Geometry: New Tools for New Technologies: Hour 2: Unit 3: Topology: Knot Theory

How is geometry used to program a robot's movement? How do zoo planners use geometry to make habitats that are enjoyable and safe? Why do people who plan garbage pickups and snowplow routes need geometry? Geometry: New Tools for New Technologies I and II explore the exciting world of Geometry in the 20th century.

The six shows in this video series demonstrate contemporary geometry in action. In the videos, your students learn about applications to architecture, archaeology, DNA research, packaging design, fire station location, scheduling events, and others. The accompanying print materials give your students the opportunity to take part in the mathematical modeling of these situations. The videos range in length from about 8 minutes to about 11.5 minutes. The print materials for each video include a video viewing guide, a set of discussion questions, and one or two sets of exercises.

Unit 3: Topology: Knot Theory (7:46)

Summary of the Video

A short segment at the beginning of the video shows that knots are common and important and introduces topology as the branch of geometry that studies knots. Dr. Nicholas Cozzarelli talks about the importance of knots and topology in DNA research. Graphics and demonstrations with rope are used to introduce basic knot terminology, to show how knots are transformed, and to give an example of how knots are classified. Following the video, students examine three different ways of characterizing knots. They are encouraged to make actual knots from pieces of string in order to understand properties of knots.

Video support materials are available as part of COMAP full membership. Each video is accompanied by a user's guide with reproducible student exercises and quizzes.