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Alternative Proofs for the Side Trisector Lengths Theorem of a Triangle Rahmayani, Indah; Mashadi, Mashadi; Gemawati, Sri
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.70223.91-100

Abstract

In general, discussions regarding the line for side trisectors are still relatively limited compared to angle trisectors. For angle trisectors, most studies only discuss Morley’s Theorem and its extensions. Meanwhile, for side trisectors, existing papers usually calculate the lengths using both the sides and the angles of the triangle. A common problem is how to find the side trisectors length from its opposite vertex when only the side lengths are known. Furthermore, if the side trisector line is extended to form a tangential excircle, can we determine its radius. In this article, we discuss several alternative proofs to determine the lengths produced by side trisectors in a triangle. The main focus is to derive a formula for the side trisectors length using only the original side lengths and to find the radius of the tangential excircle. These proofs are done simply by using several geometric approaches, such as trigonometry, Stewart’s Theorem, and the Pythagorean Theorem. The result provide a standard formula for the trisector length, which is then used to find the radius of the tangential excircle in the constructed triangle
PELATIHAN MICROSOFT OFFICE UNTUK MENINGKATKAN KOMPETENSI GURU DI DESA MEKONG Sri Gemawati; Musraini, M; Rike Marjulisa; Ayunda Putri; Irsan Taufik Ali
Jurnal Pengabdian Masyarakat Multidisiplin Vol 8 No 1 (2024): Oktober
Publisher : LPPM Universitas Abdurrab

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36341/jpm.v8i1.5253

Abstract

Microsoft Office training for teachers in Mekong Village, West Tebing Tinggi District, aims to enhance teachers' technical competence in using software that is essential for the modern educational process. Skills in Microsoft Word, Excel, and PowerPoint are expected to help teachers optimize the learning process, prepare teaching materials, and carry out administrative tasks more effectively. This training is highly relevant, especially for teachers in remote areas where the use of technology is often limited but very much needed to support more interactive learning and better-organized administration. The training is conducted face-to-face with a combination of lectures and hands-on practice, designed to ensure participants can understand and apply the material well. The training is conducted face-to-face with a combination of lectures and hands-on practice, designed to ensure participants can understand and apply the material well. Teachers are trained in the use of important Microsoft Office features, such as creating mass mailings using mail merge in Word, analyzing student grade data in Excel with formulas like IF, VLOOKUP, and HLOOKUP, and creating interactive presentations in PowerPoint. With this method, the transfer of knowledge and skills occurs optimally, and participants can immediately apply the knowledge they have gained in the context of their daily work. The evaluation of the training results shows a significant improvement in participants' competencies, with an average increase of 25% based on pre-test and post-test results. In conclusion, face-to-face Microsoft Office training has proven effective in enhancing teachers' technical skills. For further development, it is recommended to have advanced training with a longer duration and more in-depth material, so that teachers are better prepared to face technological challenges in the world of education.
Faktorisasi Matriks Pascal Melalui Matriks k-Tribonacci Mirfaturiqa Mirfaturiqa; Sri Gemawati; Silfia Rini; weriono weriono; Sri Mawarni
Jurnal Sains Matematika dan Statistika Vol. 12 No. 1 (2026): JSMS Januari 2026
Publisher : Universitas Islam Negeri Sultan Syarif Kasim Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24014/jsms.v12i1.38785

Abstract

Artikel ini membahas  hubungan matriks Pascal  dan matriks k-tribonacci , dari hubungan dari kedua matriks tersebut diperoleh sebuah definisi matriks baru yaitu matriks . Kemudian, dengan matriks baru  diperoleh faktorisasi dari matriks Pascal melalui matriks k-tribonacci yaitu .
On Derivations of Pseudo BN-algebras Mahiroh; Sri Gemawati; Syamsudhuha
Desimal: Jurnal Matematika Vol. 9 No. 2 (2026): Desimal
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v9i2.32008

