{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:37:28Z","timestamp":1760150248639,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>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 \u2211n=044tan\u20611+4n\u00b0. 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.<\/jats:p>","DOI":"10.3390\/computation11110222","type":"journal-article","created":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T08:15:56Z","timestamp":1699258556000},"page":"222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2850-0974","authenticated-orcid":false,"given":"David","family":"Nocar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Education, Palack\u00fd University Olomouc, \u017di\u017ekovo n\u00e1m. 5, 77900 Olomouc, Czech Republic"}]},{"given":"George","family":"Grossman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48858, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9852-3616","authenticated-orcid":false,"given":"Ji\u0159\u00ed","family":"Va\u0161ko","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Education, Palack\u00fd University Olomouc, \u017di\u017ekovo n\u00e1m. 5, 77900 Olomouc, Czech Republic"}]},{"given":"Tom\u00e1\u0161","family":"Zdr\u00e1hal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Education, Palack\u00fd University Olomouc, \u017di\u017ekovo n\u00e1m. 5, 77900 Olomouc, Czech Republic"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s40751-016-0024-6","article-title":"Using Digital Resources for Motivation and Engagement in Learning Mathematics: Reflections from Teachers and Students","volume":"2","author":"Chao","year":"2016","journal-title":"Digit. Exp. Math. Educ."},{"key":"ref_2","unstructured":"Bailey, D.H., Borwein, J.M., Martin, U., Salvy, B., and Taufer, M. (2023, July 28). Opportunities and Challenges in 21st Century Experimental Mathematical Computation: ICERM Workshop Report. Available online: https:\/\/www.davidhbailey.com\/dhbpapers\/ICERM-2014.pdf."},{"key":"ref_3","first-page":"1089","article-title":"Utilizing the symbolic capabilities of a computer algebra system","volume":"Volume 3","author":"Maron","year":"1996","journal-title":"Technology-Based Re-Engineering Engineering Education, Proceedings of Frontiers in Education FIE\u201996 26th Annual Conference, Salt Lake City, UT, USA, 6\u20139 November 1996"},{"key":"ref_4","unstructured":"Mourrain, B., and Prieto, H. (2000). A Framework for Symbolic and Numeric Computations, INRIA. 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From MathWorld\u2014A Wolfram Web Resource. Available online: https:\/\/mathworld.wolfram.com\/Multiple-AngleFormulas.html."},{"key":"ref_10","unstructured":"Weisstein, E.W. (2023, July 26). \u201cTangent\u201d. From MathWorld\u2014A Wolfram Web Resource. Available online: https:\/\/mathworld.wolfram.com\/Tangent.html."},{"key":"ref_11","unstructured":"Hastings, C., Mischo, K., and Morrison, M. (2016). Hands-on Start to Wolfram Mathematica and Programming with the Wolfram Language, Wolfram Media. [2nd ed.]."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/11\/222\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:18:14Z","timestamp":1760131094000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/11\/222"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,6]]},"references-count":11,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["computation11110222"],"URL":"https:\/\/doi.org\/10.3390\/computation11110222","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2023,11,6]]}}}