Triangles are magical. In structural engineering they are the only sided shape that can't be distorted or collapse at the joints. In drama they are always dynamic. Unlike quartets, which tend to settle into static pairs, triangles present the constant possibility of any two people uniting against the third. It is no wonder they are so often chosen by storytellers of all kinds.
Trios are so complex that I feel the need to break them down into subcategories. First there is the non-romantic trio, which is extremely common. Kirk-Spock-McCoy, the Three Amigos, the Three Musketeers, Charlie's Angels, the Three Stooges, Granny Weatherwax-Nanny Ogg-Magrat, Vezzini-Inigo Montoya-Fezzik and Westley-Inigo Montoya-Fezzik, Marlin-Nemo-Dory, Mowgli-Bagheera-Baloo, the three Ghostbusters, Frodo-Sam-Gollum, Sunny-Violet-Klaus, and Nancy Drew-George-Bess are just some of the many, many examples.
Next there are the all-romantic trios, of which there are three types. First is the true love triangle, which is rare but tends to be beloved when it is done properly. Perhaps the preeminent example is the movie Casablanca. There is also Dr. Zhivago, Cyrano de Bergerac, Jules et Jim, and many treatments of the classic Arthur/Guinevere/Lancelot triangle.
More common is the temporary love triangle that collapses into a pair. Many, many novels of romantic suspense take the form of one woman with two rival suitors, one who turns out to be a bad guy (or the bad guy) and the other who is her true love. But the "wrong person" doesn't have to be evil. The middle person of a love triangle often simply chooses the partner who is the best person--or at least best-suited for him or her. Sometimes love triangles end with the "wrong" suitor realizing that they are wrong and sacrificing him- or herself, as in A Tale of Two Cities. This is also the resolution of the love triangle between Jack, Elizabeth, and Will portrayed in the second and third Pirates of the Caribbean movies. Jack sacrifices his chance to live forever to save Will's life and allow Will and Elizabeth to be together.
Another possibility is that the "wrong" suitor decides to pair up with a fourth person instead, as in the Twilight series when the Edward/Bella/Jacob triangle ends up with Jacob realizing that Bella's and Edward's daughter is his true love. The wrong suitor can be a bad person, as when the Elinor/Edward/Lucy triangle is resolved at the end of Sense and Sensibility by having Lucy elope with Edward's brother, or they can be a good person, as Jacob is in Twilight, but simply have a change of heart.
I should point out, by the way, that not all love triangles are trios. For instance, Ron/Hermione/Krum is a love triangle but those three characters are never grouped into a trio. Similarly, Strike/Robin/Matthew is a love triangle but never a trio in the action plot--or at least not so far.
There is one more type of trio with all three people romantically involved--the ménage à trois, either true polyamory where everybody loves everybody or happy, consensual polygamy. Some movies that use this geometry are Paint Your Wagon, Y Tu Mamá También, Professor Marston and the Wonder Women, and Threesome.
Romantic trios don't always have all three people involved in the love story. A very common pattern, especially in adventure stories, is the two-plus-one trio with a romantic couple and a "third wheel" who for whatever reason is never a factor in the romance. The third person might be ineligible by reason of age, sexual orientation, blood relationship, social class, species, or simply not being portrayed as an attractive partner. A classic example would be the three protagonists of the movie Shrek, where Shrek and Fiona have a love story and Donkey is never considered as a romantic option (though he does get a mostly-offstage romance with a minor character). Or it could be that two people in the trio are already in an established relationship when the book or movie begins. An example is Ferris and his girlfriend Sloane in Ferris Bueller's Day Off, where their friend Cameron is part of trio of protagonists but doesn't challenge the Ferris/Sloane pairing.
The two-plus-one pattern is very, very popular for plotty adventure stories and it is easy to understand why. It has all the dramatic advantages of the trio but the romance doesn't take over the whole work like it tends to do in love triangle and ménage à trois geometries. Examples are almost endless: Luke and Han/Leia in the original Star Wars, Anakin/Padmé and Obi-Wan in the prequels, Indy/Marian and Sallah in the first Indiana Jones movie and Indy/Willie and Short Round in the second, Jack and Will/Elizabeth in the first Pirates of the Caribbean movie, Alladin/Jasmine and the Genie in Aladdin, Thor/Jane and Darcy in Thor, Tony/Pepper and Rhodey in Iron Man, Ben/Abigail and Riley in National Treasure, Rick/Evelyn and Jonathan in The Mummy, Jake/Neytiri and Dr. Grace Augustine in the movie Avatar, Aang/Kotara and Sokka in the TV cartoon Avatar, Korra/Mako and Bolin in the earliest episodes of The Legend of Korra, Anna/Kristoff and Olaf in Frozen, Picard and Riker/Troi in Star Trek, the Next Generation, Marty/Jennifer and Doc in Back to the Future, Belle/Beast and Maurice in Beauty and the Beast, Clark/Lois and Jimmy Olsen in Superman, Sherlock and Watson/Mary in Sherlock, Meg/Calvin and Charles Wallace in A Wrinkle in Time, Butch/Etta and Sundance in Butch Cassidy and the Sundance Kid, Neo/Trinity and Morpheus in The Matrix, Old Zorro and Young Zorro/Elena in The Mask of Zorro and ... I'm sure you can think of others.
