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Lopez Gonzalez, M. DoloresAuthorLopez, MCorresponding AuthorLantaron, SAuthor

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Article

New Ways to Calculate the Probability in the Bertrand Problem

Publicated to:Mathematics. 12 (1): 3- - 2024-01-01 12(1), DOI: 10.3390/math12010003

Authors: Rodrigo, J; Lopez, M; Lantaron, S; Pavlov, V

Affiliations

Univ Politecn Madrid, Dept Matemat & Informat Aplicadas Ingn Civil & Nav - Author
Univ Pontificia Comillas, Dept Matemat Aplicada - Author

Abstract

We give two new ways of calculating the probability of a chord of circumference randomly selected being larger than the side of an equilateral triangle inscribed in the circumference (this problem is known as the Bertrand paradox). The first one employs an immersion in R4, and the second one uses a direct probability measure over the set of chords.

Keywords

Bertrand paradoxInvariancesProbability measures

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 21/490, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 1.12, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jun 2025)

Impact and social visibility

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/82004/

As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

  • Views: 80
  • Downloads: 41

Leadership analysis of institutional authors

the author responsible for correspondence tasks has been LOPEZ GORRIA, MARTA.