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You tend to get cyclic repeats when dividing by primes Isaac Send a noteboard - 25/05/2010 11:58:34 AM
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.... (8

Suggestions, O Math Gurus...?


My suggestion would be not to even waste time looking at numerological items of note unless you've gotten to the state of mathematical and hard science training where calculus and ordinary differential equations are something you think intuitively in. Almost all these sorts of things, once you have the background, are about as coincidental as as the fact that any integer times nine will have a product that's digits add up to nine. 81, 8+1=9, 72, 7+2=9, etc. You get the same thing in any base if you multiply the last digit in the radix times another integer of the radix... radix for decimal is 0-9, binary 0-1, hexadecimal 0-f (01-15), so that 5xf=4B (5x15= 75), and 4+B =f (4+11=15) same as with Xx9 in decimal. This is of course not a coincidence, by multiplying a number by the last digit before the tens place, you ensure it's product will shed one from the one's digit for each number it adds on to the ten's digit, regardless of your base.

It used to thrill numerologists that rivers, the longer they got, grew increasingly close to Pi as the relation between the straight-line distance from mouth to source and the actual path distance of a river. A freaky, almost divine coincidence. But it's not. While intuitively one would think that a river would begin by following the path of least resistance - which they do - that the older it was the more erosion would cause it to move in a straight line... but this is not the case, because such an assumption ignores the basic concepts of fluid mechanics, one of the few areas that still follows an almost entirely Newtonian Mechanics concept.

In reality, on a relatively homogeneous substrate with a fairly even line of altitude descent from source to mouth, instead of eroding into a straight line a river will erode itself into a path that looks much like a sine wave, not a straight line. What seems a mystic thing, on examination, is simply a byproduct of normal natural laws. This is the case for almost all these sorts of 'coincidences' except when it's not an artifact of a human-imposed system, where such things regularly pop up but rarely have any more significance than the amazing coincidence that in centigrade, water boils and freezes at exactly 100 and 0 degrees at exactly 1 atmosphere of pressure and require exactly 1 calorie to heat 1 cubic centimeter 1 degree centigrade, which weighs exactly one gram... this is, of course, not a coincidence of any sort.

Personally I'd just advise you to avoid anything numerological on general principle unless you feel like taking a course on number theory.

The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.
- Albert Einstein

King of Cairhien 20-7-2
Chancellor of the Landsraad, Archduke of Is'Mod
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Continuing the Math Theme, WTF Is Up with the Seven? - 25/05/2010 02:12:09 AM 651 Views
Base 10 number system - 25/05/2010 02:16:49 AM 487 Views
I Kinda Figured, but Why Does 7 Conflict with Base 10 So Much? - 25/05/2010 02:27:51 AM 479 Views
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You're a day early - 25/05/2010 09:10:30 AM 431 Views
Got me on a technicality. - 25/05/2010 09:19:54 AM 332 Views
Re: Got me on a technicality. - 25/05/2010 09:27:59 AM 371 Views
But we're AWESOME! - 25/05/2010 09:47:30 AM 471 Views
- 25/05/2010 09:50:43 AM 349 Views
You tend to get cyclic repeats when dividing by primes - 25/05/2010 11:58:34 AM 566 Views
I actually DO feel like taking a course on number theory. - 25/05/2010 12:12:10 PM 524 Views
Re: I actually DO feel like taking a course on number theory. - 25/05/2010 01:46:10 PM 365 Views
Well, I'm not vouching for Wikipedias claim, just reiterating it. - 25/05/2010 02:35:23 PM 583 Views
It's usually right but I wouldn't but much value on the implied importance - 25/05/2010 04:22:52 PM 426 Views
If you say so; I really try hard not to channel Pythagoras. - 26/05/2010 09:26:22 AM 596 Views
Re: If you say so; I really try hard not to channel Pythagoras. - 26/05/2010 10:00:37 AM 543 Views
The "leading zero" thing IS a bit misleading. - 26/05/2010 11:06:59 AM 676 Views
Re: The "leading zero" thing IS a bit misleading. - 26/05/2010 12:33:08 PM 398 Views
i have a book you're welcome to try reading.... - 26/05/2010 07:30:46 AM 357 Views
Yeah, I keep getting much that impression. - 26/05/2010 09:07:41 AM 340 Views
Why is 6 afraid of 7? *NM* - 25/05/2010 02:15:59 PM 187 Views
There it is again! Because 7 is a gluttonous beast. - 25/05/2010 02:27:58 PM 402 Views

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