PEMOTONGAN TRIANGULASI POLIGON DAN KORESPONDENSINYA DENGAN PLANAR BINARY ROOTED TREE DAN CONWAY-COXETER FRIEZE PATTERN

NAZWA BILL QISTY, . (2026) PEMOTONGAN TRIANGULASI POLIGON DAN KORESPONDENSINYA DENGAN PLANAR BINARY ROOTED TREE DAN CONWAY-COXETER FRIEZE PATTERN. Sarjana thesis, UNIVERSITAS NEGERI JAKARTA.

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Abstract

Triangulasi poligon, planar binary rooted tree, dan Conway–Coxeter frieze pattern merupakan objek-objek kombinatorik yang saling berkorespondensi. Penelitian ini bertujuan untuk mengkaji pemotongan triangulasi poligon berdasarkan suatu diagonal internal serta korespondensinya dengan planar binary rooted tree dan Conway–Coxeter frieze pattern. Penelitian ini menggunakan metode studi pustaka dengan pendekatan teoritis. Suatu poligon tertriangulasi P dipotong oleh diagonal internal sehingga diperoleh subpoligon P1 dan P2. Pemotongan tersebut direpresentasikan pada planar binary rooted tree B sehingga diperoleh subtree B1 dan B2, kemudian dikonstruksi Conway–Coxeter frieze pattern yang bersesuaian. Hasil penelitian menunjukkan bahwa frieze pattern F1 dan F2 yang bersesuaian dengan P1 dan P2 termuat di dalam frieze pattern F yang bersesuaian dengan P. Selain itu, Conway-Coxeter frieze pattern yang dikonstruksi dari B1 dan B2 identik dengan F1 dan F2. Dengan demikian, korespondensi antara triangulasi poligon, planar binary rooted tree, dan Conway–Coxeter frieze pattern tetap dipertahankan pada proses pemotongan. ***** Polygon triangulations, planar binary rooted trees, and Conway–Coxeter frieze patterns are combinatorial objects that exhibit correspondences with one another. This study aims to investigate the cutting of polygon triangulations along an internal diagonal and its correspondence with planar binary rooted trees and Conway–Coxeter frieze patterns. This research employs a literature study method with a theoretical approach. A triangulated polygon P is cut along an internal diagonal to obtain two subpolygons, P1 and P2. This cutting process is represented on a planar binary rooted tree B, resulting in two subtrees, B1 and B2, from which the corresponding Conway–Coxeter frieze patterns are constructed. The results show that the frieze patterns F1 and F2 corresponding to P1 and P2 are contained in the frieze pattern F corresponding to P. Moreover, the Conway–Coxeter frieze patterns constructed from B1 and B2 are identical to F1 and F2, respectively. Therefore, the correspondence among polygon triangulations, planar binary rooted trees, and Conway–Coxeter frieze patterns is preserved under the cutting process.

Item Type:	Thesis (Sarjana)
Additional Information:	1). Dr. Lukita Ambarwati, S.Pd, M.Si. ; 2). Dr. Yudi Mahatma, M.Si.
Subjects:	Sains > Matematika
Divisions:	FMIPA > S1 Matematika
Depositing User:	Nazwa Bill Qisty .
Date Deposited:	28 Aug 2026 08:18
Last Modified:	28 Aug 2026 08:18
URI:	http://repository.unj.ac.id/id/eprint/72543

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