liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Remarkable curves in the Euclidean plane
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2014 (English)Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
Abstract [en]

An important part of mathematics is the construction of good definitions. Some things, like planar graphs, are trivial to define, and other concepts, like compact sets, arise from putting a name on often used requirements (although the notion of compactness has changed over time to be more general). In other cases, such as in set theory, the natural definitions may yield undesired and even contradictory results, and it can be necessary to use a more complicated formalization.

   The notion of a curve falls in the latter category. While it is intuitively clear what a curve is – line segments, empty geometric shapes, and squiggles like this: – it is not immediately clear how to make a general definition of curves. Their most obvious characteristic is that they have no width, so one idea may be to view curves as what can be drawn with a thin pen. This definition, however, has the weakness that even such a line has the ability to completely fill a square, making it a bad definition of curves. Today curves are generally defined by the condition of having no width, that is, being one-dimensional, together with the conditions of being compact and connected, to avoid strange cases.

   In this thesis we investigate this definition and a few examples of curves.

Place, publisher, year, edition, pages
2014. , 37 p.
Keyword [en]
Curves, Cantor curves, Peano curves, Sierpinski carpet, one-dimensional, Menger curve
National Category
URN: urn:nbn:se:liu:diva-112576ISRN: LiTH-MAT-EX--2014/06--SEOAI: diva2:768460
Subject / course
Available from: 2014-12-04 Created: 2014-12-04 Last updated: 2014-12-08Bibliographically approved

Open Access in DiVA

Remarkable curves in the Euclidean plane(667 kB)243 downloads
File information
File name FULLTEXT01.pdfFile size 667 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Granholm, Jonas
By organisation
Mathematics and Applied MathematicsThe Institute of Technology

Search outside of DiVA

GoogleGoogle Scholar
Total: 243 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 427 hits
ReferencesLink to record
Permanent link

Direct link