On Transcendental Numbers: New Results and a Little History

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.

Keywords

• Euler’s identity
• Euler’s relation
• transcendental numbers
• transcendental operations/functions
• transcendence
• Yang-Baxter equation, hyperbolic functions, logical implication