Visualizing Spherical Harmonics Using a Balloon

Highlights of the activity

1. This small group activity is designed to help students visualize various spherical harmonics.
2. Students draw a particular spherical harmonic's magnitude and phase at different locations on the surface of a balloon, which represents the domain of the spherical harmonic.
3. The entire class wrap-up discussion includes group presentations of each spherical harmonic, allowing students to gain a visual understanding of the roles of the indices $\ell$ and $m$ in the spherical harmonics.

Reasons to spend class time on the activity

When students first experience spherical harmonics, they sometimes find it challenging to visualize how the function varies as $\theta$ and $\phi$ change. This activity helps students better understand how each component of a spherical harmonic affects the function's phase and magnitude across the sphere. Groups also have the opportunity to compare their spherical harmonic to other balloon representations to determine how spherical harmonics change for different values of $\ell$ and $m$.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

Student Handouts

cfballoonhand.pdf

cfballoonhand.tex