Turning Knots into Flowers and Related Undergraduate Research. Issue 9 (1st November 2017)

• Record Type: Journal Article
• Authors: Adams, Colin
• Is Part Of: American Mathematical Monthly. Volume 124:Issue 9(2017)
• Page Start: 791
• Page End: 806
• Publication Date: 2017-11-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.4169/amer.math.monthly.124.9.791
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: Knot theory is an excellent area for research by students. There are pretty pictures, plentiful opportunities to experiment, and deep mathematics. One recent area that presents many possibilities for research is a generalization of the usual projections of knots where at each crossing, two strands cross. At each crossing in an n -crossing projection, n strands cross. It turns out that every knot has an n -crossing projection and therefore an n -crossing number. Moreover, every knot has a projection with just one n -crossing. In fact, there is always such a projection that looks like a flower. We will discuss student work on these ideas and further possibilities for research.