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Arfah, Arfah
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Journal : EIGEN MATHEMATICS JOURNAL

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On the Iterated Cevian Triangle in Finite Euclidean Space Arfah, Arfah
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.336

Abstract

This paper investigates the iterative process of constructing Cevian triangles in a finite Euclidean plane. First, we prove that starting from an initial triangle, the process of iteratively taking Cevian triangles converges to a unique fixed point. Second, we show this convergence process is surjective onto the interior of the triangle; that is, for any target point in the interior, one can find an initial point whose sequence of iterated Cevian triangles converges to that target. Finally, we examine the limiting configuration of an infinite iteration and characterize a novel property intrinsic to the discrete nature of the finite geometric space, setting it apart from the classical real Euclidean case.
Co-Authors Aditya Pratama Afriyanti, Suviya Ahmad Sirulhaq Akhmad Akhmad Alwi, Muhammad Alwi Andi Nur Insan Burhanudin Burhanudin Dahlia Dahlia Dean Amri, Ary Enggrani Fitri, Lucky Fadlu, Fadlu Fahar, Abustan Fitriana Fitriana Haslinda Haslinda, Haslinda Hendra Hendra Heriyani, Heriyani Hidayati, Pratiwi Nur LUBIS, PAULINA M Aris Akbar Mansur, Narti Maryani, Sri Muliyadi Hamid NUR FITRIANI Nurhasanah Nurhasanah Nurida Isnaeni Nurmiwati, Nurmiwati Olfa, Ein Maria Paelongan, Ardi Payung, Otniel Pidola, Viras Alti Prasetio, Primadi Pratiwi Nur Hidayati Pratiwi, Heni Putra, Dios Nugraha Rafiqi Ramadhani Surya, Natasya Rasmaranti, Rasmaranti Retnoningsih Retnoningsih Ridhwan Ridhwan, Ridhwan Riyani Fitri Lubis Roihan, Muhammad S, Aswandikari Saharudin Saharudin Scheilla Aprilia Murnidayanti Sugiman Sugiman Susianti, Susianti Suyasa, Made Thursina, Mulyani Yunus, Kartini Zami Aprizal, Yusuf