Event Title
All Tied Up: Mapping Trisecants of the Figure Eight Knot
Presentation Type
Oral and/or Visual Presentation
Presenter Major(s)
Mathematics
Mentor Information
Clark Wells
Department
Mathematics
Location
Kirkhof Center 2201
Start Date
11-4-2012 5:00 PM
Keywords
Mathematical Science
Abstract
The figure eight knot is commonly used in rock climbing, sailing and other activities. If you attach the two ends of this rope, you can no longer untie this knot. This is the mathematical Figure Eight Knot. Given any two points on this knot, there is a line in space that intersects both. This is known as a secant. If this line intersects the knot in at least one other point, we have identified a trisecant. For our research, we have found all of the trisecants of the Figure Eight knot. We have classified them visually by representing them on a Mobius strip and the surface of a Torus. We will explain these surfaces and the mapping process in a way that is interesting and accessible to a general audience.
All Tied Up: Mapping Trisecants of the Figure Eight Knot
Kirkhof Center 2201
The figure eight knot is commonly used in rock climbing, sailing and other activities. If you attach the two ends of this rope, you can no longer untie this knot. This is the mathematical Figure Eight Knot. Given any two points on this knot, there is a line in space that intersects both. This is known as a secant. If this line intersects the knot in at least one other point, we have identified a trisecant. For our research, we have found all of the trisecants of the Figure Eight knot. We have classified them visually by representing them on a Mobius strip and the surface of a Torus. We will explain these surfaces and the mapping process in a way that is interesting and accessible to a general audience.