tag:blogger.com,1999:blog-3889388775673754833.post2831782401852815869..comments2022-11-27T10:19:27.872-05:00Comments on Stealing Commas: Base twelve math - Division Ruleschris the cynichttp://www.blogger.com/profile/06872875475212333027noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3889388775673754833.post-76629466575756589982015-05-04T18:27:42.587-04:002015-05-04T18:27:42.587-04:00My favorite base is actually 6. I think it makes f...My favorite base is actually 6. I <em>think</em> it makes for reasonably easy division for one through ten (i.e. 14), but eleven and thirteen (15 and 21) look to be tricky. Tricky enough that I wouldn't even try to use a trick for them.* Given that 7 is a smaller prime number than either 11 or 13, though, and only base 12 of those considered here handles 13 easily, I still feel like it's the superior choice.<br /><br />That said, the other disadvantage of Base 6 is that numbers are longer. Almost 30%, if I'm doing my logarithms correctly.<br /><br />-<br /><br />* Actually, I think I would use my #1 standard trick, which is "divide from right to left". To give an example in Base 10: if I wanted to know if 4459 was a multiple of 7, I would subtract 49 to get 4410, subtract 21 from 441 to get 420, and then see that 42 is a multiple of 7. The disadvantage of this method, of course, is that it doesn't preserve remainders for non-multiples - 4559 equals 2 mod 7, but at the end of my process you have 43 = 1 mod 7 (corresponding to 100 = 2 mod 7).Packbathttp://packbat.net/w/noreply@blogger.comtag:blogger.com,1999:blog-3889388775673754833.post-34940931700112790672011-12-23T09:03:46.660-05:002011-12-23T09:03:46.660-05:00Twelve seems to be a decent compromise between div...Twelve seems to be a decent compromise between divisibility and size of symbol set (if the latter's not crucial, base 60 is very pleasant)... it's the use of what I have to call duodecimal, for non-integers, where it really starts to get useful.Firedrakenoreply@blogger.com