explain xkcd - User contributions [en]

410: Math Paper

2013-03-12T02:54:19Z

174.51.77.200: /* Transcript */

{{comic
| number = 410
| date =
| title = Math paper
| image = math_paper.png
| titletext = That's nothing. I once lost my genetics, rocketry, and stripping licenses in a single incident.
}}

==Explanation==
:It's all basically just a set up to use the joke about Imaginary Friends by taking "friendly numbers" into the complex (imaginary) plane.

:Imaginary numbers on the complex plan are of the form '''a''' + '''b'''''i'' where '''a''' and '''b''' are constants and ''i'' is the square root of negative 1 (an impossibility in the plane of "regular" numbers).

:Joel Bradbury has a wonderful explanation of Friendly Number on his site http://joelbradbury.net/notes/friendly_numbers. The following explanation of Friendly Numbers is taken from his site:

:What are Friendly Numbers?
:We need first to get define a divisor function over the integers, written σ(n) if you’re so inclined. To get it first we get all the integers that divide into n. So for 3, it’s 1 and 3. For 4, it’s 1, 2, and 4, and for 5 it’s only 1 and 5.

:Now sum them to get σ(n). So σ(3) = 1 + 3 = 4, or σ(4) = 1 + 2 + 4 = 6, and so on.

:For each of these n, there is something called a characteristic ratio. Now that’s just the divisors function over the integer itself ( σ(n)/n . So the characteristic ratio where n = 6 is σ(6)/6 = 12/6 =2.

:Once you have the characteristic ratio for any integer n, any other integers that share the same chacteristic are called friendly with each other. So to put it simply a friendly number is any integer that shares its characteristic ratio with at least one other integer. The converse of that is called a solitary number, where it doesn’t share it’s characteristic with anyone else.

:1,2,3,4 and 5 are solitary. 6 is friendly with 28. ( σ(6)/6 = (1+2+3+6)/6 = 12/6 = 2 = 56/28 = (1+2+4+7+14+28)/28 = σ(28)/28.

==Transcript==
:Lecturer: In my paper, I use an extension of the divisor function over the Gaussian integers to generalize the so-called "friendly numbers" into the complex plane. [Points to equations on the board]
:Guy in room: Hold on. Is this paper simply a build-up to an "imaginary friends" pun?
:[Lecturer stands speechless]
:Lecturer: It MIGHT not be.
:Guy in room: I'm sorry, we're revoking your math license.

{{comic discussion}}

410: Math Paper

2013-03-12T02:53:50Z

174.51.77.200: /* Explanation */

{{comic
| number = 410
| date =
| title = Math paper
| image = math_paper.png
| titletext = That's nothing. I once lost my genetics, rocketry, and stripping licenses in a single incident.
}}

==Explanation==
:It's all basically just a set up to use the joke about Imaginary Friends by taking "friendly numbers" into the complex (imaginary) plane.

:Imaginary numbers on the complex plan are of the form '''a''' + '''b'''''i'' where '''a''' and '''b''' are constants and ''i'' is the square root of negative 1 (an impossibility in the plane of "regular" numbers).

:Joel Bradbury has a wonderful explanation of Friendly Number on his site http://joelbradbury.net/notes/friendly_numbers. The following explanation of Friendly Numbers is taken from his site:

:What are Friendly Numbers?
:We need first to get define a divisor function over the integers, written σ(n) if you’re so inclined. To get it first we get all the integers that divide into n. So for 3, it’s 1 and 3. For 4, it’s 1, 2, and 4, and for 5 it’s only 1 and 5.

:Now sum them to get σ(n). So σ(3) = 1 + 3 = 4, or σ(4) = 1 + 2 + 4 = 6, and so on.

:For each of these n, there is something called a characteristic ratio. Now that’s just the divisors function over the integer itself ( σ(n)/n . So the characteristic ratio where n = 6 is σ(6)/6 = 12/6 =2.

:Once you have the characteristic ratio for any integer n, any other integers that share the same chacteristic are called friendly with each other. So to put it simply a friendly number is any integer that shares its characteristic ratio with at least one other integer. The converse of that is called a solitary number, where it doesn’t share it’s characteristic with anyone else.

