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Exploring Metallic Ratios

机译:探索金属比率

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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".
机译:巨大的文学已经写了巨大的金色比例,但许多人听说过其普遍的版本,称为金属比,本文介绍。还详细讨论了导出它们的方法。这将有助于进一步探索实数的宇宙。在数学中,序列在理解任何由某些模式组成的任何特定问题的复杂性方面发挥着重要作用。例如,人口生长,物质的放射性衰减,物体的寿命均遵循称为“几何进展”的序列。事实上,据说最近的新型电晕病毒(Covid-19)的速率遵循大约2和3之间的常见比率的几何进展。几乎所有科学用途序列的分支,例如遗传工程师使用DNA序列,电气工程师使用Morse-Thue序列,此列表继续进行。在用于科学调查的大量序列中,最着名和熟悉的是斐波纳契序列以意大利数学家Leonard Fibonarci通过他的书“Liber Abaci”于1202年出版。在本文中,我将尝试引入序列类似于斐波纳契序列,并尝试概括它以识别称为“金属比”的一般数字。

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