1000: "1000 Comics"

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early
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Re: 1000: "1000 Comics"

Postby early » Sun Jan 08, 2012 3:21 am UTC

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public function getRandomComment() {
   return 'Congrat\' from France for this 3E8 th comic !'; // Yeah, I had luck getting my comment on a fair dice roll ;)
} 

Wish you all the best for this new year.

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neoliminal
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Re: 1000: "1000 Comics"

Postby neoliminal » Sun Jan 08, 2012 4:30 am UTC

I wonder if he could have done this if he was drawing in a more traditional comic style rather than in stick figures.
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Mint
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Re: 1000: "1000 Comics"

Postby Mint » Sun Jan 08, 2012 2:26 pm UTC

Made an account just to say congrats and thanks for brightening my day three days a week. I look forward to every comic.

CuBr
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Re: 1000: "1000 Comics"

Postby CuBr » Sun Jan 08, 2012 2:57 pm UTC

GenericAnimeBoy wrote:What, no red spiders?

5:00 in first zero. Also something similar at 5:00 in second zero, but I think that's a biologist and squid.

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SirMustapha
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Re: 1000: "1000 Comics"

Postby SirMustapha » Sun Jan 08, 2012 6:20 pm UTC

neoliminal wrote:I wonder if he could have done this if he was drawing in a more traditional comic style rather than in stick figures.


Of course! It would probably just take a lot more effort and time to do that, maybe a full week to... oh, wait... No, Randall definitely couldn't do that.

Jeff_UK
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Re: 1000: "1000 Comics"

Postby Jeff_UK » Sun Jan 08, 2012 8:44 pm UTC

Is that
Spoiler:
Wizard Whitebeard, at the bottom of the last 0?
"Please only print this post if you really need to"
...hmm....I wonder how much extra energy is required to generate that request...We need a cost/benefit analysis, STAT!

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Djehutynakht
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Re: 1000: "1000 Comics"

Postby Djehutynakht » Sun Jan 08, 2012 9:56 pm UTC

I like it. Ah the memories...

koopa00
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Re: 1000: "1000 Comics"

Postby koopa00 » Mon Jan 09, 2012 4:03 am UTC

Plz, make it a gigantic poster. Love it.

n17182559
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Re: 1000: "1000 Comics"

Postby n17182559 » Mon Jan 09, 2012 4:13 am UTC

In the middle you can connect the binary dots and see a heart! What do I win?
Thank you for your comics!

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VectorZero
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Re: 1000: "1000 Comics"

Postby VectorZero » Mon Jan 09, 2012 6:30 am UTC

shpoffo wrote:ohh Randal.........

..It'll be a big square-number milestone.......

I see what you did there...
Van wrote:Fireballs don't lie.

Keybounce
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Re: 1000: "1000 Comics"

Postby Keybounce » Mon Jan 09, 2012 7:41 am UTC

A square number?

31 * 31 = 961
32 * 32 = 1024

Right.
EDIT: Are there any numbers between 1001 and 1024 that have rational square roots?
<this space on hold>

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Splarka
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Re: 1000: "1000 Comics"

Postby Splarka » Mon Jan 09, 2012 9:33 am UTC

Keybounce wrote: Are there any numbers between 1001 and 1024 that have rational square roots?


1004.89?
HTTP/1.1 - 203

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keithl
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Re: 1000: "1000 Comics"

Postby keithl » Mon Jan 09, 2012 2:32 pm UTC

The uniformity of the placement of the characters, and the uniform line widths, is remarkable. Far too uniform for this to be a pure "imagine and start drawing" comic. I hypothesize that Randall developed some analysis methods and perhaps wrote some code to help him prepare "Radiation" and "Money", and perhaps size and shade the continents in the two "Online Communities" cartoons. He may have re-purposed some of that code for "1000 Comics". Hopefully when he sells the zillion-pixel poster of this, somebody (with way too much time) can reverse engineer it.

chuckie987
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Re: 1000: "1000 Comics"

Postby chuckie987 » Mon Jan 09, 2012 4:02 pm UTC

Iv been tryin to figure out if the binary numbers make a special number like 1000 but its quite hard to find out what order they go in anybody know??

