Last Saturday was the first math circle meeting. It was great fun to meet all the students, and to see everyone working together. We had a very one- and two-dimensional day. Instructor 1 (let's call this instructor M) used mardi gras beads as a manipulative to help students understand homotopy classes of knots. Instructor 2 (let's call this one D) classified planar Euclidean transformations using a combination of socratic dialogue and small group discussion. Instructor 3 (let's call this one L) built quotient spaces of the plane via discrete isometric actions.
Can you figure out how the mobius band was cut to create this configuration? (Solution)
Some mathematical highlights from the day -- showing that reflections generate all other Euclidean planar transformations, the follow-up observation that "no matter what" is a strong statement after a student's comment that "we need to show that no matter what we do to the knot, it will never be unknotted", quotienting a torus to obtain a mobius band and slicing it along thirds lengthwise.
No comments:
Post a Comment