Andrew Cooper

A few years ago I got turned on to Geogebra, probably the world’s most awesome and low-barrier-to-entry mathematical software. The best part of Geogebra is that you can do most everything through the web client or the mobile app. (I have the desktop client, but I never use it!)

Here are some doodads I’ve built with Geogebra.

Visualizing Directional Derivatives

This gadget illustrates one way to think about the directional derivative. There are versions of this same gadget for partial derivatives and the tangent plane, too.

3D Riemann Sums over a Rectangle

A tool for visualizing how the Riemann sums obtained by taking a product partition of the rectangle approximate the volume under the graph. You can specify how many subintervals to partition and into, and change the function .

3D Riemann Sums over a Non-Rectangular Region

The same as the previous applet, but this one is over the region , .

Level Sets

A tool for visualizing the relationship between the level curves of a function , the graph of , and the intersection of the graph with horizontal planes.

The Frenet-Serret Frame

You specify a curve, and this applet animates its Frenet-Serret frame.

The Matrix of a Reflection

Change the slider to alter the slope of the line; watch as the reflections of the points and — and the image of Satan from the Codex Gigas — move along with the line. The matrix representing the reflection is obtained from the coordinates of the reflected points.

Constructing Lines in the Poincaré Disk

This isn’t a Geogebra gadget itself, but it shows how awesome Geogebra is for doing exploratory assignments.