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Technical Report: UTEP-CS-20-112

Published in Applied Mathematical Sciences, 2020, Vol. 14, No. 18, pp. 881-886.


At first glance, many definitions in mathematics -- especially in elementary mathematics -- seem arbitrary. Why is 1 not considered a prime number? Why is a square considered to be a particular case of a parallelogram -- in some old textbooks, a parallelogram was defined in such a way as to exclude the square. In his 2018 article, Art Duval explained many such definitions by a natural requirement to make the corresponding results (theorems) as simple as possible. However, elementary mathematics is not just about theorems and proofs, it is also about computations. In this paper, we show that from the computational viewpoint, it is also preferable, e.g., to view a square as a particular case of a parallelogram.

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