Math / Virtual Reality / Interactive Graphical Things on the Web / Games / Just playing around ...
I've added a math related game to my site, "The Lunar Lander", a game that has been around for a decade on X-Windows ( a Unix thing that involves a mouse ).
It is a game, I mean a math problem, where you land a space craft, using rockets to slow your decent, and move back and forth by rotating and firing the engine with a non vertical vector.
It is purely a game, but it is a vector addition problem, and calculating vector components involves sine calculations, and calculating if you have enough to fuel to land safely involves more math.
I'm not suggesting it is useful as is. But a story line could be written ...
A student is given the role of being a Spacecraft Commander and has to plan a rather a complicated mission which is broken down into a series of steps such as determining how much fuel is needed to land safely from an initial situation ( position and velocity ).
The commander makes his calculation and tests it in the Virtual World, with the Lunar Lander.
The game would be transformed so that it would play scripts that the teacher would devise and the student would play out. The student wouldn't be taking a test, but would be working on achieving the goals : to explore space, to perform resupply and rescue missions, to test fly new spacecraft.
Additional gauges would be added, currently it has a 'Fuel Gauge' ( with no Units ! ).
Additional gauges would display the Position, Velocity, and Acceleration ( analog and digital displays with the appropriate units ) and these could be graphed, and the requisite equations would be provided.
Goals could be simple : During testing the rocket is placed on a car and fired horizontally.
How long does it take to get up to 60 M.P.H. ? 100 M.P.H. ?
The total mass of the vehicle, the thrust of the engine ( the Force ), and the equation :
Force = mass * Acceleration
would be given, and the Commander would do the calculations and test it out.
( Actually I would assume most calculations would be done using the Metric system. )
How quickly can you stop with a given braking force ?
How much room do you need to get up to 100 M.P.H. and then stop ?
How long will it take ?
Some things may be left to be discovered : ignoring the landing goal of the game -- if you just fly around -- you will notice that as you tilt further and further to the horizontal your clime-rate will fall to zero and you will fly horizontally.
What's the angle ( that the vertical component of the thrust vector equals the pull of gravity ) ?
Some solutions could be posed first as a simple numerical solution, then as the general solution ( and both could be then test-flown, and the test flight could be flown by the Spacecraft Commander, or by the auto-Pilot, or the Spacecraft Commander could program the auto-Pilot ! ).
What is the greatest payload you can lift off the surface of the Earth ?
Calculate how much fuel you need to fly over The Big Mountain ?
On an arbitrary planet ?
( Before landing on a foreign planet I like to know if I can leave ... It pays to call ahead and ask 'What's gravity like down there?' I suppose you could just orbit and do a little math ... )
I don't have the source to either but I could create what would be needed to set up reasonable math problems involving angles and such with one or two balls.
I have known of Mr. Abreu by way of your Polyhedra pages, his Platonic Solids applet is very similar to one of mine ( I have more objects but mine are only monochromatic ) and I have reviewed his web pages thoroughly. I've notice he is an on-line participant of the Math Forum and will write to him soon.
For reasons I don't understand my "Supermodels Of Math" program doesn't work with the combination of a Macintosh running Netscape. I don't have a Mac so it's hard for me to diagnose the problem. I do test my applets on three browsers ( Netscape, MiSE, and Sun's HotJava ).
I have a mathematical Java Piano / Synthesizer / Oscilloscope that plays a tune on a web page ...
Just being provocative.
Paul Flavin firstname.lastname@example.org
Disclaimer : I didn't write the 'Lunar Lander'. I do have the source code (it's public domain) and I have modified it. Some guy, Newton I think, figured out most the equations, they are pretty simple, it's not rocket science ...