Previous Slide

Next Slide

Contents for Talk

Much to the suprise of most physicists, it turns out that the vast majority of mathematics faculty have never heard of the basis vectors, $\hat\theta$ and $\hat\phi$, that are adapated to cylindrical and spherical coordinates. It pays to take a few minutes to introduce these to your middle-division classes, explicitly.

We use the following kinesthetic activity. Use the following definition: “A basis vector such as $\hat x$ is defined to be the unit vector that points in the direction in which $x$ is increasing.” Then tell the students to stand up. There is an origin of coordinates on the floor in the corner of the room behind them. Ask them to close their eyes and point in the direction of, e.g. $\hat \theta$. Look particularly for students who curve their arms. Point out to everyone that even though $\theta$ is an angle, $\hat\theta$ is a vector; it is straight. More...