What makes the two-plus-one trio romances particularly interesting is not so much the reason that one person is a third wheel but the combination of the two-plus-one geometry with the geometry of leading and supporting trio members. Triangles can be either "regular," with a hero or heroine at the top and two sidekicks at the bottom, or inverted, with a lead couple at the top and a single sidekick at the bottom. Thus we have four main patterns: the love pairing at the bottom of a regular triangle (like Han/Leia in Star Wars), at the top of an inverted triangle (like Rick/Evelyn in The Mummy), or along the side of either a regular triangle (Ferris/Sloane) or--though this one is rare--an inverted triangle (Butch Cassidy/Etta Place).
Of course, a two-plus-one adventure trio was the geometry portrayed in the vast majority of the Harry Potter series.
And it was exactly this combination of geometrical possibilities that was so fiercely disputed between the Harry/Hermione and Ron/Hermione tribes in the Harry Potter shipping wars. Most of us agreed that the trio was a regular triangle that looked like this:
Our dispute was whether the romantic pairings was a regular triangle/side pairing like this:
Or a regular triangle/bottom pairing like this:
Although a significant minority of Harry/Hermione shippers thought the trio was, or was growing to be, or ought to be an inverted triangle/top pairing like this...
...or that it should/would cease to be a trio at all and become a simple pair:
The problem was that all those geometries are possible, in that they are patterns commonly seen in fictional works. However, we all now know that Rowling was writing a regular triangle/bottom pairing, which I maintain is the main reason her romantic pairings attracted so much controversy.
The most common and traditional two-plus-one geometry is hero/girl+sidekick, like Superman/Lois Lane + Jimmy Olsen. Even if the story is centered around a female protagonist rather than a male one we tend to have trios like Anne/Gilbert + Diana in Anne of Green Gables. In other words, the simplest pattern is for our hero or heroine to have both a love interest and a same-sex best friend, sibling, servant, or mentor.
The less common regular triangle/bottom pairing is generally used when the hero or heroine is in some way special, elevated, or non-sexual--a Christ figure like Luke Skywalker and Harry Potter, an unusual morally-ambiguous character like Sherlock Holmes, or just a character who needs to be kept free for future dalliances like Captain Kirk and Captain Jack Sparrow. Another example I can think of is in one of my favorite Lois Bujold novels, The Curse of Chalion. In that story the main trio is the Princess Iselle, her best friend/lady-in-waiting Betriz, and her secretary/tutor (the novel's protagonist) Cazaril. Cazaril and Betriz fall in love with each other, leaving Iselle free to make a necessary royal alliance marriage. But it is a pretty rare pattern, which makes it less surprising that many people didn't recognize it in spite of the fact that Rowling was trying to make it obvious to child readers.
Many Harry/Hermione shipper expected Ron to end up paired with Luna. The pattern would be similar to Shrek/Fiona and Donkey/Dragon, like this:
(I am assuming that Shrek, as the title character and with quite a bit of screen time before Fiona appears, is at the top of a regular triangle and Fiona and Donkey are secondary characters at the bottom. The dragon has a much smaller part and isn't part of the main trio.)
But what Rowling was actually writing looks more like this:
This is a rare pattern that maps to Watson/Mary-Sherlock/Irene and Cazaril/Betriz-Iselle/Bergon but few other works of fiction that I am aware of. And in both those cases, the primary point of view characters, Watson and Cazaril, are involved in the trio romance. Harry isn't. Rowling could have transitioned in the last two books to a good old-fashioned quartet like she used in Fantastic Beasts, like this:
Or, perhaps more accurately, like this:
She chose not to do either of those. I completely understand her reasons. We had been through many books' worth of adventures with the Trio and it felt right to continue that way. Also there were symbolic reasons: Ginny represented normal life to Harry, the life that he couldn't have unless or until he defeated Voldemort. She was the end, not the means. And, practically speaking, if Ginny had come along on the Horcrux hunt Rowling would have needed to write scenes in service of the Harry/Ginny romance, as well as Ginny-Ron and Ginny-Hermione interactions, making the book longer and even more complex. If Harry's "best source of comfort" had been with him all along it might have been hard to make him as sad and desperate as she wanted him to be. All that makes perfect sense, but it left the Harry/Ginny romance underdeveloped and unsatisfactory for many readers.
Perhaps Rowling concluded from readers' reactions that she had been wrong to choose that somewhat unusual geometry. At any rate, she is not using it for her two current series, Cormoran Strike and Fantastic Beasts. But what about the play Harry Potter and the Cursed Child that she collaborated in? How does the geometry look there?
Part One: Introduction Part Two: Pairs Part Three: Quartets and More--
Part Five: Conclusion