Math Is Fun Forum

Umm...Let's see. I think the source is on a CD somewhere, if I even have it at all.

As far as the app goes, I'd have to do a fair amount of work on it before it were usable by the general public (incomplete interface--that's the biggest pain in Java programming). I never did finish it, see. And, it's a Swing app, not an applet.

I could look at taking the applet I wrote for the original assignment (if I still have that code) and adding Suess mode in, plus a marquee zoomer. I don't know how well it would run inside a web browser. Plus, I haven't written Java in about 4 years...

You've piqued my interest; I'll look for it. If something does come of it, I'd happily release the code as open source. But, no promises.

I'm surprised you didn't mention this.

Fractal math makes my head hurt, but I love the images. One assignment for an intro to computer programming course I took years ago was to write a java applet to calculate and graphically display the mandelbrot set. Fascinated, after the course I extended the program be a real java application. It did custom color gradients, had a marquee zoomer as well as numerical inputs, supported multiple windows with multithreaded rendering, etc. I was quite proud of it. I never did get to finish it, though, and now, years later, I don't have the time.

One of the coolest graphical effects in the program was the result of a moment of insanity. In Java, you represent colors as 4 byte integers, with the ARGB channels in subsequent runs of 8 bits. Of course, in Java all integers are 4 bytes, which means that any integer at all can be interpreted as a color. The result of the mandelbrot calculations in this particular calculator was an integer, one per pixel. You can see where this is heading...

I thought it would be cool to see what happened when I plugged the mandelbrot result directly into the color representation. The result looked a lot like an illustration in a Dr. Suess book, so I called it "Suess Mode." Some of the zoomed-in pictures in Suess mode were really fantastic. I wish I had saved some.

The total number of ways a paper/ink choice combination could come out is given by p*i. So, it's 42. You seem to know that already.

So, the chance of any one of those choices coming up is 1/42. You need to figure out the probability that two paper/ink choices will come out a certain way.

The choices made in one event to not affect the probability of any given choice coming up in a second event. So, the probability of the first event happening the way it did is 1/42, and the probability of the second happening the way it did is also 1/42.

I think that, to put them together, you multiply them. This comes out 1/1764, like you said. Your teacher appears to have simply multiplied by the number of events (2), giving 1/21. That would mean that, as you add more events, the likelihood of any given series of events coming out a certain way increases, which just makes no sense at all.

To see why, imagine flipping a coin. The probability that a certain face will come up is 1/2. If you want the same face to come up again, the chances are (1/2)(1/2) = 1/4. If you were to multiply by the number of events (2), you would get a probability of 1. This would mean that a coin, once flipped, *must* turn up the same face in all subsequent flips. This is clearly not the case, and if your teacher disagrees with you, ask him if he's ever flipped a coin before.

I mean, I could be wrong, of course. Anyone?

No, but you perhaps cosined against him.

Hoo...umm...what kinds of stuff I did...well...I quit.

In the middle of my junior year, I couldn't take the inanity any longer and I quit. Read a lot of library books for a year or so, then went to college. I'm now studying Chemical Engineering and doing fine.

So I guess I'm the opposite of you; I grew up schooled and finished homeschooled.

But don't worry, a lot of people aren't like me. They loved high school for some reason. There's nothing to say you can't be one of them.

Don't worry about tests. Tests are a piece of cake, especially in High School. Just pay attention when your teacher's talking. They generally go over things so many times that it's hard not to remember them when you take the test.

With tests, fear is your enemy. Fear degrades your ability to reason and remember things. I'm sure you'll find before too long that there's really nothing to worry about anyway.

Being a homeschooler, you know how you learn best. High school will force you to learn how some crock-brained educational theorist thinks you should learn. They will try to make you work harder than you need to in order to learn the material. The trick is to somehow do their way your way, and not let the busywork get you down.

What am I talking about? I failed at that so dramatically that I'm not even sure if it's possible.

I'm trying to be reassuring. I really am. I wish you the best of luck and hope you're successful and stuff.

1. P + 1.25P + 1.4(1.25P) = 560 Kg

2.25P + 1.75P  →  4P = 560

P = 140 Kg.

O = 1.75P = 245.

2. Q = P( 1+r)
Q1 = 200( 1+0.06) = $212
Q2 = 212( 1+0.06 ) = $224.72

Q3 = 350( 1 + 0.0575 ) = $370.13
Q4 = 370.13( 1 + 0.0575 ) = $391.41

391.41 + 224.72 = 616.13

Sorry if I was cryptic. I'm feeling lazy tonight. If you need better explanation, I'll oblige.

I didn't check if this one has already been solved, but since irspow asked about it, I gave it a go.

This is a substitution problem. Since r=2v, you can plug that into p=r/4: p = 2v/4 = v/2.

P is "in terms of" v because it's by itself, and the only other variable in the equation is v.

I used the "Grapher" program that comes with Mac OS X 10.4. Yes, the blue line is tanxy = 0.

It's possible that the squiqqlies are an artifact of the way the program calculates implicit graphs. Or of the resolution reduction - I had the resolution down to half (more and it got too cluttered and didn't look as cool).

Here are some graphs of just tanxy = 0 so we can see more clearly what's going on. I also turned the resolution all the way up this time.

The first one is zoomed out a bit, because it just looks cool.

2 is the default view. I turned off the axes so it's easier to see that the function itself has "axes." If you look really closely, you can see that they don't quite meet in the middle - they're 1/x-shaped bow thingies.

Note also that every other line in the graph is smooth, and the others are jagged. Not that they're random - they definitely have a pattern to them.

In the third, I showed the region that I would focus my zooming in on.

The fourth is zoomed waaayyyy in (note the labels on the axes; I exceeded their precision, so they all look the same). These graphs seem to possess an almost fractal ability to provide detail, even when zoomed infinitely in. Note also that a definite pattern has developed, and this pattern is unaltered no matter how far I zoomed in.

#5 is just an intermediate zoomed-out view.

I love to play with these sorts of things. I could spend hours just zooming and scrolling around, looking for interesting things.

Aaaarrrrggghhh! Smilies...dancing....must...restrain...fist of death...

::deep breaths::

Ok. How hard would it be to add a profile option to turn off the display of the smilies below the post box? Well, maybe pretty hard, since you'd probably have to add a database field and all the headaches that entails. Maybe I can get used to them, but...but...D'oh!