059 Bursa, Turkey
e-mail: gsoydan@uludag.edu.tr

Department of Mathematics, Kocaeli University, 41380 Izmit-Kocaeli, Turkey
e-mail: turkery@kocaeli.edu.tr

Hava Eğitim Komutanlığı, Konak-Izmir, Turkey
e-mail: yusufdogru1@yahoo.com

Abstract.   In this paper, we determine some results of the triangles with coordinates of vertices involving the terms of the sequences {Ukn} and {Vkn} where Ukn are terms of a second order recurrent sequence and Vkn are terms in the companion sequence for odd positive integer k, generalizing works of Čerin. For example, the cotangent of the Brocard angle of the triangle Δkn is cot(ΩΔkn = (Uk(2n+3)V2k - Vk(2n+3)Uk) / ((-1)nU2k).

2020 Mathematics Subject Classification.   11B37, 11Y55, 05A19.

Key words and phrases.   Second order sequence, triangle, orthologic, paralogic, homologic.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/ydkx2cwq49

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