Abstract

Derivation theory plays a fundamental role in implication-based algebra by providing operator frameworks that reveal the structural behavior of algebraic systems. Although numerous derivation concepts have been established for BN-algebras and related implication algebras, an appropriate derivation framework for pseudo BN-algebras has remained unavailable because their dual-operation structure cannot be accommodated by existing derivation formulations. This study aims to establish a unified derivation framework for pseudo BN-algebras through the introduction of algebraically compatible operator mappings. Using a deductive mathematical approach, two auxiliary binary operations, ⊛ and , are constructed to define Type 1 and Type 2 (l,r)-derivations, (r,l)-derivations, and left derivations. Their fundamental properties are then investigated through formal definitions, propositions, and rigorous mathematical proofs. The obtained results show that both derivation systems satisfy regularity conditions, preserve essential identities involving the distinguished zero element, and maintain structural consistency with the defining axioms of pseudo BN-algebras. More importantly, the proposed framework demonstrates that derivation theory for pseudo BN-algebras cannot be obtained by directly extending existing derivation concepts but instead requires new algebraic constructions that are intrinsically determined by the interaction of their two binary operations. Consequently, this study establishes the first derivation framework for pseudo BN-algebras, broadens the scope of derivation theory within implication-based algebra, and provides a rigorous theoretical foundation for future investigations of generalized derivations, derivation-induced ideals, homomorphisms, congruence relations, fuzzy derivations, and other operator structures on generalized implication algebras.
Matematika dan Konseling: Pendekatan Interdisipliner untuk Mendukung Pembelajaran dan Kesejahteraan Emosional Anak-anak TKI di Malaysia Rahmi; Yuslenita Muda; Amirah Diniaty; Kartini; Sri Gemawati; Rita Desfitri; Andi Susanto; Zubaidah Amir
Jurnal SOLMA Vol. 15 No. 2 (2026)
Publisher : Universitas Muhammadiyah Prof. DR. Hamka (UHAMKA Press)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22236/solma.v15i2.22057

Abstract

Background: Kegiatan pengabdian kepada masyarakat ini bertujuan memberikan dukungan pembelajaran dan pendampingan psikososial bagi anak-anak TKI di Sanggar Bimbingan Amin, Malaysia, melalui pendekatan interdisipliner antara matematika dan konseling. Metode: Kegiatan dilaksanakan pada 8–10 Desember 2024 dengan melibatkan 20 anak usia 3–13 tahun melalui pembelajaran matematika menyenangkan, permainan edukatif, diskusi interaktif, dan terapi diri menggunakan art therapy. Hasil: Hasil kegiatan menunjukkan bahwa anak-anak mengikuti kegiatan dengan antusias, menunjukkan respons positif terhadap pembelajaran matematika berbasis permainan, serta merasa lebih nyaman mengekspresikan pengalaman dan perasaan mereka dalam sesi art therapy. Program ini memberikan manfaat awal bagi penguatan rasa percaya diri, interaksi sosial, dan suasana belajar yang lebih suportif. Kesimpulan: Secara umum, pendekatan interdisipliner ini berpotensi mendukung perkembangan akademik dan emosional anak-anak TKI, namun evaluasi yang lebih terukur masih diperlukan untuk menilai dampak program secara lebih meyakinkan.
Co-Authors Abd. Ghafur Bin Ahmad Abd. Ghafur Bin Ahmad Abdul Hadi Ade Nova Rahma Ade Novia Rahma Agusni ' Alberta Rika Pratiwi Ali Subroto Amalina Amalina, Amalina Amirah Diniaty Andriani, Dessy Ani Ani Ardiansyah Yan Hakim Nasution Asli Sirait Ayunda Putri Ayunda Putri Barutu, Fabelia Andani Beauty, Meivy Andhika Bona Martua Siburian Chitra Valentika Danil Hendry Gamal, Moh Delisa Pratiwi Dessy Andriani Dessy Andriani . Egytia Yattaqi Elsi Fitria Endah Dwi Jayanti Endang Lily Fabelia Andani Barutu Gamal, M.D.H Hasriati Hasriati Hendra Maryulis Husnul Khatimah Husnul Khatimah Ihda Hasbiyati Indryantika, Nessy Irma . Fitri IRSAN TAUFIK ALI Jufri Jufri Jufri Jufri Jufri, Jufri Kartini Kartini Kartini Leli Deswita Lydia . Ariftalia M. D. H. . Gamal M. Imran M. Mashadi M.D.H Gamal M.D.H Gamal Mahiroh Mardani Fitra Mas hadi Mashadi Mashadi ' Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mirfaturiqa Mirfaturiqa, Mirfaturiqa Misra Herlina Musraini M Musraini, M Musraini, Musraini Mu’tamar, Khozin novelia . . Novita Yuliardani Novrialman ' Nur Meliana Sari Nurbai, Reihani Jemila Oki Rasdana Pratiwi, Delisa Puteri Januarti Putri, Ayuni Rahmayani, Indah Rahmi Rahmi Ramadhan, Andi Rio Ramadhani Fitri Fitri Rika Pratiwi Rika Pratiwi Rike Marjulisa Rita Desfitri Riza . Gushelsi Rora Oktafia Selva Amelia Sandi Silfia Rini Sri . Handayani Sri Mawarni Sri Sukmawati Sugianti, Khoirunnisa Surlina Surlina Susanto, Andi Susilawati, S. Syamsudhuha Syamsudhuha Syamsudhuha Welly Desriyati Wellya Aziz weriono weriono Wita . Maywidia Yeni . Azrida Yuliardani, Novita Yulismansyah ' Yuslenita Muda Zubaidah Amir Zulkarnain Zulkarnain