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Doing hands on geometrical calculus is easy, and can be understood quite easily. What's I actually found difficult, was not the concept, but the memorization of how go obtain the integral or derivative of a functions. So many rules, that seemingly had no logic to them. The derivative of sin(x) is cos(x). Why? most students probably couldn't tell you that. Looking at a proof I found, it actually seems quite non-obvious, and not something most beginner calculus students could figure out on their own.

You don't need to know basic algebra to perform basic algebra. Basic math combined with the properties of real numbers (mostly intuitive themselves) makes basic algebra intuitive. Building these problems out as traditional equations involves a bunch of extra steps that serves no purpose except to satisfy a teacher who wants you to show your work. It's sort of like unit conversion. They give lessons on this and show frustrating slow processes where you put numbers over other numbers and toss in a conversion factor. But nobody would actually go through that garbage to convert a unit you added a bunch of extra crap to the problem just to cancel it out later.

A foot is 12 inches. If you have 36 inches how many feet do you have?

Anyone who understands multiplication and division can solve this problem without being taught a formal unit conversion process. If writing this down they would write 36/12 = 3.

http://www.math.com/school/subject2/lessons/S2U2L1GL.html

You would need a glider gun that shoots out more glider guns.

Which would be hella fun, actually.

There is a breeder pattern that uses a set of ships to produce a stream of glider guns, but (being regular Gosper Glider Guns) they don't move once they've been created.

The applet on Paul Callahan's page has it stored as one of the example patterns.

Using the rules specified in the parent post: try working out how the following pattern will turn out (without simulating it on a computer!).

OXX
XXO
OXO

where:
X - a live cell
O - an empty cell

Should be very easy, as the rules are SO SIMPLE, right???

see the R-pentomino in:
http://www.math.com/students/wonders/life/life.html

But you'd probably be really glad you have them if you need them.

should have included math.com

Do we know this? I'm no astronomer, so I don't. Just how much can an orbit be altered by a collision? (Or at least, one that doesn't pulverize both objects).

I'm no astronomer either, but we can run some numbers found a la Google and give ourselves some reasonable estimates. Anybody who IS an astronomer is free to correct my numbers, but my intention is merely a "back of the napkin" class estimate.

How fast does an asteroid travel? The average speed of an asteroid is 25km/second. Since I'm am American, to me that's about 15 miles per SECOND.

Earth is 7,926 Miles across. For these figures I'll use 8,000 miles.

Asteroids are somewhere between 1.8 and 4.5 AU from the sun. The earth is 1 AU from the son. Since both orbit the sun, and the average distance of earth from the sun is 0 AU (orbit being roughly circular) let's say that the average distance of an asteroid from Earth is about 2.2 AU. Since earth is 1 AU and that is 93 Million miles, we'll say that the average asteroid is about 93 million * 2.2 miles from the Earth. That's 204.6 million miles from the Earth.

So let's assume that two rocks hit. What are the odds that the asteroid goes out and whacks the Earth, straight away? Well, we'd end up with a 204.6 MILLION MILE RADIUS on the inside of a very large sphere. Using the formula for calculating the surface of a sphere, we get 261,348,480,000,000,000 square miles of area that the asteroid could potentially hit. Compare that to the actual area of Earth to hit (a circle 2*pi*r) =~ 50,000 miles.

In short, you have a 50,000 in 261,348,480,000,000,000, or 1 in 5,226,969,600,000. (one in about 5 trillion)

These are very VERY VERY small odds, even if my back-of-the-napkin calculations are off by several orders of magnitude. Let's give you some idea just how BIG 5 trillion is. There have been about 1 billion seconds since Jan 1, 1972. To wait 1 trillion seconds is to wait about 30,000 years. If asteroids were to collide every SINGLE SECOND it would STILL take over 30,000 YEARS for one to hit the Earth directly.

Now, these figures are rough. They do not take into account orbital mechanics, etc. But even so, the numbers are very small (large as odds against?) indeed.

I used to play Life on the trusty C64, this is at least the second digital simulation :) http://www.math.com/students/wonders/life/life.htm l

before.

Equipment:
Brain and / or calculator.

Method:
Visit the manufacturers homepage for each item you want to build into your system, find the technical specifications for that item, then find the specification for the maximum power draw for that item.

Write that figure down, then repeat the process for each of the other system components. When you have data for all the devices, add them together to produce a total.

Result:
Buy a PSU that covers that total figure in normal usage.

Next week we will be covering another difficult subject - Wearing trousers ~ How not to fall over while putting them on.

Todays program was brought to you by the letters D,U,H !

Hey thats the game of life http://www.math.com/students/wonders/life/life.htm l. I remember programming that one for multiple school classes. One of my friends even made it his screen saver.

Like many of you, I am reminded of my old high school security expoits. I took a C++ course in my junior year. I already knew C++ and was just taking it for transcript purposes, so I wrote little side projects during class instead of actually following along with the lesson. One of these projects was a Windows 98 password logger with the option of logging the user/pass to a file, FTP site, or email address. Within a week of installing it on just one school library computer, I had a password-protected database of student, teacher and administrator usernames and passwords available to me online. I told a couple friends about it, and one got caught changing his grades. He didn't rat me out though, thank God! I miss those days... not the classes or the bull students went through, just messing around on the school's network without them even knowing it. Another side project was a sick implementation of Life.

