5 ms·

142857

100 points by merraksh 11y ago

dstyrb 11y ago
Hahaha, I like how they include: "If it is multiplied by 2, 3, 4, 5, or 6, the answer will be ... 2/7, 3/7, 4/7, 5/7, or 6/7 respectively." Was it surprising to multiply 1/7 by two and get 2/7? Has science gone too far?
- misframer 11y ago
  The point of that sentence, which you have excluded, was about the cyclical permutations.
  - dstyrb 11y ago
    I said the clause was an unnecessary inclusion, the ellipses are there specifically to highlight that. The rest of the article is about the cyclicity of the digit.
    - mikeash 11y ago
      Your ellipses completely change the meaning. The clause may be unnecessary (as is the entire article) but the bit you complain about is useful if you don't chop things out first.
      - dstyrb 11y ago
        Well, not sure it was a complaint, I was just lightheartedly commenting that it was a bit redundant, but ok, umbrage seems a reasonable response. And yeah, that's pretty much the point of eliding bits of text, to put things together that weren't together before; I'm almost positive that's why we invented that specific punctuation mark. It's like saying: "The 35th president of the United States, JFK, who was widely known for the space race and the bay of pigs, was elected after the 34 presidents before him." And my comment is like: "The 35th president of the United States ... was elected after the 34 presidents before him."
        mikeash 11y ago
        My point is that ellipses are for when you're excising something that is redundant to your purposes and whose omission doesn't change the overall meaning. Your example with JFK is fine. Here's a counterexample where it doesn't work: "JFK had an affair with Marilyn Monroe, who was a famous Hollywood actress." -> "JFK... was a famous Hollywood actress." I maintain that your shortened quote is more like this. The article says that 142857, when multiplied, produces numbers which correspond to the digits of 2/7, 3/7, 4/7, etc. Your version of the quote omits the words "correspond to," changing it from an observation about how an integer matches the decimal expansion of a fraction to an observation about how multiplying a number gets you a multiple of that number.
        deleted 11y ago
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        deleted 11y ago
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- tomvbussel 11y ago
  Ask a random person if 1 and 0.999999... are the same number and most people will tell you they aren't the same number. Yet: 1 = 3 * (1/3) = 3 * 0.33333... = 0.99999... (they're also epsilon close for every epsilon larger than zero). So yes, this kind of stuff is surprising for a lot of people.
  - partisan 11y ago
    I'd like to have everyone in the world give me their money and I will promptly return that money times 0.99999... They are the same number, after all.
    - mikeash 11y ago
      Aside from the obvious problems trustworthiness and transaction costs, what would be wrong with that?
    - qu4z-2 11y ago
      I'd like to have everyone in the world give me their money and I will return that money times 1.0000000001 about a week later, after making bank off the interest. Sadly there seems to be no general enthusiasm for this plan. :) Also: Tell you what... you give me your account details, and I'll send you (1 - 0.9999...) times my money. Deal?
popctrl 11y ago
Hey neat, my favorite number is on HN! Here's an interesting video showing this stuff (And more) in a more user-friendly way https://www.youtube.com/watch?v=WUlaUalgxqI https://www.youtube.com/watch?v=WUlaUalgxqI
- rbonvall 11y ago
  It's also my favorite number, but I don't think any of us likes it more than the guy in the video :) Thanks for sharing. I learned about 142857 when reading The Man Who Counted as a kid. I remember getting obsessed with it and discovering more properties (much fewer than the ones shown on the video), e.g.: 142 + 857 = 999 14 + 28 + 57 = 99
  - zyrthofar 11y ago
    You can go even further. 142 + 857 = 999; 9 + 9 + 9 = 27; 2 + 7 = 9 14 + 28 + 57 = 99; 9 + 9 = 18; 1 + 8 = 9 1 + 4 + 2 + 8 + 5 + 7 = 27; 2 + 7 = 9 Also, 1428 + 57 = 1485; 1 + 4 + 8 + 5 = 18; 1 + 8 = 9 14 + 2857 = 2871; 2 + 8 + 7 + 1 = 18; 1 + 8 = 9 1 + 42857 = 42858; 4 + 2 + 8 + 5 + 8 = 27; 2 + 7 = 9 1 + 42857 = 42858; 42 + 858 = 900; 9 + 0 + 0 = 9 This is kinda creepy. I wasn't really expecting the "also" additions to work.
    - schoen 11y ago
      If you have any multiple of 9 and repeatedly add the digits, you get back to 9: https://en.wikipedia.org/wiki/Digital_root https://en.wikipedia.org/wiki/Digital_root Conversely, if you have any number whose digits added together sum to 9 (or a multiple of 9), the original number is a multiple of 9. So, all of your original sum numbers (999, 99, 27, 1485, 2871, and 42858) are themselves multiples of 9, which will be the case for any number obtained by adding a set of numbers which together contain all and only the digits 142857. That means a lot of other "also" additions will work out too! You can even change the order, like 578 + 214 = 792 (a multiple of 9, and hence the digital root will end up being 9). Any order and any choice of how to break the numbers will work, because of the digital root property (and, importantly, the rule that "The digital root of a + b is congruent with the sum of the digital root of a and the digital root of b modulo 9").
baseballmerpeak 11y ago
1/7 = 0.14+0.0028+0.000056+0.00000112+0.0000000224+... 14=2(7) 28=4(7) 56=8(7) 112=16(7) 224=32(7)
tomkwok 11y ago
There is a detailed explanation on Quora [0] that I stumbled upon some time ago. [0]: http://www.quora.com/Why-does-the-number-142857-have-such-interesting-properties http://www.quora.com/Why-does-the-number-142857-have-such-in...
caligastia 11y ago
There is a priceless video at https://www.youtube.com/watch?v=UKPwZqUUrQo https://www.youtube.com/watch?v=UKPwZqUUrQo of the Gurdjieff movements, the dance at 3:24 is an expression of a computational process.

