I mean, I'm REALLY not one of those guys who gets all mystical about numbers; I understand that they merely represent real world physical relations, and all the "mystical" BS is just our failure to recognize some of them. There's nothing "magical" about the fact 2+2=2X2=2^2, it's just the nature of those functions and the number itself, just as when 3+3+3+3+3+3+3+3+3=3X3X3=3^3. It would take too long than anyone but me wants to spend explaining why 1/3^4 gives the first ten integers, in order, as a decimal, but I DO understand it (generally speaking. ) It makes sense, just as the numerator of a fraction with denominator 9 should be itself as a repeating decimal; dividing by 9, after all, is the same as dividing by 10-1.
So why does 1/7 become 0.142857...? Even the part with the final digits being 5 and 7 rather than 5 and 6 makes a kind of sense, just as 1/81=0.123456790... because 10 comes after 9, which carries over to make the 9 a 10 as well, which carries over to make the 8 a 9, hence 0.123456790... instead of continuing with the 8; it's still there, but the nature of the rest of the number "disguises" it. But 1/7, I've looked at it every which way for years and it doesn't make sense why it does that, why one single function performed on one single digit integer can yield a far more complex repeating decimal. Even 1/6 makes sense; it's just half of 1/3. But you can't do that with 7; it's prime. It just keeps getting weirder....
Suggestions, O Math Gurus...?
So why does 1/7 become 0.142857...? Even the part with the final digits being 5 and 7 rather than 5 and 6 makes a kind of sense, just as 1/81=0.123456790... because 10 comes after 9, which carries over to make the 9 a 10 as well, which carries over to make the 8 a 9, hence 0.123456790... instead of continuing with the 8; it's still there, but the nature of the rest of the number "disguises" it. But 1/7, I've looked at it every which way for years and it doesn't make sense why it does that, why one single function performed on one single digit integer can yield a far more complex repeating decimal. Even 1/6 makes sense; it's just half of 1/3. But you can't do that with 7; it's prime. It just keeps getting weirder....

Suggestions, O Math Gurus...?
Formerly Mat Bloody Cauthon on Wotmania, blessed be its name
Continuing the Math Theme, WTF Is Up with the Seven?
25/05/2010 02:12:09 AM
- 649 Views
25/05/2010 08:19:12 AM
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Number theory holds a concept called "cyclic numbers."
25/05/2010 06:04:43 AM
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"If leading zeros are not permitted on numerals, then 142857 is the only cyclic number in decimal. "
25/05/2010 06:27:36 AM
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Happy Birthday...?
25/05/2010 08:56:59 AM
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You're a day early
25/05/2010 09:10:30 AM
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Got me on a technicality.
25/05/2010 09:19:54 AM
- 330 Views
Re: Got me on a technicality.
25/05/2010 09:27:59 AM
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But we're AWESOME!
25/05/2010 09:47:30 AM
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25/05/2010 09:50:43 AM
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Number THEORY is great fun, but too many folks make math too tedious, I'm afraid.
25/05/2010 09:53:21 AM
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You tend to get cyclic repeats when dividing by primes
25/05/2010 11:58:34 AM
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I actually DO feel like taking a course on number theory.
25/05/2010 12:12:10 PM
- 522 Views
Re: I actually DO feel like taking a course on number theory.
25/05/2010 01:46:10 PM
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Well, I'm not vouching for Wikipedias claim, just reiterating it.
25/05/2010 02:35:23 PM
- 581 Views
It's usually right but I wouldn't but much value on the implied importance
25/05/2010 04:22:52 PM
- 425 Views
If you say so; I really try hard not to channel Pythagoras.
26/05/2010 09:26:22 AM
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Re: If you say so; I really try hard not to channel Pythagoras.
26/05/2010 10:00:37 AM
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Why is 6 afraid of 7?
*NM*
25/05/2010 02:15:59 PM
- 187 Views
