Curvilinear Basis Vectors

Highlights of the activity

1. This kinesthetic activity is designed to introduce students to the geometric understanding of basis vectors adapted to cylindrical and spherical coordinates.
2. Students are asked to point in the direction of the $\hat r$, $\hat \phi$, $\hat \theta$, $\hat z$ in reference to an origin placed in the classroom.
3. The whole class discussion focuses the directions of the curvilinear basis vectors and that these directions change depending on the position of the basis vector in space while the directions of $\hat x$, $\hat y$, and $\hat z$ are independent of their positions.

Reasons to spend class time on the activity

In mathematics classes, students learn about cylindrical and spherical coordinates, but typically they do not learn about the basis vectors (e.g. $\hat r$, $\hat \theta$, and $\hat \phi$) that are adapted to these coordinates. Indeed, many mathematics faculty are not familiar with this notation.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

Student Handouts

vfbasisvectorshand.pdf