Scratch

One thing I'd like to see are more "advanced" math functions. Stuff like sin cos and tan would be nice.

Hi tstirler
For now there are some tricks that I use to generate sine waves. I first thought about lookup tables, but then I remembered that cosine comes from a circle, so I made this project
http://scratch.mit.edu/projects/jay/243
where I just set the y-value of the cosine wave to the y-value of the ball that's moving in a circle. Then I move the cosine wave constantly in the x direction.

I also noticed this project
http://scratch.mit.edu/projects/Canthiar/6123
which generates a sine wave by using the mathematical functions that Scratch does have.

I thought about Canthiar's suggestion about using a sprite to calculate trig functions and came up with the following little project:

http://scratch.mit.edu/projects/Roberth/8335

Canthiar got the x and y components mixed up, but otherwise was spot on.  I also used a circle 150 units in size to help add to the resolution of the numbers.  This is also a fantastic way of demonstrating trig functions and explaining this to a group of kids that these numbers aren't just pulled out of the air, but have real meaning in a physical sense.

I added as the value of "infinity" for a tangent of 90 to be 1000000, but this is just an arbitrary value.  The code got an error when you divided by 0 (as it should!) and threw in a special test case for that possibility.  This would also be an interesting example to explain limit theory from an introductory viewpoint, and explaining what happens as you get closer and closer to 90 degrees for a tangent but don't quite get there... and perhaps to give a mathematical explanation that can also be demonstrated with a Scratch program.

Canthiar didn't mix up the x and y axes, the Scratch team did.  And I understand that they did it deliberately, though why they wanted to use non-standard angle naming, and make the default angle 90 degrees is still a mystery to me.

Canthiar wrote:

If you're deciding on which functions to add then I would think that sin, cos, and sqrt would be the most used.

Here is a square root to round out the set:

http://scratch.mit.edu/projects/DrJim/8537

(The reference URL was long enough that the notes are below the screen.)

Canthiar wrote:

DrJim, how many iterations does it take for your square root to converge?

It's quadratically convergent so it usually "improves" by about two significant figures every itteration.  Not something you can count on, however.  If your initial guess is wildly off or you're at troublesome points (say 0.999999) you can take longer.  Also this particular algorith does not (I'm pretty sure) let you know when you have an exact square root, i.e., it won't specifically tell you 5 is the exact square root of 25.

For more details, take  a quick look at the Wiki references or do a general search on the subject. There is apparently a very fast square root algorithm used in the "Quake 3" engine - but I've never tried it.

Dr. Jim's algorithm, like Canthiar's, is the standard Newton iteration.  One has to be a bit careful when handling zero, but it is a fine algorithm. 

The fast algorithms usually make a quick initial guess (using the structure of floating point numbers) then do a few iterations of Newton's method.  Since we have no access to the bits of the floating-point representation in scratch, Newton's method is likely to be the best we can do.

Ahhhhh!!!! Mega Necropost!!!!!

This seems to be quite an old [and misplaced!] thread. Being that the thread is old, I'll have the thread closed.

Discussions about new requests for the next version of Scratch can be made in the 'Suggestions' forum.