Number symmetry
Guillermo el Gato
The boy was learning his multiplication tables and when he wrote down
the 9s, it looked like this.
9, 18, 27, 36, 45, 54, 63, 72, 81, 90.
He said, "That's funny, if you start in the middle the numbers mirror
each other: {45,54} {36,63} and so on."
I thought "That's a ma boy!" Then I thought I wonder if there's a name
for that. I don't really have the mathematical vocabulary to begin a
proper google search, so I thought I'd throw it out to the group that
knows everything: y'all.
Hugs,
Guillermo el Gato
Peter Boulding
wrote in <ikr2n2$qoo$1...@online.de>:
>Long time no see.
Indeed. Welcome back.
--
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Guillermo el Gato
> On Fri, 04 Mar 2011 17:06:57 +0100, Guillermo el Gato<dev...@example.com>
> wrote in<ikr2n2$qoo$1...@online.de>:
>
>> Long time no see.
>
> Indeed. Welcome back.
>
>
FWIW, I'm deeply, deeply diappointed in Obama.
Peter Boulding
wrote in <ikr4r1$sm2$1...@online.de>:
>FWIW, I'm deeply, deeply diappointed in Obama.
Mm--likewise. I happen to have just been reading about the latest charges
thrown at Bradley Manning, and it occurs to me that (a) his case really does
closely mirror that of Daniel Ellsberg (the guy who leaked the Pentagon
Papers) and that (b) Manning is in greater danger from Obama than Ellsberg
was from Nixon.
I'm reminded of the story of a UK Conservative Party candidate who, on being
introduced to Margaret Thatcher, asked what she considered to be her
greatest achievement. "Tony Blair", she replied.
Seems to me that Barak Obama is Dick Cheney's greatest achievement.
Greg Goss
"Casting out nines". If something is divisible by nine, then the
digits themselves add up to nine. This was a quick-check for adding
columns of numbers before calculators. The remainder modulo nine of
the sum-of-digits in a long series is the same as the remainder m9 of
the answer.
http://en.wikipedia.org/wiki/Casting_out_nines
In the example at hand, for a two-digit number adding to nine, once
one digit is chosen, the other digit is forced.
--
Tomorrow is today already.
Greg Goss, 1989-01-27
Hactar
I think that happens because 9=10-1. Then for certain multiples of 9,
you get:
N*9=N*(10-1)
=N*10 - N*1
=N*(9+1) + N*(-1)
Note that 9+1 + -1 = 9. This only works for N<10.
You see a similarly odd thing with multiples of 11: 11, 22, ... 99 but
that would take more thought to explain than C allows me right now.
--
-eben QebWe...@vTerYizUonI.nOetP royalty.mine.nu:81
A neutrino enters a bar. The bartender asks "Can I get you anything?"
The neutrino replies "Nope, just passing through." -- rdu_voyager on Fark
Guillermo el Gato
I think that describes this example very well.
Is there some sort of more general property that describes nunbers that
are related in this way? Generally speaking, like where there exists a
kernel function K(x)=y, where the digits of y are the reverse order of
the digits of x.
For example, (I'm just pulling digits out of the air): {123,321}
{128,821}. It seems like there would be some kind of name for this.
Where's Ramanujan when you need him?
Mac
<pjbn...@UNSPAMpboulding.co.uk> wrote:
>On Fri, 04 Mar 2011 17:43:07 +0100, Guillermo el Gato <dev...@example.com>
>wrote in <ikr4r1$sm2$1...@online.de>:
>
>>FWIW, I'm deeply, deeply diappointed in Obama.
>
>Mm--likewise. I happen to have just been reading about the latest charges
>thrown at Bradley Manning, and it occurs to me that (a) his case really does
>closely mirror that of Daniel Ellsberg (the guy who leaked the Pentagon
>Papers) and that (b) Manning is in greater danger from Obama than Ellsberg
>was from Nixon.
>
>I'm reminded of the story of a UK Conservative Party candidate who, on being
>introduced to Margaret Thatcher, asked what she considered to be her
>greatest achievement. "Tony Blair", she replied.
>
>Seems to me that Barak Obama is Dick Cheney's greatest achievement.
I suspect a far bigger part is the fact the natural champions of
(overly?) free information were outside of the tent for Nixon, but
inside for Obabma. If Johnson had been Ellsberg's nemesis, he would
have seen jail; if it had been Kennedy, it might have even been worse
still. People are less happy with their own secrets being leaked.
There's also that Bush, like Nixon, had less risk of being seen as
soft on national security.
Bob
http://en.wikipedia.org/wiki/Method_of_complements , which is
especially handy for cashiers making change from bills that are powers
of 10.
Opus the Penguin
> Is there some sort of more general property that describes nunbers
> that are related in this way? Generally speaking, like where there
> exists a kernel function K(x)=y, where the digits of y are the
> reverse order of the digits of x.
>
> For example, (I'm just pulling digits out of the air): {123,321}
> {128,821}. It seems like there would be some kind of name for
> this. Where's Ramanujan when you need him?
