Editing 410: Math Paper
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==Explanation== | ==Explanation== | ||
− | + | This comic is a set up to use the joke about {{w|imaginary friend}}s by taking the concept of "{{w|friendly number}}s" into the complex plane, which comprises numbers that have both a real and an imaginary part. Such a pun is both so obvious and so terrible that Cueball's superiors deem that he has lost the right to carry a "math license". | |
− | + | This is a recurring theme in earlier xkcd comics, being banned from holding presentations at conferences because said presentations are just elaborate puns. The title text takes the joke a step further, with the added hilarity of making the audience ask just how the hell Cueball was able to work a {{w|striptease}} into a presentation about genetic engineering and astrophysical rocket study. This is what TV Tropes calls a "[http://tvtropes.org/pmwiki/pmwiki.php/Main/NoodleIncident noodle incident]". | |
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− | The title text takes the joke a step further, with the added hilarity of making the audience | ||
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===Math=== | ===Math=== | ||
− | An {{w|imaginary number}} is a number that can be written as a real number multiplied by the imaginary unit ''i'', which is defined by its property ''i<sup>2</sup> = -1'' (an impossibility for regular, " | + | An {{w|imaginary number}} is a number that can be written as a real number multiplied by the imaginary unit ''i'', which is defined by its property ''i<sup>2</sup> = -1'' (an impossibility for regular, "real" numbers, for which all squares are positive). The name "imaginary number" was coined in the 17th century as a derogatory term, since such numbers were regarded by some as fictitious or useless, but over time many applications in science and engineering have been found. |
− | An imaginary number ''bi'' can be added to a real number ''a'' to form a {{w|complex number}} of the form ''a + bi'' | + | An imaginary number ''bi'' can be added to a real number ''a'' to form a {{w|complex number}} of the form ''a+bi'', where ''a'' and ''b'' are called, respectively, the real part and the imaginary part of the complex number. If ''a'' and ''b'' are both integers, the complex number is called a {{w|Gaussian integer}}. |
− | Joel Bradbury | + | Joel Bradbury has a wonderful explanation of {{w|friendly number}}s on [http://joelbradbury.net/notes/friendly_numbers his site]: |
− | :What are Friendly Numbers? | + | :What are Friendly Numbers? |
:We need first to 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. | :We need first to 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 = 7, and so on. | :Now sum them to get σ(n). So σ(3) = 1 + 3 = 4, or σ(4) = 1 + 2 + 4 = 7, 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 | + | :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 characteristic are called friendly with each other | + | :Once you have the characteristic ratio for any integer n, any other integers that share the same characteristic 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 | + | :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== | ==Transcript== | ||
− | :[Cueball | + | :[Cueball points to equations on the board.] |
:Cueball: 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. | :Cueball: 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. | ||
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− | : | + | :Professor: Hold on. Is this paper simply a giant build-up to an "imaginary friends" pun? |
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− | :[ | + | :[Cueball stands speechless for two panels.] |
− | + | :Cueball: It <u>MIGHT</u> not be. | |
− | + | :Professor: I'm sorry, we're revoking your math license. | |
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− | :Cueball: It <u> | ||
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{{comic discussion}} | {{comic discussion}} | ||
− | + | [[Category:Math]] | |
[[Category:Comics featuring Cueball]] | [[Category:Comics featuring Cueball]] | ||
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[[Category:Banned from conferences]] | [[Category:Banned from conferences]] | ||
− | [[Category: | + | [[Category:Public speaking]] |
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