Open AccessPattern Classification of Continued Fractions With Square Number as Base
Author(s) -
A. Venkatachalam,
P. Balamurugan
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1362/1/012084
Subject(s) - combinatorics , mathematics , sequence (biology) , fraction (chemistry) , base (topology) , square (algebra) , rank (graph theory) , order (exchange) , notation , hexagonal crystal system , geometry , arithmetic , crystallography , mathematical analysis , chemistry , biochemistry , organic chemistry , finance , economics
In number theory, study of number sequences is an enthusiastic area. Among these the sequence of polygonal numbers gives a unique richness in is applicability. Polygonal numbers which have both order, rank of are of various dimensions. Here, the study is only on two dimensional figurate numbers. Here the ratios of polygonal numbers are studied as continued fractions. In this paper different types of properties and characteristics of sequence of continued fraction which represent ratios of polygonal number of same rank are discussed. As any polygonal can be sub divided into smaller squares, square numbers have been taken as base here. Based upon on this study the nature and periodicity of the general sequence can be studied in detail. Notations: 1. 〈 u 0 , u 1 , u 2 , u 3 , …., u n 〉 – Continued fraction expansion 2. S 5, n - Pentagonal number 3. S 6, n - Hexagonal number 4. S 7, n - Heptagonal number AMS Classification: 11A55