Editing 1292: Pi vs. Tau
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==Math details== | ==Math details== | ||
Possibly, [[Randall]] used [http://www.wolframalpha.com/ Wolfram|Alpha] to calculate the result (he uses it a lot, for example [http://what-if.xkcd.com/70/ What-if 70: The Constant Groundskeeper] or [http://what-if.xkcd.com/62/ What-if 62: Falling With Helium]). | Possibly, [[Randall]] used [http://www.wolframalpha.com/ Wolfram|Alpha] to calculate the result (he uses it a lot, for example [http://what-if.xkcd.com/70/ What-if 70: The Constant Groundskeeper] or [http://what-if.xkcd.com/62/ What-if 62: Falling With Helium]). | ||
β | However, when the comic was published, there was a bug in Wolfram|Alpha so that, when getting 200 octal digits from "pau", it just calculates the decimal value rounded to 15 significant digits (this is 4.71238898038469) and expands that as octal digits as far as needed. | + | However, when the comic was published, there was (and still is, as of April 29, 2014) a bug in Wolfram|Alpha so that, when getting 200 octal digits from "pau", it just calculates the decimal value rounded to 15 significant digits (this is 4.71238898038469) and expands that as octal digits as far as needed. |
This gives a periodically repeating number. In the first 200 digits of the octal expansion, the sequences 666 and 6666 do occur, twice and once, respectively. There are 4 occurrences, however, in the first three hundred and ten (310 in base 8 equals 200 in base 10) digits: | This gives a periodically repeating number. In the first 200 digits of the octal expansion, the sequences 666 and 6666 do occur, twice and once, respectively. There are 4 occurrences, however, in the first three hundred and ten (310 in base 8 equals 200 in base 10) digits: |