I can imagine this in the science books of the future. I usually check with a few cases to see if I understand the subject correctly, but sometimes I have enough samples to test.
This would be great: the student can see the default example, learn the subject and then try to check if he understood it correctly seeing how it behaves changing the parameters!
In a physics course I took some years ago, we used Mathematica notebooks for that. The professor had written out explanations of a few subjects we were studying in the style of tutorial notes or a paper handout, but within Mathematica so you could change the parameters and see updates in real time.
I am currently working on interactive 2-d physics simulation in the browser with much the same ideas. On the desktop we have apps like KDE Step but I haven't found anything similar for the web.
Currently I have particles,disks and boxes working with gravitation, coulomb and custom-defined forces. I also implemented Runge-Kutta method of integration instead of horribly inaccurate Euler's method. You can manipulate the objects, their parameters and laws even while the simulation is running.
I need to add basic collision detection and things like springs, links, and linear/angular motors and embedding the simulation as a widget before polishing it up and releasing.
Email me in case this sounds interesting and you would like to stay updated.
Precisely. In physics, testing extreme cases and boundary conditions is one of the first ways to get a better understanding of a system. Tangle can be a great tool to empower learners to do this visually.
This would be great: the student can see the default example, learn the subject and then try to check if he understood it correctly seeing how it behaves changing the parameters!