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Properties and Applications of Pascal's Triangle and Pascal's Pyramid
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Abstract
With the increasing application of mathematics in modern society, a deep understanding of mathematical foundational theories becomes particularly important. This paper primarily investigates Pascal's Triangle and its three-dimensional extension, Pascal's Pyramid, and explores their properties and applications. The purpose of the study is to show their applications in different math-related areas, including algebra, probability theory, and combinatorial mathematics through literature review and mathematical modeling. This paper used case and data analysis to explore the relationships between Pascal's Triangle and the Fibonacci sequence, as well as Pascal's Pyramid and the Tribonacci sequence. The results show that Pascal's Triangle not only plays a role in binomial expansion, but also demonstrates its importance in trinomial expansions. This paper also preliminarily explores the generalization of Pascal's Triangle and Pyramid based on ab and abc models. By extending these models, this paper can offer new insights into their potential for advancing theoretical and applied mathematics, suggesting ways for future research in enhancing and applying these mathematical structures.
Keywords
Pascal’s Triangle, Pascal’s Pyramid, Fibonacci sequence, Tribonacci sequence
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Cite this article
Chen,S. (2025). Properties and Applications of Pascal's Triangle and Pascal's Pyramid. Theoretical and Natural Science,84,36-39.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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Volume title: Proceedings of the 4th International Conference on Computing Innovation and Applied Physics
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