I hate to state the obvious, but Math.com is where I've spent some time brushing up on all the math I've forgotten.

I'd love a math tutor style of program that would fluidly walk you through from basic math all the way to calc and trig, automatically adjusting to your rate of learning based on little exercises.

Your talkin about the wrong Game of Life, check out this one: Game of Life.

There are more pictures at Benjamin Chaffin's page.
There is more information on the games and rules at Sven's page, that includes a comparison of Chaffin's notation to Gardner's and a comparison of Worms to the Game of Life.

Even on the off chance that the About network doesn't have all the information you need, they have a large number of links to sites with relevant information across the Web, so there's a very good chance that you will be able to use them to find what you are looking for.
Also...although these are not strictly an answer to your question, I would still heartily encourage you to follow the links to these (listed in a suggested order of reading...my probably misguided opinion only) text files, web pages, and books, as I think they could be of enormous benefit to both your children and yourself...indeed, anyone who wishes to read them. Although I understand that several of these could possibly only be understood at tertiary level, they also as far as I know are not normally included in *general* curriculums, and IMHO they should be.

• The Allegory of the Cave by Plato
• Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences, by Rene Descartes
• Guide to Ethics & Morality
• The Logic FAQ
• The Art of War, by Sun Tzu
• The Wealth of Nations, by Adam Smith
• The Sovereign Individual, by James Davidson
• The 48 Laws of Power, by Robert Greene
• The Prince, by Niccolo Machiavelli

It used to be in the past that the education systems of most nations didn't want us to know the why (philosophy, religion, history, political theory) of life, but were content enough to let us know the how. (Science without analysis, numeracy and literacy skills, etc) Now however we are seeing that primarily in America, but also in other places, government education departments no longer even want to allow people to know the how.

Mathematics is part of the how - a means to an end, a way of solving problems - but it is not a destination in itself. The material I've given you links to in my second section is concerned with finding out *why* - "Why am I here? Who am I? How do I know what reality is? What do I want to do with my life? What moral values do I believe in?"
The answers to these questions are far more important than becoming merely literate or mathematically capable for their own sake. Figure out what your purpose is first, and the rest, although still requiring work, will be relatively easy. That is what the links in the second list will help you do, and it's not something you'll be taught to do in any contemporary public school, either...Governments consider people with purpose to be highly dangerous.

It's here.

Or, you can buy it here.

So, I suppose this and this and the other several thousand responses I got to *one* google query "math help" don't exist on the internet. Or maybe they are not "a good source for education".

That is if the complexity you and I are referring to were even semantically equivalent. But, the complexity in the way both Wolfram and I mean is more akin to "structure". For instance, in the Game of Life, the "emergence" of, say, gliders and producers from its simple rules cannot be expressed with algorithmic complexity semantics.

And my original assertion is that I believe it's probably unlikely that there will ever be mathematics to describe that kind of complexity. Because, what we find complex or interesting in that context is merely a reflection of the bias we gain from our environment ("things that fly", "things that cycle", etc).

I know what roman numerals are, thank you very much. It seems that you don't know what the SI prefixes are.

For your reference:

http://www.math.com/tables/general/numnotation.htm

Have a nice day.

It uses an oscilloscope tube to draw the time in green phosphor arcs - no pixels.

Very nice!

If you don't feel like figuring out how to drive a CRT directly, there are some interesting things you can do with just a regular oscilloscope set to XY mode. Next time you're at Fry's, go to the aisle where they have all the oscilloscopes and function generators. This works best on a CRT scope, not a digital sampling scope. Hook two function generators to the scope inputs and set it to XY mode. Set the function generators to a sine wave, and play with the frequencies. You can generate all sorts of interesting lissajous figures.

I once made a project using a PIC, a couple of DACs, and two stepper motors. The stepper motors were wired up like a "poor man's galvanometer" - the were driven by the DACs to move back and forth within a step. By mounting the motors at 90 degrees and hitting them with a laser pointer, I was able to make a pretty groovy portable laser show for about $40 worth of components.

Another thing you can do if you don't feel like making your own hardware is to hook your sound card's left and right outputs to an oscilloscope. The you could write some simple software to draw these kinds of figures on the scope by just sending the wave forms out of your sound card. Unfortunately the frequency response is limited to the audible range so this is not ideal. A simple resistor-ladder DAC on the parallel port might work better because you could have <20HZ frequencies.

It's amazing what you can do with a little geometry....

the answer to this question should be obvious to anyone that thinks about it... but i think our blinkered, reductionist, view of biology ("genotype == phenotype", "genes == organism") stops it being obvious to many people.

the information is stored in the molecules that make up your body, in combination with the laws of physics. think about a pool of water. you can describe it with a simple "take one molecule of water, replicate by 10^30". however, does that information describe the pool of water? nope - think about waves, interference patterns, surface tension, etc, etc...

the point is that the genes can create a structure that is initially uniform, but allows structure to form by virtue of the interactions of its elements. think about Conway's Life - it's described by some very, very simple rules - its complexity evolves from those rules (its "laws of physics") and the cells (its "molecules")

so you can see that our genes don't need to describe us in our entirety, but merely describe a structure from which something like us can arise, given the usual laws of physics and interactions with the external environment.