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All Journal EKOMBIS REVIEW: Jurnal Ilmiah Ekonomi dan Bisnis Jurnal PENA : Penelitian dan Penalaran JURNAL MANAJEMEN Journal of Economic, Bussines and Accounting (COSTING) BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Ilmu Administrasi Negara (JUAN) Journal of Economic, Management, Accounting and Technology (JEMATech) Jurnal Samudra Ekonomi dan Bisnis Jambura Nursing Journal Jurnal Onoma: Pendidikan, Bahasa, dan Sastra Variance : Journal of Statistics and Its Applications InPrime: Indonesian Journal Of Pure And Applied Mathematics Jurnal Inovasi Pendidikan dan Sains Jurnal Ilmu Manajemen Universitas Tadulako (JIMUT) Jurnal Ilmiah ASET Amsir Law Jurnal (ALJ) Lumbung Inovasi: Jurnal Pengabdian Kepada Masyarakat Absorbent Mind MATHunesa: Jurnal Ilmiah Matematika Healthy Tadulako Journal (Jurnal Kesehatan Tadulako) Jurnal Cakrawala Ilmiah Jurnal Ilmiah Pendidikan Dasar (JIPDAS) Pattimura International Journal of Mathematics (PIJMath) Jurnal Ilmiah MEA (Manajemen, Ekonomi, dan Akuntansi) Jurnal Riset Mahasiswa Matematika AACENDIKIA: Journal of Nursing Innovative: Journal Of Social Science Research Seminar Nasional Hasil Penelitian LP2M UNM Sammajiva: Jurnal Penelitian Bisnis dan Manajemen Jurnal Inovasi Bisnis Indonesia (JIBI) GEMBIRA (Pengabdian Kepada Masyarakat) Indonesian Journal of Community Empowerment Indonesian Journal of Mathematics and Applications RETORIKA : Jurnal Kajian Komunikasi dan Penyiaran Islam Journal of Mathematics, Computation and Statistics (JMATHCOS) Mammiri: Jurnal Pengabdian Masyarakat Journal of Community Service Journal of Muhammadiyah’s Application Technology Jurnal Ad'ministrare: Jurnal Pemikirian Ilmiah dan Pendidikan Administrasi Perkantoran Indonesian Journal of Computational and Applied Mathematics
Asriadi Asriadi
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Journal : Journal of Mathematics, Computation and Statistics (JMATHCOS)

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Reformulation and Generalization Of Van Aubel's Theorem Using Complex Variables Laiya, Gusti Hari Fajar; Asriadi, Asriadi; Achmad, Novianita; Ismail, Sumarno; Nurwan, Nurwan
Journal of Mathematics, Computations and Statistics Vol. 8 No. 2 (2025): Volume 08 Nomor 02 (Oktober 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i2.9051

Abstract

This research aims to reformulate and generalize Van Aubel’s Theorem using a complex number approach. Classically, Van Aubel’s Theorem states that if squares are constructed externally on the sides of an arbitrary quadrilateral, then the line segments connecting the centers of opposite squares are congruent and perpendicular to each other. Through a complex algebra approach, this research systematically reconstructs the proof of the theorem and extends its application to more complex geometric forms. The representation of points, rotations, and lines in the complex plane is employed to reprove and develop generalizations of the theorem. The results demonstrate that the use of complex numbers facilitates geometric analysis and reveals new patterns in geometric relationships. This research contributes to the advancement of modern geometry through algebraic methods and opens opportunities for further exploration of complex numbers in solving other geometric problems.
Application of Complex Numbers to Prove Several Theorems in Plane Geometry Lamuda, Zulfatra; Asriadi, Asriadi; Panigoro, Hasan S.
Journal of Mathematics, Computations and Statistics Vol. 8 No. 2 (2025): Volume 08 Nomor 02 (Oktober 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i2.9273

