On proofs of the lrrationality of the square root of 2

Document Type : Research Paper

Authors

1 Department of Computer Science, Birjand University of Technology, Birjand, Iran

2 Department of Basic Sciences, Birjand Girls' Technical and Vocational School, Technical and Vocational University, Birjand, Iran

Abstract

This article reviews some of the most famous proofs of the irrationality of the square root of 2. Given the nature of defining irrational numbers, we will see that most proofs (except Proof No. 23) have been done either directly or indirectly using proof by contradiction. We have tried to mention cases that have the potential to be generalized to a proof for the irrationality of the square root of other numbers as well. Some proofs have been slightly modified to ensure clarity of the resulting text. Additionally, some new results have been obtained in certain cases.

Keywords

References

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History

  • Receive Date: 18 October 2019
  • Revise Date: 16 December 2019
  • Accept Date: 19 December 2019
  • Publish Date: 23 August 2019

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