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.
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 .
The same as the previous applet, but this one is over the region , .
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.
You specify a curve, and this applet animates its Frenet-Serret frame.
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.
This isn’t a Geogebra gadget itself, but it shows how awesome Geogebra is for doing exploratory assignments.