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All Journal Matematika: Jurnal Teori dan Terapan AdMathEdu : Jurnal Ilmiah Pendidikan Matematika, Ilmu Matematika dan Matematika Terapan Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Journal of the Indonesian Mathematical Society Jurnal KARISMATIKA Jurnal Sains Matematika dan Statistika Journal of Medives Jurnal Penelitian Pendidikan IPA (JPPIPA) MUST: Journal of Mathematics Education, Science and Technology BAREKENG: Jurnal Ilmu Matematika dan Terapan Jambura Journal of Mathematics JURNAL MATHEMATIC PAEDAGOGIC InPrime: Indonesian Journal Of Pure And Applied Mathematics Unri Conference Series: Community Engagement Journal of Science and Technology Mathematics and Applications (MAp) Journal Euclid Jurnal Matematika Integratif Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang Science, Technology, and Communication Journal Jcommits : The Journal of Community Empowerment, Innovation, and Sustainability
Sri Gemawati
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Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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The k-Tribonacci Matrix and the Pascal Matrix Gemawati, Sri; Musraini, Musraini; Mirfaturiqa, Mirfaturiqa
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.24131

Abstract

This article discusses the relationship between the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn, by first constructing the k-Tribonacci matrix and then looking for its inverse. From the inverse k-Tribonacci matrix, unique characteristics can be constructed so that general shapes can be constructed, and then from the relationship of the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn obtain a new matrix, i.e. Un(k). Furthermore, a factor is derived from the relationship of the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn i.e. Pn = Tn(k)Un(k).
The Existence of Cocyclic Formed by Angle Trisectors in a Butterfly Quadrilateral and its Application in Physics Mardani Fitra; Mashadi; Sri Gemawati
Jurnal Penelitian Pendidikan IPA Vol 11 No 2 (2025): February
Publisher : Postgraduate, University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jppipa.v11i2.9909

Abstract

One of the most intriguing results related to angle trisectors in convex quadrilaterals is Morley's Theorem, which several authors have subsequently extended to non-convex quadrilaterals. Numerous studies have explored the side lengths of angle bisectors, angle trisectors, and the area ratios formed by angle trisectors in both convex and non-convex quadrilaterals. However, no research has discussed the problem of angle trisectors in butterfly quadrilaterals. Therefore, this paper aims to extend the concept of angle trisectors to butterfly quadrilaterals. Various other quadrilaterals will be formed from the construction of these angle trisectors. By employing the concept of concyclic, we will demonstrate the existence of several concyclic quadrilaterals arising from this trisector construction. Triangle angles in butterfly quadrilaterals in geometry play an important role in physics. Geometry provides a visual and mathematical language that allows us to describe, analyze, and understand various physical phenomena.
Faktorisasi Matriks Pascal Melalui Matriks k-Tribonacci Mirfaturiqa, Mirfaturiqa; Gemawati, Sri; Rini, Silfia; weriono, weriono; Mawarni, Sri
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 .
SUATU KAJIAN DERIVASI YANG DIINDUKSI OLEH ENDOMORFISMA PADA PSEUDO BG-ALJABAR Ramadhani Fitri Fitri; Sri Gemawati; Susilawati Susilawati
MUST: Journal of Mathematics Education, Science and Technology Vol 10 No 2 (2025): DECEMBER
Publisher : Universitas Muhammadiyah Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30651/must.v10i2.30742

Abstract

Penelitian ini mengembangkan konsep derivasi pada pseudo BG-aljabar melalui pendekatan berbasis endomorfisma. BG-aljabar (P; ∗, 0) adalah himpunan tak kosong P dengan operasi biner ∗ dan konstanta 0 yang memenuhi aksioma (BG1) p ∗ p = 0, (BG2) p ∗ 0 = p, dan (BG3) (p ∗ q) ∗ (0 ∗ q) = p untuk setiap p, q ∈ P. Pseudo BG-aljabar (R; ∗, ⋄, 0) merupakan generalisasi BG-aljabar dengan dua operasi biner yang memenuhi (PBG1) p ∗ 0 = p ⋄ 0 = p, (PBG2) p ∗ p = p ⋄ p = 0, dan (PBG3) (p ∗ q) ⋄ (0 ∗ q) = (p ⋄ q) ∗ (0 ⋄ q) = p untuk setiap p, q ∈ R. Penelitian ini memperkenalkan dua jenis derivasi utama, yaitu f-derivasi dan (f, g)-derivasi, yang masing-masing dikonstruksi melalui operasi gabungan (⊛) dan operasi simetris (⊙). Metode penelitian menggunakan pendekatan aksiomatik-deduktif dengan teknik pembuktian teorema berbasis sistem aksioma pseudo BG-aljabar. Hasil penelitian menunjukkan bahwa pendekatan menggunakan endomorfisma, baik dengan satu fungsi f maupun pasangan fungsi (f, g), menghasilkan kerangka derivasi yang konsisten dan dapat dikarakterisasi secara sistematis. Teorema fundamental membuktikan bahwa f-derivasi kiri reguler identik dengan endomorfisma penginduksinya. Kerangka teoretis yang dihasilkan memberikan landasan untuk eksplorasi derivasi pada struktur aljabar pseudo lainnya.
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
Co-Authors Abd. Ghafur Bin Ahmad Abd. Ghafur Bin Ahmad Abdul Hadi Ade Nova Rahma Ade Novia Rahma Afriastuti, Sherly Agusni ' Alberta Rika Pratiwi Ali Subroto Amalina Amalina, Amalina Andriani, Dessy Ani Ani Ardiansyah Yan Hakim Nasution Asli Sirait 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 Leli Deswita Lydia . Ariftalia M. D. H. . Gamal M. Imran M. Mashadi M.D.H Gamal M.D.H Gamal Mardani Fitra Mas hadi Mashadi Mashadi ' Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mashadi Mirfaturiqa, Mirfaturiqa Misra Herlina 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 Ramadhan, Andi Rio Ramadhani Fitri Fitri Rika Pratiwi Rika Pratiwi Rike Marjulisa Rini, Silfia Riza . Gushelsi Rora Oktafia Selva Amelia Sandi Siswanti, T. Fuja Sri . Handayani Sri Mawarni, Sri Sri Sukmawati Sugianti, Khoirunnisa Surlina Surlina Susilawati, S. Syamsudhuha Syamsudhuha Welly Desriyati Wellya Aziz Weriono Wita . Maywidia Yattaqi, Egytia Yeni . Azrida Yuliardani, Novita Yulismansyah ' Zulkarnain Zulkarnain