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Axioms 2018, 7(1), 15; https://doi.org/10.3390/axioms7010015

On Transcendental Numbers: New Results and a Little History

1
Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania
2
Romanian Academy, 125 Calea Victoriei Street, 010071 Bucharest, Romania
This article is dedicated to the memory of my friend and esteemed colleague, Professor Solomon Marcus, who passed away on 17 March 2016. His enthusiasm and optimism will be sadly missed.
*
Author to whom correspondence should be addressed.
Received: 19 January 2018 / Revised: 1 February 2018 / Accepted: 20 February 2018 / Published: 1 March 2018
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang–Baxter Equations 2017)
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Abstract

Bringing toghether mathematical and philosophical ideas related to transcendental numbers, this paper begins with a survey on transcendence and transcendental numbers, it then presents several properties of the transcendental numbers e and π , and then it gives the proof of a new inequality for transcendental numbers. Also, in relationship with these topics, we study solutions to the Yang-Baxter equation from hyperbolic functions and from logical implication. View Full-Text
Keywords: Euler’s identity; Euler’s relation; transcendental numbers; transcendental operations/functions; transcendence; Yang-Baxter equation, hyperbolic functions, logical implication Euler’s identity; Euler’s relation; transcendental numbers; transcendental operations/functions; transcendence; Yang-Baxter equation, hyperbolic functions, logical implication
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Marcus, S.; Nichita, F.F. On Transcendental Numbers: New Results and a Little History. Axioms 2018, 7, 15.

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