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Creating ‘Nice’ Problems in Elementary Mathematics — III

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Abstract

We consider here the ‘meta-problem’ of creating ‘nice’ problems in elementary mathematics, ‘nice’ being defined as a problem in which the input data, as well as the answers, are rational numbers. The classical example of this is that of generating Pythagorean triples. Many examples of this kind arise when we study Euclidean geometry and the theory of equations. We consider a few problems of this genre.

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Suggested Reading

  1. Al Cuoco, “Meta-Problems in Mathematics,” College Mathematics Journal, Vol.31, No. 5, Nov 2000.

  2. Haran Mouli, Mahavir Gandhi, Sarth Chavan, “Rational ‘Twin’ Isosceles Triangles,” At Right Angles, November 2021 (to appear)

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  4. Ion Pătraşcu & Florentin Smarandache, “Non-Congruent Triangles with Equal Perimeters and Arias,” http://fs.unm.edu/ScArt/CP-NonCongruentTriangles.pdf

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Acknowledgement

The author would like to thank an anonymous reviewer who read the initial draft of the article with considerable care and took the trouble to include detailed comments and suggestions in the referee report. These have been of great help in revising the article.

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Authors and Affiliations

  1. Sahyadri School (KFI), Tiwai Hill, Rajgurunagar, Pune, 410 513, India

    Shailesh A. Shirali

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  1. Shailesh A. Shirali
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Correspondence to Shailesh A. Shirali.

Additional information

Shailesh Shirali is currently Director of Sahyadri School. He has been in the field of mathematics education for several decades. He has written many mathematics books for school students and teachers and serves as Chief Editor of the magazine At Right Angles. He has a deep interest in ancient Indian mathematics.

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Shirali, S.A. Creating ‘Nice’ Problems in Elementary Mathematics — III. Reson 27, 339–352 (2022). https://doi.org/10.1007/s12045-022-1325-2

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  • DOI: https://doi.org/10.1007/s12045-022-1325-2

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