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Introduction to Simpsons-Math

February 2004

The Simpsons actually is one of the longest-running shows in television history [0]. It is one of the television shows which is popular all over the world. Here in Germany The Simpsons have an average viewing figure of about 1.1 million spectators (in January 2004).

However, no matter what you personally think about cartoons, The Simpsons can offer a variety of things to you. A child might love all the yellow characters and a mature person might discover analogies to his own real life.

Anyway, I'm always fascinated by things like math in Simpsons episodes. One of the most spectacular episodes has been 3F04 - Treehouse of Horror VI. When Homer enters the 3D space we can see a lot of Math (computer science included) in just a few seconds! Most of the equations are only for very short time (about one second) visible. The recognition of information is just too hard when watching it once or maybe twice. I've compiled some screenshots of the 3F04 episode with a brief interpretion of the content.

Frink rules!

Hex string

The picture above shows a hexadecimal [1] ASCII [2] string left of Homer's body. A computer scientist will speedy perceive it and could decode it as an ASCII string. If you want to decode it by yourself, you could check [1] and [2] in the table below.

However, it could also be done in Linux:

$ echo 0x4672696e6b2072756c657321|xxd -r
Frink rules!$

Yes, they hex string means 'Prof. Frink!'.



Right of his nose we will see a part of an simple equation, it is just a addition of one and one which is equal to two. Well, what is so spectacular on this? You might have heard about the Peano axioms [5] in a university lecture. So what do they say? "Every natural number a has a successor, denoted by a + 1." [5]. Were the men behind the Simpsons hinting to them by this simple equation? In fact, this is just a theory, you can think about what you want.

P = NP and eϖi = -1


In this figure we see two great formulas. The red marked formula at the right is called Euler Formula [7] and combines in this case all importand constants: i, 0, 1, e and pi! (i:=sqrt(-1) is a complex number, read [4] for further information).

e^PI*i = -1 => cos PI + i sin PI
because cos PI = -1 and sin PI = 0 => e^PI*i = -1

I won't discuss the P=NP formula on the left side here. It is part of the complexity theory and one of the most importand open questions in computer science. No proof for this thesis is found yet. If you want to get further informations, your should read about the P=NP question in [3]. It is also sometimes used as an computer scientist joke. ;)

178212 + 184112 = 192212


Everybody will rapidly see the left equation is wrong! No worries, I don't think they just made an simple mistake. In my opinion, this is just an big hint to Fermat's last theorem [6].

Further reading

[0] The Simpsons
[1] Hexadecimal numbers
[3] The P=NP question
[4] Brief introduction to complex numbers
[5] Peano axioms
[6] Fermat's last theorem
[7] Euler Formula

Related Sites offers a great collection of math stuff within the Simpsons. This site comes from the accademic world.

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