Technically this should be called a “love angle,” and “love triangle” should be reserved for situations where the two suitors are also in love with each other.
Been a while since I’ve seen it, but I’m pretty sure this is what Lion in Winter was about. (Note that the backstabbing can be figurative or, if you’re working in a genre with a high level of violence, literal.)
Not always a fun story. Sometimes too real. (Also, there’s no law that says each character’s in-degree must be the same as their out-degree. But it’s just good storytelling.)
My friend Becky Dinerstein Knight wrote a juicy book called Hex that was, to oversimplify its geometry, a more scandalous version of this.
Watch out for characters falling in love across enemy lines. This may make for good theater, but it totally ruins the bipartite structure.
There’s just no rational way to factor that guy.
Freaky Friday-style plotlines often overlook a crucial source of horror: all of those people who wake up, mortified and aggrieved, to discover that they’re still in the same stupid body.
Pro tip: if you’re writing this screenplay, you’re going to need a bigger whiteboard.
I feel like you already know this and used the last two plots in an IYKYK way. They were used in the Futurama episode, The Prisoner of Benda, where several characters use a machine to swap bodies. It turns out you can’t directly swap back, so more swaps happen to try to fix things leaving everything a mess. Two of the Harlem Globetrotters prove that you can fix everything by adding two new bodies and routing all the transpositions through them. The episode was written by Ken Keeler, who has a Ph.D in math. He actually proved a group theory theorem to make sure it all worked.
https://en.wikipedia.org/wiki/The_Prisoner_of_Benda
I come here with a relevant observation to make around the crossovers between pop culture and mathematical theory, only to find someone has beaten me to the punch???
Well played Jeff… wellllll played…
This reminds me of some weird graph theory thoughts that were going through my head on one of my daily walkaround a couple of weeks ago.
We have a bipartite directed graph with four vertices: two red and two blue. It has four edges, one coming out of each vertex. If the blue vertices are indistinguishable and the red are distinguishable, how many different graphs are possible? I make it five.
But first of all, let’s link it to real life. We have two heterosexual males and two heterosexual females. Each of the four only fancies one of the two of the opposite sex. So the four possibilities are:
– the disconnected graph, the perfect scenario where they can be paired off
– the worst scenario is the cyclical graph: A1 fancies B1 who fancies A2 who fancies B2 who fancies A1. No action going on there.
– the two legged table graph or golden couple scenario. Both guys fancy the same woman and both women fancy the same guy. Two get it together and there’s no chance of any action between the other two.
– the two kite and streamer graphs. One of the four is fancied twice, one not at all and the other two once. One pair gets together and of the remaining pair, one fancies the other but it’s not mutual. There are two versions of this, depending on whether it’s the remaining women fancying the remaining man or vice versa.
It’s interesting comparing the two kite and streamer graphs and the feelings of the two in the kite that get it together:
– if both women fancy the same guy, then both in the kite are happy: he had two to choose from and she won him ahead of the other woman
– if both guys fancied the same woman, they’re happy but not quite as happy as before: while he’s still happy bout being chosen, he’s not as happy about it as the woman in the other example, and the woman who both men fancied feels a bit guilty about rejecting one of them.
It’s what made me think, yeah, those two kite and streamer graphs are definitely different.
Rejected titles for math screenplays include: The Commutative Diagram; The Star Domain and The Field with Zero Characteristic
The Futurama Body swap theorem was the subject of a question on University Challenge on the day this post came out.
There is a section in Anthony Trollope’s Barchester Towers when four people have four conversations. In each case, one of them is sure they’ve been very clear, but they’ve been completely misunderstood. Perhaps a quadrilateral of miscommunication>
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