I'm not sure about any of that. But it reminds me of what happens
when you square any number up to 9 digits where each digit is 1. The
resulting number's digits count up to the number of digits in the
original number then count back down again. E.g.
11*11 = 121 (i.e. 11 has 2 digits, so count up to 2 then back down)
111*111 = 12321
1111*1111 = 1234321
...
111111111*111111111 = 12345678987654321
--
Opus the Penguin
The best darn penguin in all of Usenet
Snidely
> In article <ikr2n2$qoo$1...@online.de>,
> Guillermo el Gato <dev...@example.com> wrote:
>> Long time no see.
>>
>> The boy was learning his multiplication tables and when he wrote down
>> the 9s, it looked like this.
>>
>> 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.
>>
>> He said, "That's funny, if you start in the middle the numbers mirror
>> each other: {45,54} {36,63} and so on."
>>
>> I thought "That's a ma boy!" Then I thought I wonder if there's a name
>> for that. I don't really have the mathematical vocabulary to begin a
>> proper google search, so I thought I'd throw it out to the group that
>> knows everything: y'all.
>
> I think that happens because 9=10-1. Then for certain multiples of 9,
> you get:
>
> N*9=N*(10-1)
> =N*10 - N*1
> =N*(9+1) + N*(-1)
>
> Note that 9+1 + -1 = 9. This only works for N<10.
>
> You see a similarly odd thing with multiples of 11: 11, 22, ... 99 but
> that would take more thought to explain than C allows me right now.
Try it with the first 5 multiples of 04, written in base 5.
/dps
Alan J
news:8tck9v...@mid.individual.net...
In hexadecimal, multiples of 15 do the same thing:
0f 1e 2d 3c 4b 5a 69 78, 87 96 a5 b4 c3 d2 e1 f0
--
Alan
Hactar
4, 13, 22, 31, yep. Same deal. So that explanation can be
generalized. I love it when that happens.
--
-eben QebWe...@vTerYizUonI.nOetP royalty.mine.nu:81
> A: It's annoying as hell
> Q: Why do most people hate top-posting? -- Lots42 The Library Avenger
http://www.fscked.co.uk/writing/top-posting-cuss.html
Geronimo Granjero
wrote:
> In hexadecimal, multiples of 15 do the same thing:
> 0f 1e 2d 3c 4b 5a 69 78, 87 96 a5 b4 c3 d2 e1 f0
Multiples of 0f, Shirley?
Hactar
It seems that in any positive integer base, the sum of the digits of
N*(10-1) (0<N<10) is 10-1. Correct?
--
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Paul Ciszek
In base N, the digits of the non-zero integer multiples of (N-1) have
to add up to a multiple of (N-1), whose digits have to add up to...
until you arrive at (N-1). This is a subset of a more general phenomenon
called casting out (N-1)'s, or obtaining a digital root. The URL is truly
atrocious, but google martin gardner digital root and click on the first hit.
So, what the kid noticed was the result of two facts:
1) The digits of the multiples of 9 have to add up to 9
2) The first digit is going to work its way up as you increase the multiplier.
Therefore, the second digit has to work its way down, and you end up with
the pattern shown.
--
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plausible prose man
Hey, man...what's up?
Alan J
news:1qf848-...@pc.home...
> In article <almarsoft.3409...@nntp.earthlink.net>,
> Geronimo Granjero <use...@bauerstar.com> wrote:
>> On Fri, 4 Mar 2011 21:00:52 -0000, "Alan J" <not...@dontuse.invalid>
>> wrote:
>> > In hexadecimal, multiples of 15 do the same thing:
>>
>> > 0f 1e 2d 3c 4b 5a 69 78, 87 96 a5 b4 c3 d2 e1 f0
>>
>> Multiples of 0f, Shirley?
Yes.
> It seems that in any positive integer base, the sum of the digits of
> N*(10-1) (0<N<10) is 10-1. Correct?
Probably. It's true for binary, and it works for 7 in octal:
7 16 25 34, 43 52 61 70
--
Alan
Guillermo el Gato
> Hey, man...what's up?
A little bit of this, a little bit of that. Sometimes it's tacos,
sometimes it's not.
Things kinda got busy, so I decided to lay low for a while. That while
lasted a lot longer than I thought it would. Things are still busy, but,
y'know, fuck it. There's always some time for the AFCAns.
It's great to see so many familiar names around here! And then there's
Binny, Bonde, Freiler and Wilson. Oh, well. I guess you have to take the
bad with the good.
Guillermo el Gato
> In base N, the digits of the non-zero integer multiples of (N-1) have
> to add up to a multiple of (N-1), whose digits have to add up to...
> until you arrive at (N-1). This is a subset of a more general phenomenon
> called casting out (N-1)'s, or obtaining a digital root. The URL is truly
> atrocious, but google martin gardner digital root and click on the first hit.
>
> So, what the kid noticed was the result of two facts:
> 1) The digits of the multiples of 9 have to add up to 9
> 2) The first digit is going to work its way up as you increase the multiplier.
> Therefore, the second digit has to work its way down, and you end up with
> the pattern shown.
