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All Journal Jurnal Pengabdian Masyarakat dan Riset Pendidikan Pentagon: Jurnal Matematika dan Ilmu Pengetahuan Alam
Septika Aulia Putri
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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.
Analisis Biaya dan Tingkat Layanan Sistem Antrian Call Center Menggunakan Model M/M/S: Penelitian Nerli Khairani; Rizky Suhaila Hsb; Septika Aulia Putri; Sesy Ophelia Tampubolon
Jurnal Pengabdian Masyarakat dan Riset Pendidikan Vol. 4 No. 2 (2025): Jurnal Pengabdian Masyarakat dan Riset Pendidikan Volume 4 Nomor 2 (October 202
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31004/jerkin.v4i2.3117

Abstract

This study aims to analyze cost optimization and service level in a call center queueing system using the M/M/S model. The main problem addressed is the imbalance between operational cost efficiency and customer service quality in determining the optimal number of servers. The research applies a quantitative approach with a case study design based on 1,251 historical observations of call center performance. Data were analyzed using the M/M/S queueing model with arrival and service rate parameters of 8.27 customers per hour and 22.85 customers per hour per server, respectively. The results indicate that the two-server configuration is the optimal solution, achieving a 96.8% service level and an operational cost of Rp 56,601 per hour, meeting industry standards while maintaining cost efficiency. This configuration yields a 45.3% improvement in service level compared to one server with a 61.8% cost increase, while adding a third server provides only marginal improvement. The findings provide practical implications for call center management in balancing financial and service quality aspects. In addition, this study offers educational value as a learning resource in applied mathematics and operations research courses.
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 Muthia Shafa Nazahra Nerli Khairani Rizky Suhaila Hsb Sesy Ophelia Tampubolon