New Ways to Calculate the Probability in the Bertrand Problem
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 R<sup>4</sup>, and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/1/3 |
| _version_ | 1797358463844614144 |
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| author | Javier Rodrigo Mariló López Sagrario Lantarón |
| author_facet | Javier Rodrigo Mariló López Sagrario Lantarón |
| author_sort | Javier Rodrigo |
| collection | DOAJ |
| description | 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 R<sup>4</sup>, and the second one uses a direct probability measure over the set of chords. |
| first_indexed | 2024-03-08T15:02:24Z |
| format | Article |
| id | doaj.art-69017d96d4b84712a1d7ebd08243e044 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T15:02:24Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-69017d96d4b84712a1d7ebd08243e0442024-01-10T15:03:15ZengMDPI AGMathematics2227-73902023-12-01121310.3390/math12010003New Ways to Calculate the Probability in the Bertrand ProblemJavier Rodrigo0Mariló López1Sagrario Lantarón2Departamento de Matemática Aplicada, Universidad Pontificia Comillas, 28015 Madrid, SpainDepartamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Universidad Politécnica de Madrid, 28040 Madrid, SpainDepartamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Universidad Politécnica de Madrid, 28040 Madrid, SpainWe 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 R<sup>4</sup>, and the second one uses a direct probability measure over the set of chords.https://www.mdpi.com/2227-7390/12/1/3probability measuresBertrand paradoxinvariances |
| spellingShingle | Javier Rodrigo Mariló López Sagrario Lantarón New Ways to Calculate the Probability in the Bertrand Problem Mathematics probability measures Bertrand paradox invariances |
| title | New Ways to Calculate the Probability in the Bertrand Problem |
| title_full | New Ways to Calculate the Probability in the Bertrand Problem |
| title_fullStr | New Ways to Calculate the Probability in the Bertrand Problem |
| title_full_unstemmed | New Ways to Calculate the Probability in the Bertrand Problem |
| title_short | New Ways to Calculate the Probability in the Bertrand Problem |
| title_sort | new ways to calculate the probability in the bertrand problem |
| topic | probability measures Bertrand paradox invariances |
| url | https://www.mdpi.com/2227-7390/12/1/3 |
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