International journal of Engineering Research-Online A Peer Reviewed International Journal Vol.1., Issue.2., 2013 Articles available onlne http://www.ijoer.in RESEARCH ARTICLE ISSN: 2321-7758 OBSERVATIONS ON RHOMBIC DODECAHEDRAL NUMBER M.A.GOPALAN 1,V.SANGEETHA*,MANJU SOMANATH 2 1Professor,Department of Mathematics,Srimathi Indira Gandhi College,Trichy-2,India. *Assistant Professor,Dept.of Mathematics, National College,Trichy-1,India. Phone:9790451555,e-mail:[email protected] 2 Assistant Professor,Dept.of Mathematics, National College,Trichy-1,India. Article Received: 16/09/2013 Article Revised on: 20/09/2013 Article Accepted on:21/09/2013 ABSTRACT We obtain different relations among Rhombic Dodecahedral Number and other two, three and four dimensional figurate numbers. Keywords-Polygonal number, Pyramidal number, Centered Polygonal number, Centered Pyramidal number, Rhombic Dodecahedral number, Special numbers. MSC Classification Number: 11D99 V.SANGEETHA Author for Correspondence : Email:prasansangee@ gmail.com INTRODUCTION Fascinated by beautiful and intriguing number polygonal numbers can be summed up to form solid patterns, famous mathematicians, share their three dimensional figurate numbers called Pyramidal insights and discoveries with each other and with numbers [1,4,5and 6].In this communication,we deal readers. Throughout history, number and numbers with a special number called Rhombic Dodecahedral [2,3,7-18] have had a tremendous influence on our Number and various culture and on our language. Polygonal numbers can interesting relations among these numbers are be illustrated by polygonal designs on a plane. The - exhibited by means of theorems involving the relations. 283 V.SANGEETHA et al International journal of Engineering Research-Online A Peer Reviewed International Journal Vol.1., Issue.2., 2013 Articles available onlne http://www.ijoer.in Notation - Rhombic Dodecahedral number - Polygonal number of rank n with sides m - Centered Polygonal number of rank n with sides m - Pyramidal number of rank n with sides m - Centered Pyramidal number of rank n with sides m - Prism number of rank n with sides m - Pronic number of rank n - Gnomonic number - Octahedral number - Centered Octahedral number - Icosahedral number - Centered Icosahedral number - Dodecahedral number - Stella octangula number - Centered Dodecahedral number - Centered Cube number - Centered Square number - Truncated Tetrahedral number -Truncated Octahedral number -Pentatope number - Hauy Rhombic Dodecahedral number - Hauy Octahedral number - nth d-dimensional nexus number - m-gram number of rank n - Star number INTERESTING RELATIONS 1. Proof: 2. Proof: 284 V.SANGEETHA et al International journal of Engineering Research-Online A Peer Reviewed International Journal Vol.1., Issue.2., 2013 Articles available onlne http://www.ijoer.in 3. Proof: 4. Proof: 5. Proof: 6. Proof: 7. Proof: 8. Proof: 9. Proof: 285 V.SANGEETHA et al International journal of Engineering Research-Online A Peer Reviewed International Journal Vol.1., Issue.2., 2013 Articles available onlne http://www.ijoer.in 10. Proof: 11. Proof: 12. Proof: 13. Proof: 14. Proof: 286 V.SANGEETHA et al International journal of Engineering Research-Online A Peer Reviewed International Journal Vol.1., Issue.2., 2013 Articles available onlne http://www.ijoer.in 15. Proof: 16. is a Square Integer. Proof: 17. Proof: 18. Proof: 19. is a Nasty Number. Proof: . 20. is a Cubic integer. Proof: . 21. is a Nasty number. Proof: 287 V.SANGEETHA et al International journal of Engineering Research-Online A Peer Reviewed International Journal Vol.1., Issue.2., 2013 Articles available onlne http://www.ijoer.in 22. Proof: REFERENCES [10]. Gopalan M.A. and Devibala S., “On [1]. Beiler A.H., “Ch.18 in Recreations in the Lanekel Number” Antarctica J.Math.,4(1) Theory of Numbers”, The Queen of (2007),35-39. Mathematics Entertains, New [11]. Gopalan M.A.,Manju Somanath and York,Dover,(1996),184-199. Vanitha.N., “A Ramarkable Lanekel [2]. Bert Miller, “Nasty Numbers”, The Sequence”,Proc.Nat.Acad.Sci. India 77 (A) Mathematics Teachers, 73(9), (1989),649. II (2007),139-142 [3]. Bhatia B.L., and Mohanty Supriya, “Nasty [12]. Gopalan M.A.,Manju Somanath and Numbers and their Vanitha.N., “On R2 Numbers”,Acta characterization”,Mathematical Ciencia Indica,XXXIIIM (2) (2007),617-619. Education,I(1) (1985) 34-37. [13]. Gopalan M.A. and Gnanam A., “Star [4]. 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