Mathematics and Statistics Vol. 8(4), pp. 388 - 391
DOI: 10.13189/ms.2020.080403
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Exploring Metallic Ratios

R. Sivaraman ^*
Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Chennai – 600 106, Tamil Nadu, India

ABSTRACT

Huge amount of literature has been written and published about Golden Ratio, but not many had heard about its generalized version called Metallic Ratios, which are introduced in this paper. The methods of deriving them were also discussed in detail. This will help to explore further in the search of universe of real numbers. In mathematics, sequences play a vital role in understanding of the complexities of any given problem which consist of some patterns. For example, the population growth, radioactive decay of a substance, lifetime of an object all follow a sequence called "Geometric Progression". In fact, the rate at which the recent novel corona virus (COVID – 19) is said to follow a Geometric Progression with common ratio approximately between 2 and 3. Almost all branches of science use sequences, for instance, genetic engineers use DNA sequence, Electrical Engineers use Morse-Thue Sequence and this list goes on and on. Among the vast number of sequences used for scientific investigations, one of the most famous and familiar is the Fibonacci Sequence named after the Italian mathematician Leonard Fibonacci through his book "Liber Abaci" published in 1202. In this paper, I shall try to introduce sequences resembling the Fibonacci sequence and try to generalize it to identify general class of numbers called "Metallic Ratios".

KEYWORDS
Golden Ratio, Silver Ratio, Bronze Ratio, Metallic Ratios, Shift Operator, Recurrence Relation, Platinum Ratio, Rhodium Ratio

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] R. Sivaraman , "Exploring Metallic Ratios," Mathematics and Statistics, Vol. 8, No. 4, pp. 388 - 391, 2020. DOI: 10.13189/ms.2020.080403.

(b). APA Format:
R. Sivaraman (2020). Exploring Metallic Ratios. Mathematics and Statistics, 8(4), 388 - 391. DOI: 10.13189/ms.2020.080403.