The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry
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 cont...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/11/11/222 |
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| author | David Nocar George Grossman Jiří Vaško Tomáš Zdráhal |
| author_facet | David Nocar George Grossman Jiří Vaško Tomáš Zdráhal |
| author_sort | David Nocar |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><msubsup><mo stretchy="true">∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mn>44</mn></mrow></msubsup><mrow><msup><mrow><mrow><mrow><mi mathvariant="normal">tan</mi></mrow><mo></mo><mrow><mfenced separators="|"><mrow><mn>1</mn><mo>+</mo><mn>4</mn><mi>n</mi></mrow></mfenced></mrow></mrow></mrow><mrow><mo>°</mo></mrow></msup></mrow></mrow><mo>.</mo></mrow></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-09T16:55:15Z |
| format | Article |
| id | doaj.art-efb8674a61e44a89a896206f61204aed |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-09T16:55:15Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-efb8674a61e44a89a896206f61204aed2023-11-24T14:36:24ZengMDPI AGComputation2079-31972023-11-01111122210.3390/computation11110222The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in TrigonometryDavid Nocar0George Grossman1Jiří Vaško2Tomáš Zdráhal3Department of Mathematics, Faculty of Education, Palacký University Olomouc, Žižkovo nám. 5, 77900 Olomouc, Czech RepublicDepartment of Mathematics, Central Michigan University, Mount Pleasant, MI 48858, USADepartment of Mathematics, Faculty of Education, Palacký University Olomouc, Žižkovo nám. 5, 77900 Olomouc, Czech RepublicDepartment of Mathematics, Faculty of Education, Palacký University Olomouc, Žižkovo nám. 5, 77900 Olomouc, Czech RepublicThis 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><msubsup><mo stretchy="true">∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mn>44</mn></mrow></msubsup><mrow><msup><mrow><mrow><mrow><mi mathvariant="normal">tan</mi></mrow><mo></mo><mrow><mfenced separators="|"><mrow><mn>1</mn><mo>+</mo><mn>4</mn><mi>n</mi></mrow></mfenced></mrow></mrow></mrow><mrow><mo>°</mo></mrow></msup></mrow></mrow><mo>.</mo></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2079-3197/11/11/222student motivation for mathematicsmathematical software limitationstrigonometric multiple-angle formulapolynomial equationsfundamental theorem of algebraVieta’s formula |
| spellingShingle | David Nocar George Grossman Jiří Vaško Tomáš Zdráhal The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry Computation student motivation for mathematics mathematical software limitations trigonometric multiple-angle formula polynomial equations fundamental theorem of algebra Vieta’s formula |
| title | The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry |
| title_full | The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry |
| title_fullStr | The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry |
| title_full_unstemmed | The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry |
| title_short | The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry |
| title_sort | accuracy of computational results from wolfram mathematica in the context of summation in trigonometry |
| topic | student motivation for mathematics mathematical software limitations trigonometric multiple-angle formula polynomial equations fundamental theorem of algebra Vieta’s formula |
| url | https://www.mdpi.com/2079-3197/11/11/222 |
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