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Physical Meaning Often Leads to Natural Derivations in Elementary Mathematics: On the Examples of Solving Quadratic and Cubic Equations

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Uncertainty, Constraints, and Decision Making

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 484))

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Abstract

Usual derivation of many formulas of elementary mathematics—such as the formulas for solving quadratic equation—often leave un unfortunate impression that mathematics is a collection of unrelated unnatural tricks. In this paper, on the example of formulas for solving quadratic and cubic equations, we show that these derivations can be made much more natural if we take physical meaning into account.

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Acknowledgements

This work was supported in part by the National Science Foundation grants:

\(\bullet \) 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science), and

\(\bullet \) HRD-1834620 and HRD-2034030 (CAHSI Includes).

It was also supported:

\(\bullet \) by the AT&T Fellowship in Information Technology, and

\(\bullet \) by the program of the development of the Scientific-Educational Mathematical Center of Volga Federal District No. 075-02-2020-1478.

Author information

Authors and Affiliations

  1. Information Technology Systems Department, El Paso Community College (EPCC), 919 Hunter Dr., El Paso, TX, 79915-1908, USA

    Christian Servin

  2. Department of Teacher Education, University of Texas at El Paso, 500 W. University El Paso, Texas, 79968, USA

    Olga Kosheleva

  3. Department of Computer Science, University of Texas at El Paso, 500 W. University El Paso, Texas, 79968, USA

    Vladik Kreinovich

Authors
  1. Christian Servin
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  2. Olga Kosheleva
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  3. Vladik Kreinovich
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Corresponding author

Correspondence to Vladik Kreinovich .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  2. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Servin, C., Kosheleva, O., Kreinovich, V. (2023). Physical Meaning Often Leads to Natural Derivations in Elementary Mathematics: On the Examples of Solving Quadratic and Cubic Equations. In: Ceberio, M., Kreinovich, V. (eds) Uncertainty, Constraints, and Decision Making. Studies in Systems, Decision and Control, vol 484. Springer, Cham. https://doi.org/10.1007/978-3-031-36394-8_22

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