Association of two square difference identity to regular polygons and circles

Recep Aslaner; Aziz Ilhan

doi:10.29333/pr/14341

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Recep Aslaner ¹ , Aziz Ilhan ¹ ^*

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¹ Faculty of Education, Inonu University, Malatya, TÜRKİYE^* Corresponding Author

Abstract

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the “two square difference identity” expressed for the square, which is a flat polygon, made with different approaches. With side lengths a, b, and a>b, it has been shown that the identity given by the equation (difference of area) a²-b²=(a-b)(a+b) is true for other regular polygons as well. In the study, direct proof method was used within the framework of the principle of conservation of measure, which is one of the basic principles of geometry teaching. GeoGebra program, which is a dynamic geometry software, was preferred for drawing geometric shapes used in proofs. In order to generalize the number n, a different fragmentation technique was preferred to the proofs made using different drawings for equilateral triangle and square, which are the simplest regular polygons. It has also been shown that this identity is true for circles viewed as polygons with an infinite number of sides.

Keywords

association
geometry teaching
identities
difference of two squares
visualization
dynamic geometry software
GeoGebra

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

PEDAGOGICAL RES, Volume 9, Issue 2, April 2024, Article No: em0199

https://doi.org/10.29333/pr/14341

Publication date: 01 Apr 2024

Online publication date: 08 Mar 2024

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How to cite this article

APA

Aslaner, R., & Ilhan, A. (2024). Association of two square difference identity to regular polygons and circles. Pedagogical Research, 9(2), em0199. https://doi.org/10.29333/pr/14341

Vancouver

Aslaner R, Ilhan A. Association of two square difference identity to regular polygons and circles. PEDAGOGICAL RES. 2024;9(2):em0199. https://doi.org/10.29333/pr/14341

AMA

Aslaner R, Ilhan A. Association of two square difference identity to regular polygons and circles. PEDAGOGICAL RES. 2024;9(2), em0199. https://doi.org/10.29333/pr/14341

Chicago

Aslaner, Recep, and Aziz Ilhan. "Association of two square difference identity to regular polygons and circles". Pedagogical Research 2024 9 no. 2 (2024): em0199. https://doi.org/10.29333/pr/14341

Harvard

Aslaner, R., and Ilhan, A. (2024). Association of two square difference identity to regular polygons and circles. Pedagogical Research, 9(2), em0199. https://doi.org/10.29333/pr/14341

MLA

Aslaner, Recep et al. "Association of two square difference identity to regular polygons and circles". Pedagogical Research, vol. 9, no. 2, 2024, em0199. https://doi.org/10.29333/pr/14341