Geogebra Gadgets – Andrew A Cooper

I very recently 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.

3D Riemann Sums over a Rectangle

A tool for visualizing how the Riemann sums obtained by taking a product partition of the rectangle $[0,2]\times[0,3]$ approximate the volume under the graph. You can specify how many subintervals to partition $[0,2]$ and $[0,3]$ into, and change the function $f(x,y)$ .

3D Riemann Sums over a Non-Rectangular Region

The same as the previous applet, but this one is over the region $0\leq y\leq 2$ , $0\leq x\leq 3-\frac{3}{4}y^2$ .

Level Sets

A tool for visualizing the relationship between the level curves of a function $f(x,y)$ , the graph of $f(x,y)$ , 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 $(1,0)$ and $(0,1)$ -- 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.