Examples and Constructions

Horst Martini (), Luis Montejano and Déborah Oliveros
Additional contact information
Horst Martini: Chemnitz University of Technology, Faculty of Mathematics
Luis Montejano: Universidad Nacional Autónoma de México, Campus Juriquilla, Instituto de Matemáticas
Déborah Oliveros: Universidad Nacional Autónoma de México, Campus Juriquilla, Instituto de Matemáticas

Chapter Chapter 8 in Bodies of Constant Width, 2019, pp 167-195 from Springer

Abstract: Abstract This chapter is dedicated to concrete examples of constant width sets and procedures on how to construct them. The most notorious convex body of constant width is undoubtedly the Reuleaux triangle of width h which is the intersection of three disks of radius h and whose boundary consists of three congruent circular arcs of radius h. In Section 8.1, we will see that the Reuleaux triangle can be generalized to plane convex figures of constant width h whose boundary consists of a finite number of circular arcs of radius h. They are called ReuleauxReuleaux polygons polygons. The plan for the rest of the chapter is the following: In Section 8.2, we will study the 3-dimensional analogue of the Reuleaux triangle, and in Section 8.3, we will construct Meissner’s mysterious bodies from it. In fact, in this section, we will use the concepts of ball polytope and Reuleaux polytopeReuleaux polytope to construct 3-dimensional bodies of constant width with the help of special embeddings of self-dual graphs. In Section 8.4, we will give a procedure of finitely many steps to construct 3-dimensional constant width bodies from Reuleaux polygons, and in Section 8.5, we will construct constant width bodies with analytic boundaries.

Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-03868-7_8

Ordering information: This item can be ordered from
http://www.springer.com/9783030038687

DOI: 10.1007/978-3-030-03868-7_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().