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

Mingyang Wei * 1
1 Nanjing foreign language school, Nanjing, Jiangsu, China, 210018

* Author to whom correspondence should be addressed.

Theoretical and Natural Science, Vol. 5, 368-385
Published 25 May 2023. © 2023 The Author(s). Published by EWA Publishing
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.
Citation Mingyang Wei. The Secrets inside the Astonishing Reuleaux Triangle and its Practicable Uses. TNS (2023) Vol. 5: 368-385. DOI: 10.54254/2753-8818/5/20230598.

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.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Authors who publish this series agree to the following terms:

1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this series.

2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this series.

3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See Open Access Instruction).

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
25 May 2023
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

Copyright © 2023 EWA Publishing. Unless Otherwise Stated