| Previous abstract | Back to issue content | Next abstract |
Volume 35, Number 3, pages 295-298 (2024)
https://doi.org/10.26830/symmetry_2024_3_295
VISUALIZING SYMMETRIC POLYGONAL NUMBER IDENTITIES
Günhan Caglayan
New Jersey City University, NJ 07305. U.S.A.
Email: gcaglayan@njcu.edu
Abstract: Mathematics often relies on visual representations to elucidate complex concepts, and "proofs without words" offer a compelling avenue for conveying intricate mathematical ideas. Building upon proof without words framework (Nelsen, 1993, 2000, 2015, 2018), this paper proposes a selected compilation of the author's own "proofs without words" focusing on symmetric polygonal number identities. Symmetric figurate numbers exhibit inherent visual patterns that make them ideal subjects for visual proofs. This presentation aims to provide educators, students, and mathematicians with an accessible resource to deepen their understanding and appreciation of mathematical symmetry. Polygonal numbers, also known as k-gonal numbers, and centered polygonal numbers, also known as centered k-gonal numbers, reside at the intersection of number theory and geometry.
References:
Caglayan, G. (2020) Centered Nonagonal Numbers are Triangular, College Mathematics Journal (MAA), 51(5), 371. https://doi.org/10.1080/07468342.2020.1820287
Caglayan, G. (2022) Plane Figurate Number Proofs without Words Explained with Pattern Blocks, Humanistic Mathematics, 12(1), 24-39. https://doi.org/10.5642/jhummath.202201.04
Deza, E., & Deza, M. (2012) Figurate Numbers, World Scientific. https://doi.org/10.1142/9789814355490
Heath, T. L. (1921) A History of Greek Mathematics (Vol. 1), Oxford University Press.
Nelsen, R. B. (1993) Proofs without words: Exercises in visual thinking, The Mathematical Association of America.
Nelsen, R. B. (2000) Proofs without words II: More exercises in visual thinking, The Mathematical Association of America.
Nelsen, R. B. (2015) Proofs without words III: Further exercises in visual thinking, The Mathematical Association of America. https://doi.org/10.5948/9781614441212
Nelsen, R. B. (2018) Nuggets of number theory: A visual approach, In Volume 55 of AMS/MAA Classroom Resource Materials. https://doi.org/10.1090/clrm/001
| Previous abstract | Back to issue content | Next abstract |