An Interesting Serendipitous Real Number

• Published in 2000
• Added on 2020-09-21

This is the story of a remarkable real number, the discovery of which was due to a misprint. Namely, in the mid-seventies, while Ciprian was at the University of Bucharest, one of his former students approached him with the following question: If \(x_1 \gt 0\) and \(x_{n+1} = \left(1 + \frac{1}{x_n}\right)^n\), can \(x_n \to \infty\)?

Comment

Known as the Foias constant.

Links

• https://link.springer.com/chapter/10.1007/978-1-4471-0751-4_8
• https://link.springer.com/content/pdf/10.1007%2F978-1-4471-0751-4_8.pdf

Other information

BibTeX entry

@article{AnInterestingSerendipitousRealNumber,
	key = {AnInterestingSerendipitousRealNumber},
	type = {article},
	title = {An Interesting Serendipitous Real Number},
	author = {John Ewing and Ciprian Foias},
	abstract = {This is the story of a remarkable real number, the discovery of which was due to a misprint. Namely, in the mid-seventies, while Ciprian was at the University of Bucharest, one of his former students approached him with the following question: 

If \(x{\_}1 \gt 0\) and \(x{\_}{\{}n+1{\}} = \left(1 + \frac{\{}1{\}}{\{}x{\_}n{\}}\right)^n\), can \(x{\_}n \to \infty\)?},
	comment = {Known as the Foias constant.},
	date_added = {2020-09-21},
	date_published = {2000-10-09},
	urls = {https://link.springer.com/chapter/10.1007/978-1-4471-0751-4{\_}8,https://link.springer.com/content/pdf/10.1007{\%}2F978-1-4471-0751-4{\_}8.pdf},
	collections = {fun-maths-facts},
	url = {https://link.springer.com/chapter/10.1007/978-1-4471-0751-4{\_}8 https://link.springer.com/content/pdf/10.1007{\%}2F978-1-4471-0751-4{\_}8.pdf},
	year = 2000,
	urldate = {2020-09-21},
	publisher = {Springer, London},
	doi = {10.1007/978-1-4471-0751-4{\_}8},
	fulltext_html_url = {https://link.springer.com/chapter/10.1007/978-1-4471-0751-4{\_}8},
	identifier = {10.1007/978-1-4471-0751-4{\_}8},
	pages = {119-126}
}