Revision as of 02:54, 12 March 2013

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Math paper

Title text: 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 + bi 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.

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