100 points by merraksh 11y ago

Hahaha, I like how they include: "If it is multiplied by 2, 3, 4, 5, or 6, the answer will be ... 2/7, 3/7, 4/7, 5/7, or 6/7 respectively." Was it surprising to multiply 1/7 by two and get 2/7? Has science gone too far?

misframer 11y ago
The point of that sentence, which you have excluded, was about the cyclical permutations.
- dstyrb 11y ago
  I said the clause was an unnecessary inclusion, the ellipses are there specifically to highlight that. The rest of the article is about the cyclicity of the digit.
  - mikeash 11y ago
    Your ellipses completely change the meaning. The clause may be unnecessary (as is the entire article) but the bit you complain about is useful if you don't chop things out first.
    - dstyrb 11y ago
      Well, not sure it was a complaint, I was just lightheartedly commenting that it was a bit redundant, but ok, umbrage seems a reasonable response. And yeah, that's pretty much the point of eliding bits of text, to put things together that weren't together before; I'm almost positive that's why we invented that specific punctuation mark. It's like saying: "The 35th president of the United States, JFK, who was widely known for the space race and the bay of pigs, was elected after the 34 presidents before him." And my comment is like: "The 35th president of the United States ... was elected after the 34 presidents before him."
      - mikeash 11y ago
        My point is that ellipses are for when you're excising something that is redundant to your purposes and whose omission doesn't change the overall meaning. Your example with JFK is fine. Here's a counterexample where it doesn't work: "JFK had an affair with Marilyn Monroe, who was a famous Hollywood actress." -> "JFK... was a famous Hollywood actress." I maintain that your shortened quote is more like this. The article says that 142857, when multiplied, produces numbers which correspond to the digits of 2/7, 3/7, 4/7, etc. Your version of the quote omits the words "correspond to," changing it from an observation about how an integer matches the decimal expansion of a fraction to an observation about how multiplying a number gets you a multiple of that number.
        deleted 11y ago
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        deleted 11y ago
        [deleted]
tomvbussel 11y ago
Ask a random person if 1 and 0.999999... are the same number and most people will tell you they aren't the same number. Yet: 1 = 3 * (1/3) = 3 * 0.33333... = 0.99999... (they're also epsilon close for every epsilon larger than zero). So yes, this kind of stuff is surprising for a lot of people.
- partisan 11y ago
  I'd like to have everyone in the world give me their money and I will promptly return that money times 0.99999... They are the same number, after all.
  - mikeash 11y ago
    Aside from the obvious problems trustworthiness and transaction costs, what would be wrong with that?
  - qu4z-2 11y ago
    I'd like to have everyone in the world give me their money and I will return that money times 1.0000000001 about a week later, after making bank off the interest. Sadly there seems to be no general enthusiasm for this plan. :) Also: Tell you what... you give me your account details, and I'll send you (1 - 0.9999...) times my money. Deal?

