The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Computation Pub Date : 2023-11-06 DOI:10.3390/computation11110222

David Nocar, George Grossman, Jiří Vaško, Tomáš Zdráhal

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Abstract

This article explores the accessibility of symbolic computations, such as using the Wolfram Mathematica environment, in promoting the shift from informal experimentation to formal mathematical justifications. We investigate the accuracy of computational results from mathematical software in the context of a certain summation in trigonometry. In particular, the key issue addressed here is the calculated sum ∑n=044tan⁡1+4n°. This paper utilizes Wolfram Mathematica to handle the irrational numbers in the sum more accurately, which it achieves by representing them symbolically rather than using numerical approximations. Can we rely on the calculated result from Wolfram, especially if almost all the addends are irrational, or must the students eventually prove it mathematically? It is clear that the problem can be solved using software; however, the nature of the result raises questions about its correctness, and this inherent informality can encourage a few students to seek viable mathematical proofs. In this way, a balance is reached between formal and informal mathematics.

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Wolfram Mathematica计算结果在三角求和中的准确性

本文探讨了符号计算的可访问性，例如使用Wolfram Mathematica环境，以促进从非正式实验到正式数学论证的转变。本文以三角学中的某一求和为例，探讨了数学软件计算结果的准确性。特别地，这里处理的关键问题是计算和∑n=044tan (1+4n)°。本文利用Wolfram Mathematica软件对和中的无理数进行了更精确的处理，通过对无理数进行符号化表示，而不是使用数值近似来实现。我们能相信Wolfram的计算结果吗，尤其是当几乎所有的加数都是无理数的时候，还是说学生们最终必须用数学方法证明它?很明显，这个问题可以用软件来解决;然而，结果的性质引起了对其正确性的质疑，这种固有的非正式性可以鼓励一些学生寻求可行的数学证明。通过这种方式，在正式数学和非正式数学之间达到了平衡。

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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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.