If you consider "win" to be "never lose, no matter how long you go," then you can't assume that you won't at some point run into a certain combination of pieces, because then you are winning only until you hit those pieces, not for as long as you play. No matter how long you go without hitting those pieces, there's always the chance that you will eventually hit them, which means that your strategy is not a guaranteed win. If there is no strategy that's a guaranteed non-loss (for ANY sequence of pieces, not just most of them), then the game can't be "beaten." There is nothing else to prove.
It's not slashdot's responsibility to provide all its readers with the best deals on all the reviewed books. I see a convenient link to a reputable reseller. Frankly, I'm not going to complain about that free service, even if I don't take advantage of it. Perhaps if posts recommending better deals were to be banned, you would have something to complain about. But, honestly, are you really going to begrudge slashdot its inobtrusive, and perhaps helpful, way of making money?
The White House recently decided that it would be prudent to investigate further before taking any action to combat global warming. Debates were mostly over what research strategy to use. Of particular concern is ensuring that the United States economy doesn't suffer too much.
There are many methods that can be used to calculate pi, including some listed by others in this thread, although those do not get a lot of digits "fast" enough; better methods are used today. See The Pi Pages for more information.
Obviously, there are not many calculations that we need a trillion digits for. However, we still know very little about pi, and it is hoped that by investigating more and more digits of it, we might find some kind of pattern, or something that might help us understand pi. The problem has been worked on by mathematicians for literally thousands of years. So, yes, there could be some use for a trillion digits of pi.
Yes, in the same way it would be funny if the same person won the lottery every day for a month--think along those lines in terms of the likeliness of that happening.:)
Slashdot Mirror
If you consider "win" to be "never lose, no matter how long you go," then you can't assume that you won't at some point run into a certain combination of pieces, because then you are winning only until you hit those pieces, not for as long as you play. No matter how long you go without hitting those pieces, there's always the chance that you will eventually hit them, which means that your strategy is not a guaranteed win. If there is no strategy that's a guaranteed non-loss (for ANY sequence of pieces, not just most of them), then the game can't be "beaten." There is nothing else to prove.
It's not slashdot's responsibility to provide all its readers with the best deals on all the reviewed books. I see a convenient link to a reputable reseller. Frankly, I'm not going to complain about that free service, even if I don't take advantage of it. Perhaps if posts recommending better deals were to be banned, you would have something to complain about. But, honestly, are you really going to begrudge slashdot its inobtrusive, and perhaps helpful, way of making money?
The White House recently decided that it would be prudent to investigate further before taking any action to combat global warming. Debates were mostly over what research strategy to use. Of particular concern is ensuring that the United States economy doesn't suffer too much.
Great!
..can be found here (a slightly more detailed explanation than the one at the link the author gives).
You can calculate specific digits (in hex) using the formula, without calculating previous digits. That does not mean there is a pattern.
There are many methods that can be used to calculate pi, including some listed by others in this thread, although those do not get a lot of digits "fast" enough; better methods are used today. See The Pi Pages for more information.
Obviously, there are not many calculations that we need a trillion digits for. However, we still know very little about pi, and it is hoped that by investigating more and more digits of it, we might find some kind of pattern, or something that might help us understand pi. The problem has been worked on by mathematicians for literally thousands of years. So, yes, there could be some use for a trillion digits of pi.
Why are you doing this? Try that.
Yes, in the same way it would be funny if the same person won the lottery every day for a month--think along those lines in terms of the likeliness of that happening. :)