popctrl 11y ago

Hey neat, my favorite number is on HN! Here's an interesting video showing this stuff (And more) in a more user-friendly way https://www.youtube.com/watch?v=WUlaUalgxqI https://www.youtube.com/watch?v=WUlaUalgxqI

rbonvall 11y ago
It's also my favorite number, but I don't think any of us likes it more than the guy in the video :) Thanks for sharing. I learned about 142857 when reading The Man Who Counted as a kid. I remember getting obsessed with it and discovering more properties (much fewer than the ones shown on the video), e.g.: 142 + 857 = 999 14 + 28 + 57 = 99
- zyrthofar 11y ago
  You can go even further. 142 + 857 = 999; 9 + 9 + 9 = 27; 2 + 7 = 9 14 + 28 + 57 = 99; 9 + 9 = 18; 1 + 8 = 9 1 + 4 + 2 + 8 + 5 + 7 = 27; 2 + 7 = 9 Also, 1428 + 57 = 1485; 1 + 4 + 8 + 5 = 18; 1 + 8 = 9 14 + 2857 = 2871; 2 + 8 + 7 + 1 = 18; 1 + 8 = 9 1 + 42857 = 42858; 4 + 2 + 8 + 5 + 8 = 27; 2 + 7 = 9 1 + 42857 = 42858; 42 + 858 = 900; 9 + 0 + 0 = 9 This is kinda creepy. I wasn't really expecting the "also" additions to work.
  - schoen 11y ago
    If you have any multiple of 9 and repeatedly add the digits, you get back to 9: https://en.wikipedia.org/wiki/Digital_root https://en.wikipedia.org/wiki/Digital_root Conversely, if you have any number whose digits added together sum to 9 (or a multiple of 9), the original number is a multiple of 9. So, all of your original sum numbers (999, 99, 27, 1485, 2871, and 42858) are themselves multiples of 9, which will be the case for any number obtained by adding a set of numbers which together contain all and only the digits 142857. That means a lot of other "also" additions will work out too! You can even change the order, like 578 + 214 = 792 (a multiple of 9, and hence the digital root will end up being 9). Any order and any choice of how to break the numbers will work, because of the digital root property (and, importantly, the rule that "The digital root of a + b is congruent with the sum of the digital root of a and the digital root of b modulo 9").

baseballmerpeak 11y ago

1/7 = 0.14+0.0028+0.000056+0.00000112+0.0000000224+... 14=2(7) 28=4(7) 56=8(7) 112=16(7) 224=32(7)

tomkwok 11y ago

There is a detailed explanation on Quora [0] that I stumbled upon some time ago. [0]: http://www.quora.com/Why-does-the-number-142857-have-such-interesting-properties http://www.quora.com/Why-does-the-number-142857-have-such-in...

caligastia 11y ago

There is a priceless video at https://www.youtube.com/watch?v=UKPwZqUUrQo https://www.youtube.com/watch?v=UKPwZqUUrQo of the Gurdjieff movements, the dance at 3:24 is an expression of a computational process.