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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15410%2F23%3A73621281" target="_blank" >RIV/61989592:15410/23:73621281 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3390/computation11110222" target="_blank" >https://doi.org/10.3390/computation11110222</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/computation11110222" target="_blank" >10.3390/computation11110222</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

The 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 ∑44????=0tan(1+4????)°. 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

The 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 ∑44????=0tan(1+4????)°. 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computation

ISSN

2079-3197

e-ISSN

2079-3197

Svazek periodika

11

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

16

Strana od-do

"222: 6 November 2023"

Kód UT WoS článku

001107791300001

EID výsledku v databázi Scopus

2-s2.0-85178283452