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142857

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Re: 142857

#11

Post by zyrthofar »

rbonvall wrote: post #9
popctrl wrote: post #3

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

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

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.

Re: 142857

#12

Post by mikeash »

dstyrb wrote: post #7
mikeash wrote: post #6

Earlier quoted context omitted.

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.

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 kn…

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.

Re: 142857

#13

Post by [deleted] »

mikeash wrote: post #12
dstyrb wrote: post #7

Earlier quoted context omitted.

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 kn…

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 articl…

[deleted]

Re: 142857

#14

Post by [deleted] »

mikeash wrote: post #12
dstyrb wrote: post #7

Earlier quoted context omitted.

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 kn…

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 articl…

[deleted]

Re: 142857

#15

Post by schoen »

zyrthofar wrote: post #11
rbonvall wrote: post #9

Earlier quoted context omitted.

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

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…

If you have any multiple of 9 and repeatedly add the digits, you get back to 9:

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").

Re: 142857

#16

Post by schoen »

schoen wrote: post #15
zyrthofar wrote: post #11

Earlier quoted context omitted.

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…

If you have any multiple of 9 and repeatedly add the digits, you get back to 9: 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…

Try this fun Python program to see how multiples of 9 are always generated no matter how you combine the digits:

  #!/usr/bin/env python
  
  import random
  
  digits = [1, 4, 2, 8, 5, 7]
  
  for times in range(20):
      digits_left = digits[:]
      nums = []
      while digits_left:
         this_num = 0
         for i in range(random.randint(1, len(digits_left))):
             digit = random.choice(digits_left)
             this_num *= 10
             this_num += digit
             digits_left.remove(digit)
         nums.append(this_num)
      print " + ".join(map(str, nums)), "=", sum(nums), "(a multiple of 9)"
Sample output:

  4271 + 58 = 4329 (a multiple of 9)
  7412 + 58 = 7470 (a multiple of 9)
  8 + 124 + 5 + 7 = 144 (a multiple of 9)
  845127 = 845127 (a multiple of 9)
  147285 = 147285 (a multiple of 9)
  1 + 824 + 75 = 900 (a multiple of 9)
  5 + 2 + 481 + 7 = 495 (a multiple of 9)
  758 + 41 + 2 = 801 (a multiple of 9)
  47125 + 8 = 47133 (a multiple of 9)
  7584 + 12 = 7596 (a multiple of 9)
  1275 + 8 + 4 = 1287 (a multiple of 9)
  475 + 12 + 8 = 495 (a multiple of 9)
  12 + 5 + 478 = 495 (a multiple of 9)
  4251 + 7 + 8 = 4266 (a multiple of 9)
  185 + 274 = 459 (a multiple of 9)
  28514 + 7 = 28521 (a multiple of 9)
  41278 + 5 = 41283 (a multiple of 9)
  457182 = 457182 (a multiple of 9)
  845712 = 845712 (a multiple of 9)
  2718 + 54 = 2772 (a multiple of 9)

Re: 142857

#18

Post by acheron »

schoen wrote: post #15
zyrthofar wrote: post #11

Earlier quoted context omitted.

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…

If you have any multiple of 9 and repeatedly add the digits, you get back to 9: 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…

I figured we all learned this from Square One: https://www.youtube.com/watch?v=Q53GmMCqmAM

Re: 142857

#19

Post by blaincate »

zyrthofar wrote: post #11
rbonvall wrote: post #9

Earlier quoted context omitted.

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

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…

you forgot

14285 + 7 = 14292; 1+4+2+9+2 = 18; 1+8 = 9

Re: 142857

#20

Post by tomvbussel »

dstyrb wrote: post #2

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?

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.
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