Irrationality proofs à la Hermite

  title={Irrationality proofs {\`a} la Hermite},
  author={Li Zhou},
  journal={The Mathematical Gazette},
  pages={407 - 413}
  • Li Zhou
  • Published 10 November 2009
  • Mathematics
  • The Mathematical Gazette
In [1] Niven used the integral to give a well-known proof of the irrationality of π. Recently Zhou and Markov [2] used a recurrence relation satisfied by this integral to present an alternative proof which may be more direct than Niven's. Niven did not cite any references in [1] and thus the origin or Hn seems rather mysterious and ingenious. However if we heed Abel's advice to ‘study the masters’, we find that Hn emerged much more naturally from the great works of Lambert [3] and Hermite [4]. 
1 Citations
We discuss the logical fallacies in an article appeared in The American Mathematical Monthly [6], and present the historical origin and motivation of the simple proofs of the irrationality of π. 1. A


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Extrait d'une lettre de Monsieur Ch. Hermite à Monsieur Paul Gordan.
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