Spoiler:
I do know that if you join the dots it makes a love heart

mpanichello
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Re: 1000: "1000 Comics"

Postby mpanichello » Mon Jan 09, 2012 6:06 pm UTC

I introduced xkcd to my girlfriend, who is a giant math geek, a few years back. She bought me a copy of the xkcd book as a gift with notes commented in...most adorable gift ever. Anyway, I showed her this comic and she got teary-eyed and thought this was cute and special. Congratulations on making so many people smile and bringing them happiness with math. One of our favorite websites!

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jjane
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Re: 1000: "1000 Comics"

Postby jjane » Mon Jan 09, 2012 6:14 pm UTC

JamusPsi wrote:Honestly?

Xkcd makes ME feel less alone.
http://xkcd.com/245/

It's good to know there's at least one other person like me.



http://xkcd.com/85/

Me too.

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SirMustapha
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Re: 1000: "1000 Comics"

Postby SirMustapha » Mon Jan 09, 2012 8:00 pm UTC

keithl wrote:The uniformity of the placement of the characters, and the uniform line widths, is remarkable. Far too uniform for this to be a pure "imagine and start drawing" comic. I hypothesize that Randall developed some analysis methods and perhaps wrote some code to help him prepare "Radiation" and "Money", and perhaps size and shade the continents in the two "Online Communities" cartoons. He may have re-purposed some of that code for "1000 Comics".


Or... maybe he just made a big, soft "1000" outline on paper, manually drew the stick figures inside it, and erased the outline afterwards? Like most normal human being would do?

He could also have simply made the 1000 outline on the computer and drag-and-dropped the stick figures into it, like the other normal human beings would do.

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PolakoVoador
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Re: 1000: "1000 Comics"

Postby PolakoVoador » Mon Jan 09, 2012 8:28 pm UTC

SirMustapha wrote:
keithl wrote:The uniformity of the placement of the characters, and the uniform line widths, is remarkable. Far too uniform for this to be a pure "imagine and start drawing" comic. I hypothesize that Randall developed some analysis methods and perhaps wrote some code to help him prepare "Radiation" and "Money", and perhaps size and shade the continents in the two "Online Communities" cartoons. He may have re-purposed some of that code for "1000 Comics".


Or... maybe he just made a big, soft "1000" outline on paper, manually drew the stick figures inside it, and erased the outline afterwards? Like most normal human being would do?

He could also have simply made the 1000 outline on the computer and drag-and-dropped the stick figures into it, like the other normal human beings would do.


Ok, and since when is Randall a normal human being?

Keybounce
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Re: 1000: "1000 Comics"

Postby Keybounce » Mon Jan 09, 2012 8:47 pm UTC

Splarka wrote:
Keybounce wrote: Are there any numbers between 1001 and 1024 that have rational square roots?


1004.89?


Ok, any integers?
<this space on hold>

Keybounce
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Re: 1000: "1000 Comics"

Postby Keybounce » Mon Jan 09, 2012 9:00 pm UTC

PolakoVoador wrote:Ok, and since when is Randall a normal human being?


Since he became orthogonal?
<this space on hold>

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markfiend
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Re: 1000: "1000 Comics"

Postby markfiend » Tue Jan 10, 2012 4:36 pm UTC

Keybounce wrote:
Splarka wrote:
Keybounce wrote: Are there any numbers between 1001 and 1024 that have rational square roots?


1004.89?


Ok, any integers?

You answered your own question.
Keybounce wrote:31 * 31 = 961
32 * 32 = 1024
Pick an integer between 31 and 32 :wink:
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Pfhorrest
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Re: 1000: "1000 Comics"

Postby Pfhorrest » Wed Jan 11, 2012 6:40 am UTC

markfiend wrote:
Keybounce wrote:
Splarka wrote:
Keybounce wrote: Are there any numbers between 1001 and 1024 that have rational square roots?


1004.89?


Ok, any integers?

