- 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 :-) ]