>
That is the information I was looking for. Thanks Paul and Greg!
Greg Goss
Freiler only seems to drop by six or seven times a year. I don't know
if he still does the "open invitation barbecue" every May (It was May,
wasn't it?) (most of the time his mood was better than the
Binny/Wilson pair. It's no crime to disagree with me.)
Joseph Nebus
>"Casting out nines". If something is divisible by nine, then the
>digits themselves add up to nine. This was a quick-check for adding
>columns of numbers before calculators. The remainder modulo nine of
>the sum-of-digits in a long series is the same as the remainder m9 of
>the answer.
>http://en.wikipedia.org/wiki/Casting_out_nines
I did once work out the casting-by-nines type procedure for
telling whether a number was divisible by 17 just by adding its digits
the right way, for fun. The sense of fun this engendered was not shared
by anyone I ever met before or since, ever. Too bad.
--
Joseph Nebus
------------------------------------------------------------------------------
Heather
<pjbn...@UNSPAMpboulding.co.uk> wrote:
>On Fri, 04 Mar 2011 17:06:57 +0100, Guillermo el Gato <dev...@example.com>
>wrote in <ikr2n2$qoo$1...@online.de>:
>
>>Long time no see.
>
>Indeed. Welcome back.
Leroy
--
Heather
Heather
Up to 10 times 9 the digits of the total add up to 1 times 9. After
that the digits of the total add up to other multiples of 9, just as
when you multiply by 3 the digits of the total add up to multiples of
3.
--
Heather
Bill Turlock
Wasn't that a Stephen King novel?
Guillermo el Gato
<blushes> Thanks!
Paul Madarasz
>Long time no see.
You're late for dinner, young man.
Paul Ciszek
In article <ikv398$i1b$1...@reader1.panix.com>,
Joseph Nebus <nebusj-@-rpi-.edu> wrote:
>In <8tck9v...@mid.individual.net> Greg Goss <go...@gossg.org> writes:
>
>>"Casting out nines". If something is divisible by nine, then the
>>digits themselves add up to nine. This was a quick-check for adding
>>columns of numbers before calculators. The remainder modulo nine of
>>the sum-of-digits in a long series is the same as the remainder m9 of
>>the answer.
>
>>http://en.wikipedia.org/wiki/Casting_out_nines
>
> I did once work out the casting-by-nines type procedure for
>telling whether a number was divisible by 17 just by adding its digits
>the right way, for fun. The sense of fun this engendered was not shared
>by anyone I ever met before or since, ever. Too bad.
To do that you would have to first convert the number to base 18 first.
Why not instead convert it to base 17 and then look at the last digit?
Mac
Brother!
Joking aside, are you the former Straight Dopelian, or am I confusing
you with someone else?
Peter Boulding
<7q82n6pl4amifts93...@4ax.com>:
>>>FWIW, I'm deeply, deeply diappointed in Obama.
>>
>>Mm--likewise. I happen to have just been reading about the latest charges
>>thrown at Bradley Manning, and it occurs to me that (a) his case really does
>>closely mirror that of Daniel Ellsberg (the guy who leaked the Pentagon
>>Papers) and that (b) Manning is in greater danger from Obama than Ellsberg
>>was from Nixon.
>>
>>I'm reminded of the story of a UK Conservative Party candidate who, on being
>>introduced to Margaret Thatcher, asked what she considered to be her
>>greatest achievement. "Tony Blair", she replied.
>>
>>Seems to me that Barak Obama is Dick Cheney's greatest achievement.
>
>I suspect a far bigger part is the fact the natural champions of
>(overly?) free information were outside of the tent for Nixon, but
>inside for Obabma. If Johnson had been Ellsberg's nemesis, he would
>have seen jail; if it had been Kennedy, it might have even been worse
>still. People are less happy with their own secrets being leaked.
>There's also that Bush, like Nixon, had less risk of being seen as
>soft on national security.
Obama: "I have actually asked the Pentagon whether or not the procedures
that have been taken in terms of his confinement are appropriate and are
meeting our basic standards. They assure me that they are."
Ellsberg: "I can just hear President Nixon saying to a press conference the
same thing: 'I was assured by the White House Plumbers that their burglary
of the office of Daniel Ellsberg's doctor in Los Angeles was appropriate and
met basic standards.'
"If President Obama really doesn't yet know the actual conditions of
Manning's detention, if he really believes, as he's said, that 'some of this
[nudity, isolation, harassment, sleep-deprivation] has to do with Private
Manning's wellbeing', despite the contrary judgments of the prison
psychologist – then he's being lied to, and he needs to get a grip on his
administration...
... "It's what the CIA calls 'no-touch torture' and its purpose...is very
clear: to demoralise someone to the point of offering a desired confession.
That's what they are after, I suspect, with Manning. They don't care if the
confession is true or false, so long as it implicates WikiLeaks in a way
that will help them prosecute Julian Assange."
--
Regards, Peter Boulding
pjbn...@UNSPAMpboulding.co.uk (to e-mail, remove "UNSPAM")
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