You answered your own question.
Keybounce wrote:31 * 31 = 961
32 * 32 = 1024
Pick an integer between 31 and 32 :wink:

Wrong question.

All questions involve whether there are any x and y in certain sets satisfying both x^2 = y and 1001 < y < 1024.

He already answered that there is no pair of integers x and y satisfying those conditions.

Then he asked if (under those conditions) there is any (unrestricted) y such that x is rational, and was given an affirmative example: 1004.89 (for which x is 31.7, a rational number).

Now he is asking if (under those conditions) there is any integer y such that x is rational. 1004.89 doesn't work a y here because it is not an integer, and there are no integers to work as x whose squares fall between 1001 and 1024, but there might (as far as has been stated so far) be a rational number with an integer square between 1001 and 1024.

Except there's not, because there are no proper (i.e. non-integer) rational numbers with integer squares at all. Proof:

Any proper rational number r is equivalent to the sum of an integer, m, and a proper fraction, n (the remainder). For example, 33/2 is equal to 16 + 1/2.

r^2 is thus equal to (m+n)^2 which is equal to (m+n)(m+n) which is equal to m^2 + 2mn + n^2.

n^2 will never be an integer, as any proper fraction squared is still a proper fraction. For example, 1/3 squared is 1/9; 5/7 squared is 25/49, etc. So the sum of the three terms will always include a proper fraction and thus never be an integer.
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markfiend
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Re: 1000: "1000 Comics"

Postby markfiend » Wed Jan 11, 2012 12:17 pm UTC

d'oh!

You are, of course, correct. :oops: :oops: :oops: :oops: :oops:
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deadmazter
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Re: 1000: "1000 Comics"

Postby deadmazter » Wed Jan 11, 2012 1:42 pm UTC

Added IMG tags for you ~~Felstaff

(spoilered for size)
Spoiler:
Image
Image

Pfhorrest wrote:
markfiend wrote:
Keybounce wrote:
Splarka wrote:
Keybounce wrote: Are there any numbers between 1001 and 1024 that have rational square roots?


1004.89?


Ok, any integers?

You answered your own question.
Keybounce wrote:31 * 31 = 961
32 * 32 = 1024
Pick an integer between 31 and 32 :wink:

Wrong question.

All questions involve whether there are any x and y in certain sets satisfying both x^2 = y and 1001 < y < 1024.

He already answered that there is no pair of integers x and y satisfying those conditions.

Then he asked if (under those conditions) there is any (unrestricted) y such that x is rational, and was given an affirmative example: 1004.89 (for which x is 31.7, a rational number).

Now he is asking if (under those conditions) there is any integer y such that x is rational. 1004.89 doesn't work a y here because it is not an integer, and there are no integers to work as x whose squares fall between 1001 and 1024, but there might (as far as has been stated so far) be a rational number with an integer square between 1001 and 1024.

Except there's not, because there are no proper (i.e. non-integer) rational numbers with integer squares at all. Proof:

Any proper rational number r is equivalent to the sum of an integer, m, and a proper fraction, n (the remainder). For example, 33/2 is equal to 16 + 1/2.

r^2 is thus equal to (m+n)^2 which is equal to (m+n)(m+n) which is equal to m^2 + 2mn + n^2.

n^2 will never be an integer, as any proper fraction squared is still a proper fraction. For example, 1/3 squared is 1/9; 5/7 squared is 25/49, etc. So the sum of the three terms will always include a proper fraction and thus never be an integer.


But can't 2mn + n^2 = an integer?
an integer y
y = 2mn +n^2
y -2mn = n^2
n^2 + 2mn - y = 0

but let's rewrite the fractional part n as 1/n,

y - 2m/n = 1/n^2
ny - 2m = 1/n
yn^2 -2mn - 1 = 0

so n = (2m + (4m^2 + 4y)^.5)/(2y)
where n, m and y are integer numbers. (since the fraction is now written as 1/n) Can this be satisfied?

so (4m^2 + 4y)^.5 has to be an integer, and so does m/y
2(m^2+y)^.5 has to be an integer, as does m/y

