Not Knot
Template:Short description Script error: No such module "about". Not Knot is a 16-minute film on the mathematics of knot theory and low-dimensional topology, centered on and titled after the concept of a knot complement. It was produced in 1991 by mathematicians at the Geometry Center at the University of Minnesota, directed by Charlie Gunn and Delle Maxwell, and distributed on videotape with a 48-page paperback booklet of supplementary material by A K Peters.
Topics
The video is structured into three parts.[1]Template:R/superscript It begins by introducing knots, links, and their classification,[2]Template:R/superscript using the trefoil knot, figure-eight knot, and Borromean rings as examples.[3]Template:R/superscript It then describes the construction of two-dimensional surfaces such as cones and cylinders by gluing together the edges of flat sheets of paper, the internal geometry of the resulting manifolds or orbifolds, and the behavior of light rays within them.[1]Template:R/superscript[4]Template:R/superscript Finally, it uses a three-dimensional version of the same construction method to focus in more depth on the link complement of the Borromean rings and on the hyperbolic geometry of this complementary space, which has a high degree of symmetry and is closely related to classical uniform polyhedra.[2]Template:R/superscript[5]Template:R/superscript The view of this space, constructed as the limit of a process of pushing the rings out "to infinity", is immersive, rendered and lit accurately, "like flying through hyperbolic space".[2]Template:R/superscript
The supplementary material includes a complete script of the video, with black-and-white reproductions of many of its frames, accompanied by explanations at two levels, one set aimed at high school students and another at more advanced mathematics students at the late undergraduate or early graduate level.[3]Template:R/superscript
Audience and reception
Reviewer James M. Kister writes that making these topics understandable to non-mathematicians in this format, as this video attempts, is "virtually impossible", and in this case "only partially successful".[3]Template:R/superscript Kister writes of pre-high-school students entranced by the visual images in the video but with no understanding of their meaning, and of academics in non-mathematical disciplines who were equally bewildered. He suggests that the true audience for this video is the mathematics students for whom the more detailed supplementary material was intended.[3]Template:R/superscript
On the other hand, while agreeing that the material is fully understandable only with significant mathematical background, L. P. Neuwirth writes that "value may surely be found for elementary school students".[6]Template:R/superscript Knot theorist Mark Kidwell suggests that, even if the details are not understood, the video could be helpful in dispelling the popular misconception that knot theory is not mathematics.[1]Template:R/superscript And in a review published over ten years after the initial release of this video, Charles Ashbacher writes that the visual effects in this video "are still capable of stunning you", that the mathematics they depict can be clearly followed, and that it should be viewed by "all mathematics students".[7]Template:R/superscript
References
- ^ a b c Page Module:Citation/CS1/styles.css has no content.Kidwell, Mark (March 1993), "Review of Not Knot and Supplement to Not Knot", Media Highlights, The College Mathematics Journal, 24 (2): 191–198, doi:10.1080/07468342.1993.11973528
- ^ a b c Page Module:Citation/CS1/styles.css has no content.Emmer, Michele (June–August 1992), "Not Knot by Charlie Gunn, et al. (review)", Leonardo, 25 (3–4): 390–391, doi:10.2307/1575876, JSTOR 1575876
- ^ a b c d Page Module:Citation/CS1/styles.css has no content.Kister, James M. (1994), "Review of Not Knot and Supplement to Not Knot", MathSciNet, MR 1176795
- ^ Page Module:Citation/CS1/styles.css has no content.Stewart, Ian (January 1994), "Knots, links and videotape", Mathematical Recreations, Scientific American, vol. 270, no. 1, pp. 152–154, JSTOR 24942566
- ^ Page Module:Citation/CS1/styles.css has no content.Abbott, Steve (July 1997), "Review of Not Knot and Supplement to Not Knot", The Mathematical Gazette, 81 (491): 340–342, doi:10.2307/3619248, JSTOR 3619248
- ^ Page Module:Citation/CS1/styles.css has no content.Neuwirth, L. P., "Review of Not Knot and Supplement to Not Knot", zbMATH, Zbl 0769.57001
- ^ Page Module:Citation/CS1/styles.css has no content.Ashbacher, Charles (Spring 2003), "Review of Not Knot", Mathematics and Computer Education, 37 (2): 263–264
