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Questions:

  • Do you have any examples from pop culture (say, a joke, or an episode of a show, or a song lyric, etc.) that utilize and/or effectively illustrate a mathematical concept?
  • Have you used any examples in class, and have they proven effective in making a concept easier to grasp at first and/or more memorable in the long term?

This comes to mind because I recently used a bit from a standup comedian to illustrate how widely-used and easily-understandable the Pigeonhole Principle is, even though most people don't really know it by that name (or any, for that matter). Here is the joke: video link, 29:33 to 29:55.

My lucky number is four billion. That doesn't come in handy when you're gambling. "C'mon 4 billion! @#%$, seven. I'm gonna need more dice: four billion divided by six, at least...

I used this example to show my students that we are comfortable with the use of the Pigeonhole Principle already (i.e. best case scenario is we roll a bunch of 6s to get as high as 4 billion, but we might need more dice), that the underlying idea is pervasive and understandable. I think this sets a nice tone for learning and applying a new concept: this is kinda new to you, mathematically speaking, but you are already familiar with it, conceptually.

I would consider examples like this one to be good answers to this question, and I welcome a list of such examples. (Consider posting multiple examples as separate answers so we can vote accordingly on each one.) Essential property of a good example: it should describe/exemplify the concept, not merely serve as a reference to the concept.

I wouldn't necessarily consider as a good answer an example like that famous episode of Futurama, the one with the "mind swap" permutation problem. It doesn't illustrate a particular concept, nor does it make anything more enlightening, nor does it show that a particular idea is already familiar to people. It is certainly interesting and very "mathy", but it's not exactly what I'm looking for. (That said, this could be an interesting example for, say, an undergrad discrete math course that happens to be studying permutations, so maybe it could be a good example. I suppose it depends on context.)

[Meta: I wanted to add a "big-list" tag to this, but I see that the relevant discussion on meta.MESE doesn't have an apparent resolution. I'm fine if this Q ends up getting deleted because we decide that "big-list" is a bad idea, but I'm also fine with this starting up the discussion again :-) ]

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    $\begingroup$ Nice question! I'd say let us wait with the tag. $\endgroup$ – quid Sep 17 '14 at 21:55
  • $\begingroup$ You might find some worthwhile jokes in the related MO post. For example, the song with lyrics posted here: mathoverflow.net/a/1109 $\endgroup$ – Benjamin Dickman Sep 17 '14 at 22:44
  • $\begingroup$ I once did a number of examples in differential equations whilst playing Sade's Smooth Operator. I think the nature of the examples is clear from the song choice. $\endgroup$ – James S. Cook Sep 18 '14 at 0:54
  • $\begingroup$ @BenjaminDickman: Yes, I forgot about that song! That would be great in an abstract algebra course. (My worry about most of the other jokes listed, though, is that they might only make sense to someone who is already familiar with the relevant concept. Plus, a lot of them are contrived, un-funny, and not from culture at large.) $\endgroup$ – Brendan W. Sullivan Sep 18 '14 at 15:33
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From Numb3rs, an American TV show (which I've never seen). Several friends notified me when it touched upon art gallery theorems (e.g., see this earlier MEd posting):


      Numb3rs
      Quote
From the Numb3rs Teacher Activity Guide:
  ActivityBook


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    $\begingroup$ I am aware this doesn't quite address the (good) question directly. But likely a number :-) of Numb3rs episodes could serve to launch into particular mathematics. $\endgroup$ – Joseph O'Rourke Sep 18 '14 at 10:57
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I think the video "Jokes with Einstein" about crossing an elephant and a banana is just right for a course such as Calculus III when you introduce cross products. Here is a link

http://www.youtube.com/watch?v=r651684kxKg

I can play it four times consecutively in class and students laugh each time. It does not seem to get old.

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There are many examples from pop culture which “utilize and/or effectively illustrate” game theoretical concepts.

You can find some examples here.

The concepts are such as e.g. Prisoner’s Dillemma, Game of Chicken, common knowledge, etc.

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This may be known already but "The Simpsons" has many (advanced) math and physics references. Here is a relevant link.

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    $\begingroup$ Could you point to some particular example(s) where the show explains or illustrates a mathematical concept? I specifically mentioned in the question that a good answer should have this property; I'm not merely looking for mathematical references in pop culture. $\endgroup$ – Brendan W. Sullivan Sep 18 '14 at 23:58
  • $\begingroup$ I updated my answer with a link that catalogues math references in the show by season (there are many jokes too). $\endgroup$ – illysial Sep 18 '14 at 23:59

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