Believe it or not, I haven't covered all the mathematical visualization sites on the web yet.

When you talk about hundreds and thousands of anything, it's somewhat easy to visualize. When you start talking about millions, billions and beyond, then it becomes harder to relate and understand. We'll start with an introduction to the concept by the Fat Boys:

How about visualizing time? How long was a million seconds, minutes or hours ago? How about a billion? How about a trillion? Over at How much is a Million? A Billion?, you can get an idea of just how long ago that was. Keep in mind that this site was posted in 2000, so at this writing, one million hours ago would be the year 1892, not 1885.

If you're curious about going all the way up to 1 nonillion (1,000,000,000,000,000,000,000,000,000,000) and beyond, this site uses paper folding to get the idea across. Just to keep you grounded, most pieces of paper can't be folded in half more than 7 times, although Britney Gallivan has folded a piece of paper in half 12 times.

Usually when you're talking about millions, billions and beyond, you're talking about money. Thanks to the MegaPenny Project, you can see how big various amounts up to 1 quintillion pennies appear. If cows are more your thing, you can see a similar visualization at the MegaMoo project.

Now that we can more easily visualize millions of dollars, how about actually having millions of dollars to spend? That would be nice, so why not try the lottery? Well, this lottery simulation (Java required) can show you why not very quickly. It simulate your average lottery, in which you pick 6 different numbers out of 50, but it goes farther than that. It assumes that you play $1 each week, and keeps track not only of your wins and losses, but what you would have if you invested that dollar in a savings account at 5% interest. After just a year or two, the difference is already shocking. Let it run for 20 years, and you'll be in awe of the amounts involved (but you can visualize them in pennies!).

Back in the original Visualizing Pi post, I mentioned various versions of the Powers of 10 concept. The most detailed version I found of this would have to be Nikon's Universcale page (Flash required). Like the previous versions, it zooms in and out, but there is more detailed descriptions as you cross the various size boundaries. You can stop and examine each item in detail, as well. There's not much instruction required to use this site. Just run your mouse over just about anything on the screen, drag to change speed and direction, and click anything that is highlighted.

For my millions and billions of readers (hey, I can dream, right?), this should be plenty to explore until next time. My next post should be up about 350,000 seconds after this one.