Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 5, 25 May 2023
Open
Access | Article
The Secrets inside the Astonishing Reuleaux Triangle and its Practicable Uses
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Abstract
The idea of the study was mainly from the concerns about whether wheels of different shapes can also fit well in cars. This paper mainly involves the demonstration of some theoretical features of the Reuleaux triangle and some practical situations of using the triangle as wheels. The aim of the study is to find out some basic features and mathematical rules of the Reuleaux triangle, in addition, the practical uses of this shape will also be studied. In order to learn expertise about this triangle, the author went through papers about geometry and some demonstrations by different mathematicians from different times. The author then made a few assumptions and tried to prove himself to find the rules of this shape more deeply. In conclusion, it found out that the Reuleaux triangle is actually a perfect constant width curve and it can be used as wheels under proper conditions. Apart from that, this paper also concluded an exact method of drawing different constant width curves.
Keywords
constant width curve, calculus, parametric function, mathematical induction.
References
1. Javier Barrallo，An introduction to the Vesica Piscis, the Reuleaux triangle and related geometric constructions in modern architecture. 2015. https://link.springer.com/article/10.1007/s00004-015-0253-9
2. Mikhail Razumov, Stress calculation of moment transmitting roll with profile on the base of Reuleaux triangle. .2014. https://www.metaljournal.com.ua/assets/Archive/en/MMI3/10.pdf
3. Horst Martini. A new construction of curves of constnant width. 2008 https://www.sciencedirect.com/science/article/abs/pii/S0167839608000745
4. Bruce B. Peterson. Intersection properties of curves of constant width. 1971 https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-17/issue-3/Intersection-properties-of-curves-of-constant-width/10.1215/ijm/1256051608.pdf
5. Stanley Rabinowtz. A polynominal curve of constant width. 1997 https://projecteuclid.org/journalArticle/Download?urlId=10.35834%2F1997%2F0901023
Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 2nd International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2023)
- ISBN (Print)
- 978-1-915371-53-9
- ISBN (Online)
- 978-1-915371-54-6
- Published Date
- 25 May 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/5/20230598
- Copyright
- © 2023 The Author(s)
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited