#### 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.