Observations on Haüy Rhombic Dodecahedral Numbers with Some Special Numbers
DOI:
https://doi.org/10.26713/cma.v15i2.2653Keywords:
Haüy rhombic dodecahedral number, Stella octangula number, Centered tetrahedral number, Dodecahedral numbers, Gnomonic numbersAbstract
In this paper, the basic definition of Haüy rhombic dodecahedral numbers and nasty numbers are given. The Haüy rhombic dodecahedral number is taken into study and we prove this number is a combination of some special numbers. Also, we investigate about the relationships between the Haüy rhombic dodecahedral, stella octangula, hex number, centered tetrahedral and gnomonic numbers. For the clear understanding of the properties of special numbers we proved fifteen theorems. Sixteen special numbers are taken into consideration for this observation. The key points are given in the proof of the theorems.
Downloads
References
K. Bezdek, On rhombic dodecahedra, Beiträge zur Algebra und Geometrie 41(2) (2000), 411 – 416, URL: https://eudml.org/doc/232769.
J. H. Conway and R. K. Guy, The Book of Numbers, 1st edition, Copernicus, New York, ix + 310 pages (1996).
J. B. Dance and T. P. Denze, Elements of the Theory of Numbers, Academic Press, 503 pages (1999).
R. Friedberg, An Adventurer’s Guide to Number Theory, Reprint edition, Dover Publications, 228 pages (1994).
A. Gnanam and B. Anitha, Sums of squares of polygonal numbers, Advance in Pure Mathematics 6(4) (2016), 297 – 301, DOI: 10.4236/apm.2016.64019.
R. Keskin and O. Karaath, Some new properties of balancing numbers and square traingular numbers, Journal of Integer Sequences 15 (2012), Article 12.1.4, URL: https://cs.uwaterloo.ca/journals/JIS/VOL15/Karaatli/karaatli5.pdf.
M. Meyyappan, Ramanujan Numbers: Mathematical Thoughts and Ideas, 1st edition, S. Chand and Company Ltd., 116 pages (1998).
B. Miller, Nasty numbers, The Mathematical Teachers 73(9) (1980), 649, URL: https://www.jstor.org/stable/27962235.
I. Niven, H. S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers, John Wiley & Sons, 529 pages (1991).
E. Özkam, A. Aydoˇgdu and Ï. Altun, Some identities for a family of Fibonacci and Lucas numbers, Journal of Mathematics and Statistical Science 3(10) (2017), 295 – 303, URL: https://www.ss-pub.org/jmss/some-identities-for-a-family-of-fibonacci-and-lucas-numbers/.
H. C. Rajpoot, Mathematical Analysis of Rhombic Dodecahedron: Application of HCR’s Theory of Polygon, 11 pages (2014), DOI: 10.13140/RG.2.2.20120.34563
P. Reka, Some properties of traingular numbers, The International Journal of Analytical and Experimental Modal Analysis 11(12) (2019), 840 – 844.
P. Shanmuganandham and T. Deepika, Effects of pentatope number on other polygonal and figurate numbers, Advances and Applications in Mathematical Sciences 21(8) (2022), 4459 – 4466.
N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences (OEIS), Sequences A0005917 (formerly M4968) and A046142, URL: https://oeis.org/.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
