Topology And Tradition: The Knot Polynomials of Ketupat Nabi

Abstract

This study explores the intersection of mathematics and culinary traditions, focusing on “Ketupat Nabi,” a dish from South Sulawesi’s Bugis community. By applying knot theory, it seeks to understand the mathematical properties of the dish’s knot diagrams. The research began with selecting traditional foods characterized by knots or ties, essential for framing the study’s focus. Photographs and cultural histories of these foods were then collected to provide context. The analysis involved comparing these culinary knots with established knot theory literature, leading to the creation of graphical knot diagrams. These diagrams underwent mathematical analysis using the Alexander polynomial, a key tool in knot theory. The ketupat’s knot diagram, featuring 24 crossing points and incapable of 3-colorability, was a primary focus. Remarkably, this study identified a unique Alexander polynomial for the Ketupat Nabi’s knot diagram, a significant addition to the knowledge of polynomials associated with 24-crossing-point knots. The identified polynomial for the ketupat Nabi’s knot diagram is: Δ 𝐾 ( 𝑡 )=− 𝑡 10 +7 𝑡 9 −21 𝑡 8 +35 𝑡 7 −35 𝑡 6 +26 𝑡 5 −26 𝑡 4 +30 𝑡 3 −37 𝑡 2 +61 𝑡 1 −79+61 𝑡 −1 −37 𝑡 −2 +30 𝑡 −3 −26 𝑡 −4 +26 𝑡 −5 −35 𝑡 −6 +35 𝑡 −7 −21 𝑡 −8 +7 𝑡 −9 − 𝑡 −10 These findings accentuate the value of interdisciplinary approaches in elucidating the multifaceted relationship between cultural and mathematical paradigms. Moreover, the research illuminates the untapped scholarly potential of traditional foods as avenues for mathematical exploration.