A New Proof for Irrationality of π
R. Sivaraman1, J. Suganthi2, P.N. Vijayakumar3
1Dr. R. Sivaraman, Associate Professor, Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Arumbakkam, Chennai (Tamil Nadu), India.
2J. Suganthi, Assistant Professor and Head, Department of Mathematics, S.S.K.V. College of Arts and Science for Women, Kilambi, Kanchipuram (Tamil Nadu), India.
3P.N. Vijayakumar, B.T. Assistant in Mathematics, Gopalapuram Boys Higher Secondary School, Chennai (Tamil Nadu), India.
Manuscript 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 | PP: 32-34 | Volume-5 Issue-1, April 2025 | Retrieval Number: 100.1/ijam.A119605010425 | DOI: 10.54105/ijam.A1196.05010425
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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.
Keywords: Irrational, Mediant, Closed Intervals, Rational Approximations.
Scope of the Article: Arithmetic