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All Journal Jurnal Pengabdian Masyarakat dan Riset Pendidikan Pentagon: Jurnal Matematika dan Ilmu Pengetahuan Alam
Muthia Shafa Nazahra
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Humanities Education Languange, Linguistic, Communication & Media Mathematics Other

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Simetri dalam Desain: Aplikasi Web untuk Pembangkitan Motif Karpet Turki Berdasarkan Grup Frieze dan Kristalografi: Penelitian Cindy Injilia S; Muthia Shafa Nazahra; Septika Aulia Putri
Jurnal Pengabdian Masyarakat dan Riset Pendidikan Vol. 3 No. 4 (2025): Jurnal Pengabdian Masyarakat dan Riset Pendidikan Volume 3 Nomor 4 (April 2025
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31004/jerkin.v3i4.1593

Abstract

This research develops a web-based application named Symmetry Studio for the generation of Turkish carpet motifs based on the principles of Group Frieze and Crystallography. This research addresses the need for a digital tool that integrates the concept of mathematical symmetry with traditional carpet design. Using research and development (R&D) methodology, the application was built with HTML, CSS, JavaScript, and p5.js library for real-time visualization. The application has interactive features including pattern type selection (frieze, crystallography, or mixed), 21 motif styles (flower, star, spiral, geometric pattern, etc.), various symmetry transformations (translation, reflection, rotation, shear reflection, etc.), and customizable color settings. Results show that the application successfully generates aesthetically pleasing Turkish carpet motifs through mathematical transformations, producing three different types of patterns: Frieze patterns for border designs, Crystallographic patterns for the main surface of the carpet, and mixed patterns for dynamic ornamental effects. The web-based platform provides accessibility through GitHub Pages, enabling widespread use in education, research, and creative industries. This research contributes to the preservation and innovation of traditional carpet design while strengthening the integration of math, art, and technology in digital design methodologies.
Supremum Pada Masalah Optimasi Fungsi Real Berdimensi Satu Menggunakan Python Aqilah, Khairunnisa; Muthia Shafa Nazahra; Rizky Suhaila Hsb; Septika Aulia Putri
Pentagon : Jurnal Matematika dan Ilmu Pengetahuan Alam Vol. 3 No. 4 (2025): Desember: Pentagon : Jurnal Matematika dan Ilmu Pengetahuan Alam
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/pentagon.v3i4.882

Abstract

The concept of supremum is fundamental in real analysis and plays a crucial role in the optimization of single-variable real functions. In practice, not all functions attain their supremum explicitly, which necessitates numerical approaches to evaluate their behavior computationally. This study aims to analyze the supremum of several one-dimensional real functions with different characteristics using a grid-search method implemented in Python. Four functions were examined: a parabolic function, a rational function with a sharp peak, a discontinuous piecewise function, and a function with a vertical asymptote. The analysis involved modeling the functions, discretizing the domain, performing numerical approximation of the supremum, verifying the results against analytical values, and using graphical visualization to observe the function behavior near the supremum. The findings indicate that the supremum of the parabolic, rational, and piecewise functions can be accurately identified, with results consistent with analytical expectations despite minor deviations caused by grid resolution limitations in the rational function. Meanwhile, the function with a vertical asymptote yields an unbounded supremum, which cannot be attained within the domain. These results demonstrate that Python provides stable and reliable numerical estimates of the supremum across various types of one-dimensional real functions, validating the effectiveness of computational methods in supporting conceptual understanding of supremum.
Co-Authors Aqilah, Khairunnisa Cindy Injilia S Rizky Suhaila Hsb Septika Aulia Putri