How fast does a bowling pin turn as you roll it along the floor along some direction? For instance, if you roll it forward and backward it will turn faster than if you rock it[…]

What’s a good way to illustrate maps that are noninjective? Above, for instance, is an illustration of the complex map for increasing values of . Transparency is used to deal with noninjectivity. However, since blending[…]

A Lie group is both a group and a manifold.  When illustrating Lie groups, one runs into several challenges: How do you suggest both the group and manifold structure?  The natural inclination is to draw[…]

A volume form on a smooth -manifold is any nonvanishing -form, i.e., a map that is linear in each argument, changes sign for any odd permutation of the arguments, and is nonzero whenever all the[…]

Consider illustrating the parabolic heat equation A key challenge here is depicting an evolution over time. A natural idea is to use animation, which can often provide effective illustrations of ideas that are otherwise difficult[…]

In the early 21st century, mathematical illustration was still a labor of love—even for very simple geometries. But it was worth it.

[A first effort at illustrating groups…] Anyone who has had their hair cut, or has been in a tacky elevator, has experienced this effect: two mirrors reflect each other, creating the illusion of a tunnel[…]

A neighborhood of a point is totally normal if for some each point is contained in a normal ball . Like, totally.

A polyhedral surface is often illustrated as a collection of polygons glued together in space, with strong lines emphasizing edges.  But for the proverbial ant crawling along the surface, these edges are difficult to detect.[…]