Abstract

Geometry is a branch of mathematics that focuses on studying the characteristics of flat and spatial structures. One of the most well-known standard flat structures is the circle. Additionally, there are triangles formed by the intersection of three line segments. This study discusses the proofs of two theorems related to circles and triangles: the radius of the circumcircle of a triangle and Heron’s theorem. Heron’s theorem is used to determine the area of an arbitrary triangle. Unlike the conventional synthetic geometry approach, this article employs an alternative method, namely complex numbers, to prove these two central theorems.
Co-Authors A. Amin, Siti Fuadillah Abdul Hafid Abdul Haliq Abdul Rahman Djamaluddin Abdullah, Ashari Abubakar, Agung Sucipto Agusyarif Rezka Nuha Al Idrus, Ainun Sukmawati Amanah AN, Indra Amir, Rahma Melati Andrianys, Irma Anisah Armayani Arsal Asis Nojeng Aslan Abidin, Aslan Aswandi, Syawal Brahim, Annisa Maharani Cendana, Amanda Puspa Damayanti, Elok Daniel Happy Putra Darman Darman Dewi Rahmawaty Isa Djihad Wungguli Dwiyanti, Andi Amytia Resty Elimawaty Rombe Faridah Faridah Fera Fera Firdaus Firdaus Gina Andyka Hutasoit Habibah, Ummu - Hamid, Abd. Haris Handar Subhandi Bakhtiar Hasan S. Panigoro Hawirah Hesti Evrianti Ikhsan Sukaria, Muhammad Imran, Nurain Indah Puspasari Kiay Demak Indryani, Rahmah IRA NURIYA SANTI Irma Satriani, Irma Irmawati Irmawati Irsan, Mohammad Irsan, Mohammad Irwan Ridwan Rahim Ismail Djakaria Isran K Hasan Jamaluddin Jamaluddin Jannah, nurjannah Kaharuddin, Nur Wildah Kai, Ferawati Khasanah, Uswatul La Ode Nashar Ladong, Fadhilah S. Laiya, Gusti Hari Fajar Lamuda, Zulfatra Mahyudin Mahyudin Mardi Mardi Mardi Mardi Marsuki, Andika Marukai, Nur Amalia Maskuri Sutomo Masse, Syukri Meggi Indrianinangsih Muallim Muallim MUH. YUNUS KASIM, MUH. YUNUS KASIM Muhammad Arham Muhammad Rifai Katili Muhammad Syarif, Muhammad Muis, Yuyun Ramadhani Munasia , Hamisah Muslimin Muslimin Muslimin Muslimin Musran, Andi Mustawa, Mustawa Mutmainna, Mutmainna Muzakir Nirma Nirma NISKY IMANSYAH YAHYA Ni’amah, Miftaku Normalia, Normalia Nur, Muhammad Awal NURDIN, DJAYANI Nurfadila Nurfadila, Nurfadila Nurfadilla, Nurfadilla Nurrahmah Nurrahmah, Nurrahmah Nursalim Nursalim Nurwan, Nurwan Pomahiya, Saiful Ponirin Ponirin, Ponirin Prabawanti, Kd. Jessika Pricylia Chintya Dewi Buntuang Rahma Rahma Rauf, Dewi Nur Angriani Resmawan Resmawan Rifni, Andi Risnawati Risnawati Risnawati Risnawati Rizkiani Iskandar Sahabuddin Latif Saharuddin Salmun K. Nasib Santi, Ira Nurya Sarnia, Wawaa Sastria, Andi Shabir, Achmad Siar Nimah Sigit Mulyono Sinta Pusvita Sari Siti Nurmardia Abdussamad Siyono, Siyono Sriwanti Sriwanti Sudarto , Sudarto Sudarto Sudarto Sudirman Sudirman Sukaria, Muhammad Ikhsan Sumarno Ismail Surayya Surayya Surayya, Surayya Suriati, Suriati Suryadi Hadi Suwandi N Syam, Anita Syamsiar, Syamsiar Syamsul Bachri Syamsul Bahri Dg. Parani Tambaru, Rachman Tediy Adrian Hermansyah Tri Ramadhani Ulopo, Asrul S Vitayanti Fattah Wahyudi, R.Firdaus Wahyuningsih Wahyuningsih Wanti, Sri Wiri Wirastuti Yuliana Yuliana Yumi, Sri Yunus, Andi Muhammad Yusri, Andi Zakiyah Zahara