由黄金比例导出的斐波那契和卢卡斯恒等式

IF 0.5 Q4 EDUCATION & EDUCATIONAL RESEARCH International Electronic Journal of Mathematics Education Pub Date : 2022-08-23 DOI:10.47443/ejm.2022.018

K. Adegoke

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引用次数: 0

摘要

通过用黄金比例α =(1 +√5)/ 2和它的逆β = - 1 /α =(1−√5)/ 2的幂来表示斐波那契数和卢卡斯数，在文献中发展了许多斐波那契和卢卡斯恒等式。在本文中，遵循相反的过程:利用众所周知的关于斐波那契数和卢卡斯数的α和β的幂的表达式，导出了许多斐波那契和卢卡斯恒等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fibonacci and Lucas Identities Derived via the Golden Ratio

By expressing Fibonacci and Lucas numbers in terms of the powers of the golden ratio α = (1 + √ 5) / 2 and its inverse β = − 1 /α = (1 − √ 5) / 2 , a multitude of Fibonacci and Lucas identities have been developed in the literature. In this paper, the reverse course is followed: numerous Fibonacci and Lucas identities are derived by making use of the well-known expressions for the powers of α and β in terms of Fibonacci and Lucas numbers.

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来源期刊

International Electronic Journal of Mathematics Education

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2.00

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0.00%

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