DOI
10.1080/17513472.2011.634320
Abstract
The formal mathematical definition of a Jordan curve (a non-self-intersecting continuous loop in the plane) is so simple that one is often lead to the unimaginative view that a Jordan curve is nothing more than a circle or an ellipse. In this paper, we pursue the theme that a Jordan curve can be quite fantastical in the sense that there are some bizarre properties such a curve might have (jagged at every point, space filling, etc.) or that such a curve can have a difficult to discover inside and outside as promised by the celebrated Jordan Curve Theorem (JCT). We explore the JCT theorem through its history and some hand drawings which not only challenge the viewer's preconceived notions of interior and exterior or that the JCT is a trivial result, but also challenge the reader's notion that a curve is a cold boring object, incapable of telling an interesting story.
Document Type
Post-print Article
Publication Date
2011
Publisher Statement
Copyright © 2011 Taylor & Francis.
DOI: 10.1080/17513472.2011.634320
The definitive version is available at: https://www.tandfonline.com/doi/full/10.1080/17513472.2011.634320
Full Citation:
Ross, Fiona, and William T. Ross. "The Jordan Curve Theorem Is Non-trivial." Journal of Mathematics and the Arts 5, no. 4 (2011): 213-19. doi:10.1080/17513472.2011.634320.
Recommended Citation
Ross, Fiona and Ross, William T., "The Jordan curve theorem is non-trivial" (2011). Department of Math & Statistics Faculty Publications. 186.
https://scholarship.richmond.edu/mathcs-faculty-publications/186