Published April 30, 2025
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A New Proof for Irrationality of π
Creators
- 1. Associate Professor, Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Arumbakkam, Chennai (Tamil Nadu), India.
- 1. Associate Professor, Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Arumbakkam, Chennai (Tamil Nadu), India.
- 2. Assistant Professor and Head, Department of Mathematics, S.S.K.V. College of Arts and Science for Women, Kilambi, Kanchipuram (Tamil Nadu), India.
- 3. B.T. Assistant in Mathematics, Gopalapuram Boys Higher Secondary School, Chennai (Tamil Nadu), India.
Description
Abstract: Ever since Lambert proved that π is irrational in 18th century, lots of wonderful proofs have been provided by various mathematicians. To this day, π remains as one of the most significant and important real number among all real numbers. In this paper, we try to prove that π is irrational in a new and elementary way. In doing so, we have obtained new rational approximations for π.
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Additional details
Identifiers
- DOI
- 10.54105/ijam.A1196.05010425
- EISSN
- 2582-8932
Dates
- Accepted
-
2025-04-15Manuscript received on 24 March 2025 | First Revised Manuscript received on 29 March 2025 | Second Revised Manuscript received on 03 April 2025 | Manuscript Accepted on 15 April 2025 | Manuscript published on 30 April 2025.
References
- Sondow, J. (2006). A Geometric Proof That e Is Irrational and a New Measure of Its Irrationality. The American Mathematical Monthly, 113(7), 637–641. DOI: https://doi.org/10.48550/arXiv.0704.1282
- J. Borwein and P. Borwein, Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity, John Wiley & Sons, New York, 1987. https://www.wiley.com/enus/Pi+and+the+AGM%3A+A+Study+in+Analytic+Number+Theory +and+Computational+Complexity-p-9780471315155
- T. Apostol, Irrationality of the square root of two - a geometric proof, Amer. Math. Monthly 107 (2000) 841-842. DOI: https://doi.org/10.2307/2695741
- R. Jayamari, R. Sivaraman, Continued Fraction Expansion for π and e, Proceedings of International Conference on Advanced Research in Mathematics and its Industrial Applications (ICARMIA), 2025, February, pp. 67 – 77. Paper Available at: https://www.researchgate.net/ publication/389215709_Continued_Fraction_Expansion_for_Pi_and _e
- R. Sivaraman, Thriving Towards Transcendental Numbers, International Journal of Advanced Science and Technology, Volume 29, No. 8s, (2020), pp. 2126 – 2131. http://sersc.org/journals/index.php/IJAST/article/view/13044