Writing π as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers-Reference-Cited by-同舟云学术

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Writing π as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers

Published:2014-07-15 Issue:05 Volume:10 Page:1309-1319
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Abrate Marco¹,Barbero Stefano²,Cerruti Umberto²,Murru Nadir³

Affiliation:

1. DIMEAS Polytechnic University of Turin, Corso Duca degli Abruzzi 24, 10129, Turin, Italy

2. Department of Mathematics, University of Turin, Via Carlo Alberto 10, 10123, Turin, Italy

3. ISTI, CNR (National Research Council) of Pisa, Via G. Moruzzi 1, 56124, Pisa, Italy

Abstract

In this paper, we study the representation of π as sum of arctangents. In particular, we highlight the role of linear recurrent sequences obtaining new identities. Moreover, we provide a method in order to express π as sum of arctangents involving the Golden mean, the Lucas numbers, and more in general any quadratic irrationality.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042114500286

Reference11 articles.

1. Gaussian Integers and Arctangent Identities for π

2. 88.38 Some observations on the method of arctangents for the calculation of π

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Three essays on Machin’s type formulas;Indagationes Mathematicae;2023-11

2. Finding golden mean in a physics exercise;Physics Education;2017-04-28

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