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Archive for the ‘Mathematics’ Category

π Day!

Posted by Doug on March 14, 2009

Yay!  It’s Pi Day!

I missed the optimal 1:59:26 AM posting time (of course, back in 1592, the optimal time was 6:53:58 AM, but that’s neither here nor there), but like I’ve always said kill it with fire everything’s better with catgirls the only good human is a dead human better late than never! Here goes, the digits of pi up to the Feynmann Point, courtesy of Pi Day:

3.

14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99 and so on…

P.S. I don’t even want to hear from any Euler’s number fanboys (or fangirls) because everybody knows that π > e.

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Posted in Holidays, Mathematics, Science | Tagged: | Leave a Comment »

A d20 Versus the Chi Squared Test

Posted by Doug on February 10, 2009

So I was trawling through the official Dungeons & Dragons forums, and came across one thread where a DM claimed that he had a player who had rolled a 20 on a twenty-sided die a total of twenty-three times in a row.  Of course, given that the odds of this occuring are 838,860,800,000,000,000,000,000,000,000 to 1, the consensus of the community seems to be that either the “lucky” player is cheating, or that the DM is full of it.

Of course, the player may not be consciously cheating, and the DM may not be deliberately lying, but just consider: assume that the odds of a player cheating (consciously or not) are 1 in 1000 (generous) and the odds of a poster in a forum repeating nonfactual information (consciously or not) are also 1 in 1000 (veeeeeerrrrrry generous).  This means that either a cheating player or a nontruthful poster are 838,860,800,000,000,000,000,000,000 times more likely than a non-cheating player actually rolling twenty-three 20s in a row.

The other forum-goers who decided to chime in brought up loaded dice (a possibility that the DM vehemently rejected), and this got me to thinking about my own dice: were they fair?  Does, for example, my green-and-white Chessex d20 have exactly the same chance of landing on any one of its twenty faces?

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Posted in Games, Mathematics, Science, Traditional RPGs | Tagged: , , | 1 Comment »