AlgTop11: Rational curvature, winding and turning

This video introduces an important re-scaling of curvature, using the natural geometric unit rather than radians or degrees. We call this the turn-angle, or tangle, and use it to describe polygons, convex and otherwise. We also introduce winding numbers and the turning number of a planar curve.

This is the 11th lecture in this beginner's course on Algebraic Topology, given by Assoc Prof N J WIldberger at UNSW.

[Cor]

Lovely idea, the number of turns. A half turn is much easier to understand than a 180 degree turn, let alone a pi turn. A perfect notion for primary school kids. However, these kids have to be able to understand the others notions of angles as well (degrees, radians, and even the 'angle' of a steep road).

[unswelearning]

Hi, Actually my students don't have a text book, they are just following this series.

[GuillermoAlcantara]

The turning number definition sounds wrong. You could have a ladder shape (rounded zig-zag) figure that will every so often point up without crossing itself, like a deformed circle. It should be 1, but by that definition it will be the same as the number of steps. I'm a newbie but I think a better definition would be to remove loops where it crosses itself and adding them depending on the direction of the loop.

[eolfeci]

This must be really nice for your student as they don't have to allot mental energy to copying the board and can just concentrate on understanding what you're saying. I'm sure they appreciate it. I know I would.