-> (2(m^2+y)^.5)/(2y) = an integer, and so does m/y , thus m = py, where P = an integer
((m^2 +y)^.5)/y = an integer, thus m^2 + y > y^2 ,

(ny)^2 = m^2 + y

(ny)^2 = y^2 + C since m^2 + y > y^2, where C is a positive integer

n^2(y^2) = y^2 + C

((n^2)-1)(y^2) = C
y^2 = C/(n^2 - 1), thus C must be greater than n^2 - 1, and it must be a multiple, thus C = K(n^2 - 1), where K is a positive integer number

y^2 = K where m/y = a positive integer, R.
y^2 = K m/y = R -> m = yR

2yn = (2m + (4m^2 + 4y)^.5)
2yn = 2yR + (4(yR) ^2 + 4y)^.5

(yn - yR)^2 = yR + Y
y(n-R)^2 = R + 1
y(n^2 - 2nR + R^2) = R + 1, since n and R are positive integers, then n^2 - 2nR + R^2 = an integer, thus (R + 1)/y = an integer, L. R + 1 = Ly
y(n^2 - 2nR + R^2) = Ly
(n-R)^2 = L


ny = m + (m^2 + Pm)^.5
ny = m + m^.5 + (m + P)^.5
thus we have a new constraint that m^.5 + (m+P)^.5 = an integer, O.

so (n-R)^2 = L , m = yR, y^2 = K, C = K(n^2 -1), m^2 + y = y^2 + C, m = Py, m^.5 + (m+P)^.5 = O, where everything here is a positive integer. satisfying: ny = (m + (m^2 + y)^.5), where n != 1
Too lazy to do more Algebra. Lacking the mathematical knowledge/tools to properly prove this. :[

Keybounce
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Re: 1000: "1000 Comics"

Postby Keybounce » Wed Jan 11, 2012 10:26 pm UTC

(I love the thread derails on this board :-).
<this space on hold>

sss7527
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Re: 1000: "1000 Comics"

Postby sss7527 » Thu Feb 02, 2012 3:50 am UTC

I'm glad I'm not the only one who noticed the 404 thing. At the same time, I thought I would be observant and viewed as insightful, so a little part of me just died. Can you guys just pretend I was the first to come up with it?

Hey, guys, what about 404?!

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phlip
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Re: 1000: "1000 Comics"

Postby phlip » Thu Feb 02, 2012 4:05 am UTC

deadmazter wrote:But can't 2mn + n^2 = an integer?

It may be possible... his proof certainly didn't show that it wouldn't be. However, your own continuation of the proof assumes that you can do:
but let's rewrite the fractional part n as 1/n,
and end up with an integer 'n' (which isn't necessarily the case - you only know that the fractional part is a rational number, not that it's specifically 1 on an integer).

A better proof of the original proposition is: take any non-integer rational number, p/q. Now, there must be a prime factor of q which is not a factor of p (q would otherwise be a factor of p, and the number would be an integer). Call this factor k. Now, consider (p/q)2 = p2/q2... now k is still a factor of q2, and is still not a factor of p2. Therefore p2/q2 is also not an integer.

Or, in the contrapositive - the square-root of an integer is either an integer or is irrational.

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enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
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say1988
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Re: 1000: "1000 Comics"

Postby say1988 » Mon Mar 12, 2012 3:11 pm UTC

Just wanted to come in and say how awsome this comic was. Not to mention all the others before it.


AvatarIII wrote:
thesingingaccountant wrote:
alun009 wrote:There is a comic 404! It might be the best one of the lot :)


HULK SUCH a dork... Somehow, it never occurred to me that there was a gaping hole between #403 and #405 (I've only been reading for about a year and a half, though I've read every single one). I "found" #404 today... The result generated a sigh-facepalm-headshake combo. I feel like a lonely, angsty fish in a barrel who just got shot.


[*url=http://comicjk.com/comic.php/404]http://www.xkcd.com/404/[/url]


Thank you for that link. It is perfect.

Also thanks for the guy who pointed out barrel boy. Just so many I kept overlooking that one.


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