Electronic Theses and Dissertation

Bilangan figuratif merupakan representasi bilangan dari pola geometri, penelitian ini berfokus pada pengkajian beberapa sifat bilangan figuratif, khususnya bilangan segitiga, persegi, pentagonal, dan heksagonal. Penelitian ini menelaaah kembali rumus ekplisit bilangan figuratif dan membuktikan kembali dengan bukti tanpa kata. Selain itu, sembilan sifat bilangan figuratif yang telah dikenal diidentifikasi kembali melalui pembuktian aljabar dan beberapa di antaranya dibuktikan menggunakan metode bukti tanpa kata, yaitu bukti yang dibatasi dengan menggunakan gambar atau visual lainnya. Metode ini memanfaatkan visualisasi geometri untuk menunjukkan kebenaran sifat-sifat tersebut. Berdasarkan hasil penelitian, rumus eksplisit untuk bilangan segitiga, persegi, pentagonal, dan heksagonal telah dibuktikan kembali melalui pendekatan visual. Selain itu, sembilan sifat bilangan figuratif berhasil diidentifikasi dan dibuktikan, baik secara aljabar maupun melalui bukti tanpa kata.

Kata kunci: Bilangan figuratif, bilangan segitiga, bilangan persegi, bilangan pentagonal, bilangan heksagonal, rumus eksplisit, bukti tanpa kata.

Figurative numbers are representations of numbers from geometric patterns. This research focuses on the study of several properties of figurative numbers, especially triangular, square, pentagonal, and hexagonal numbers. This research re-examines the explicit formulas of figurative numbers and re-proves them with wordless proofs. In addition, nine known properties of figurative numbers are re-identified through algebraic proofs and some of them are proven using the wordless proof method, namely proofs that are limited to using images or other visuals. This method utilizes geometric visualization to demonstrate the truth of these properties. Based on the research results, the explicit formulas for triangular, square, pentagonal, and hexagonal numbers have been re-proved through a visual approach. In addition, nine properties of figurative numbers have been successfully identified and proven, both algebraically and through wordless proofs. Keywords: Figurative numbers, triangular numbers, square numbers, pentagonal numbers, hexagonal numbers, explicit formulas, wordless proofs.