通过计算三角形探索多边形数筛

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Computation Pub Date : 2023-12-10 DOI:10.3390/computation11120251

Sergei Abramovich

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引用次数: 0

摘要

本文探讨了通过逐步消去原始序列的项而得到的不同边的多边形数的子序列。消除是基于特殊的规则，类似于通过消除质数的倍数来发展埃拉托塞尼斯的经典筛子。电子表格、Wolfram Alpha、Maple 和《整数序列在线百科全书》为这些适合技术强化中学数学教育课程的初级数论活动提供了支持。论文中将多边形数的子序列称为 k 阶多边形数筛，其中包括 k 的基 2 指数函数。在技术免疫/技术赋能框架的基础上，采用了不同的问题解决方法来推导此类和其他数筛。计算和数学推理的准确性通过使用一种以上数字工具的计算三角测量技术得到确认。下面简要介绍数学史上的一些相关节选。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exploring Polygonal Number Sieves through Computational Triangulation

The paper deals with the exploration of subsequences of polygonal numbers of different sides derived through step-by-step elimination of terms of the original sequences. Eliminations are based on special rules similarly to how the classic sieve of Eratosthenes was developed through the elimination of multiples of primes. These elementary number theory activities, appropriate for technology-enhanced secondary mathematics education courses, are supported by a spreadsheet, Wolfram Alpha, Maple, and the Online Encyclopedia of Integer Sequences. General formulas for subsequences of polygonal numbers referred to in the paper as polygonal number sieves of order k, that include base-two exponential functions of k, have been developed. Different problem-solving approaches to the derivation of such and other sieves based on the technology-immune/technology-enabled framework have been used. The accuracy of computations and mathematical reasoning is confirmed through the technique of computational triangulation enabled by using more than one digital tool. A few relevant excerpts from the history of mathematics are briefly featured.

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来源期刊

Computation Mathematics-Applied Mathematics

CiteScore

3.50

自引率

4.50%

发文量

201

审稿时长

8 weeks

期刊介绍： Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.