:1,2,3,4 and 5 are solitary. 6 is friendly with 28. ( σ(6)/6 = (1+2+3+6)/6 = 12/6 = 2 = 56/28 = (1+2+4+7+14+28)/28 = σ(28)/28.

==Transcript==
:Lecturer: In my paper, I use an extension of the divisor function over the Gaussian integers to generalize the so-called "friendly numbers" into the complex plane. [Points to equations on the board]
:Guy in room: Hold on. Is this paper simply a build-up to an "imaginary friends" pun?
[Lecturer stands speechless]
:Lecturer: It MIGHT not be.
:Guy in room: I'm sorry, we're revoking your math license.

{{comic discussion}}

410: Math Paper

2013-03-12T02:52:09Z

174.51.77.200: Created page with "{{comic | number = 410 | date = | title = Math paper | image = math_paper.png | titletext = That's nothing. I once lost my genetics, rocketry, and stripping l..."

{{comic
| number = 410
| date =
| title = Math paper
| image = math_paper.png
| titletext = That's nothing. I once lost my genetics, rocketry, and stripping licenses in a single incident.
}}

==Explanation==
:It's all basically just a set up to use the joke about Imaginary Friends by taking "friendly numbers" into the complex (imaginary) plane.

:Imaginary numbers on the complex plan are of the form '''a''' + '''b'''''i'' where '''a''' and '''b''' are constants and ''i'' is the square root of negative 1 (an impossibility in the plane of "regular" numbers).

:Joel Bradbury has a wonderful explanation on his site http://joelbradbury.net/notes/friendly_numbers - the following explanation of Friendly Numbers is taken from his site.

:What are Friendly Numbers?
:We need first to get define a divisor function over the integers, written σ(n) if you’re so inclined. To get it first we get all the integers that divide into n. So for 3, it’s 1 and 3. For 4, it’s 1, 2, and 4, and for 5 it’s only 1 and 5.

:Now sum them to get σ(n). So σ(3) = 1 + 3 = 4, or σ(4) = 1 + 2 + 4 = 6, and so on.

:For each of these n, there is something called a characteristic ratio. Now that’s just the divisors function over the integer itself ( σ(n)/n . So the characteristic ratio where n = 6 is σ(6)/6 = 12/6 =2.

:Once you have the characteristic ratio for any integer n, any other integers that share the same chacteristic are called friendly with each other. So to put it simply a friendly number is any integer that shares its characteristic ratio with at least one other integer. The converse of that is called a solitary number, where it doesn’t share it’s characteristic with anyone else.

:1,2,3,4 and 5 are solitary. 6 is friendly with 28. ( σ(6)/6 = (1+2+3+6)/6 = 12/6 = 2 = 56/28 = (1+2+4+7+14+28)/28 = σ(28)/28.

==Transcript==
:Lecturer: In my paper, I use an extension of the divisor function over the Gaussian integers to generalize the so-called "friendly numbers" into the complex plane. [Points to equations on the board]
:Guy in room: Hold on. Is this paper simply a build-up to an "imaginary friends" pun?
[Lecturer stands speechless]
:Lecturer: It MIGHT not be.
:Guy in room: I'm sorry, we're revoking your math license.

{{comic discussion}}

148: Mispronouncing

2013-03-12T00:04:41Z

174.51.77.200:

{{comic
| number = 148
| date = August 25, 2006
| title = Mispronouncing
| image = mispronouncing.png
| titletext = 'My pal Emad does this all the time. 'Hey man, which way to the airpart?'
}}

==Explanation==
{{incomplete}}
One type of joking is to deliberately mispronounce common words. In this strip he makes it his hobby.
*Wobsite = Website
*Blag = Blog
*Airpart = Airport

==Transcript==
:Cueball: Yeah, did you see what he said on his wobsite?
:Man 2: ...his what?
:Cueball: Wobsite.
:Man 2: ... I think you mean "website."
:Cueball: Why don't you write about it in your blag?

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Language]]
[[Category:My Hobby]]