The Shape of Love

A geometrical look at Hollywood’s most famous movie romances

Love, like Geometry, is concerned with points and analogs, the relationships created when those points are connected, and the impact those relationships have on the space around them. Love, like Geometry, is also exceedingly overwhelming and intimidating in middle school and only marginally easier to understand as you get older. I suppose the most obvious and easiest intersection between love and geometry is the idea of a “love triangle”, a misnomer of a phenomenon that primarily exists in the movies. Lots of movies are billed as “love triangles”, but most of those movies show a clear lack of understanding of basic geometry. You see, love, especially movie love, does take shape, though rarely in the form of a triangle. When you consider people as geometric points, and the relationships they form as segments of linear time, you can actually see the shapes that love can make.

Sadly, in order to make sense of all this, we need to begin with the relationships that fail. The line segments of love. In an ideal world, every relationship would carry on into forever, blissfully uninterrupted by jealousy or financial burdens or sketchy late night texts. The problem, however unfortunate it may be, is that most romantic relationships have two distinct end points. The easiest movie love line segment to illustrate this point is from 500 Days of Summer, about the failed relationship between Joseph Gordon-Levitt’s Tom and Zooey Deschanel’s Summer. Like Jennifer Aniston’s The Break Up, another line segment movie love, it’s a romantic comedy without much romance. The ending is not so much happy as it is hopeful; Tom and Summer, like the majority of us, experience heart break but continue on their separate linear paths, searching for not-promised romantic fulfilment. The line segment romance movie is not a popular or common one. Sadly, most people don’t want or need to shell out fourteen dollars to watch a relationship fail. They can just pull their cell phones out and open Snapchat.

The happier tales, of course, are the infinity love lines. Two points on the same line, traveling into and through infinity together. These are your happily ever afters, your fairy tales, your happy endings. A love line movie is often devoid of any real romantic conflict, no spurned ulterior suitors or depressingly permanent break-ups. These are your straight-up love stories, often involving castles and magical pumpkins and flying carpets and things of that ilk. The infinity love line is where we’re going to see Hollywood’s vision of a perfect princess, our Cinderellas, our Sleeping Beauties, our Julia Roberts.

Once you’ve gained an understanding of the simple, linear properties of love, it’s easier to understand the more complex amorous entanglements. Again, the most commonly misreported romantic designation in movies is the “love triangle”. Consider what a triangle really is. A triangle is a figure with three straight sides and three angles, all of them connected by three points. The connection of those points is the important factor to consider when determining the shape of a relationship. Consider The Notebook, one of the most famous movies in recent history about the effect that aging and war and distance and the US Postal Service has on relationships. It’s billed as a love triangle between Allie (Rachel McAdams), Noah (Ryan Gosling), and Lon (James Marsden). Those are our three points. Our three sides. It would seem appropriate to call the goings-on between Allie, Noah, and Lon a triangle. However, it’s the connection between points that’s lacking. The Notebook, like most love triangles, is not a triangle at all. It’s a love caret.

You see? Allie loves Noah. Noah loves Allie. Their points are connected through love. The same goes for Allie and Lon. Though clearly, Noah does not love Lon. Lon, who loses his fiancé to Noah and his pension for tortured carpentry, most certainly does not love Noah. Lon and Noah’s points are not connected. They form a caret.

Not surprisingly, Ryan Gosling is often involved in these love carets. Whether it be The Notebook or Drive or The Place Beyond the Pines or La La Land or the upcoming Song to Song, Ryan Gosling is always making people fall in love with him. It’s an easy thing to understand, this accidentally falling in love with Ryan Gosling. It seems to happen all the time.

If Ryan Gosling comes anywhere near a relationship, no matter how strong the parties involved in that relationship believe it to be, the power of Gosling’s gravity is going to draw some of that love towards him. It’s scientifically inevitable. Picture yourself and your spouse on a date. No, not just any date, but your 10th wedding anniversary. The babysitter has offered to stay late. You left your work phone at home. The pre-dinner martini has plastered a smile on your face that, in this moment, feels just about permanent. You’re sitting in the back corner at the exact same table you proposed at all those years ago. It feels like it was just yesterday. Time’s a funny thing. So is love. It shows itself differently nowadays, but your love for one another is infinitely stronger than it was a decade ago. Looking across the table at that familiar, glowing face, you allow yourself a moment to pause, to reflect on how lucky you are. You wonder what the hell you ever did to deserve someone like her. That brief moment is interrupted by the sound of a waiter’s voice. “Hi, I’m Ryan, I’ll be taking care of you tonight.” It’s him. The Goose. Ryan Gosling.

“Do you promise?”, your spouse blurts out, uncharacteristically. She instinctively throws a hand toward her mouth, as if trying to shove the words back into her mouth before they reach Ryan’s ears, which frame each side of his perfectly symmetrical face and mark the end points of his golden stubble like two school kids holding a sexy jump rope. Ryan tries but fails to stop himself from giggling, bringing the specials menu he’s been holding up toward his mouth until the only thing you can see on his face are the laugh lines around his perfectly blue eyes. He’s embarrassed, not for your wife, but for himself-as if his own handsomeness is an inconvenience to others. It’s so impossibly endearing and wonderful that if you thought it was even remotely possible, you’d start to hate him just for existing. You look across the table at your wife and notice how red she’s become. She looked the same way when you proposed to her a decade ago. You know the look. It’s not because she’s ashamed. It’s from all that blood suddenly pumping out of her heart. It’s in that moment that you realize your wife has fallen in love with him, right there on the spot. It happens that quickly. You’ve become part of a Gosling caret. Your only hope now is to convince Gosling to fall in love with you, for you and your wife and him to fall into a love triangle.

A true love triangle is very rare. A true love triangle requires three parties to be (almost) equally in love with one another. That’s a very sticky situation. There are some instances, like in Edward Norton’s Keeping the Faith and Oliver Stone’s Savages where the triangle does exist, but those movies are few and far between and one of the love-sides is usually made more of friendship than feelings of romantic attachment. It’s difficult enough to love one person, let alone two, with equal passion. For the most part, love triangles end in hurt feelings. They’re actually very sad. There’s nothing a-cute about them. I’m sorry. Let’s keep going.

There are of course other shapes that movie romance can take, such as the love circle formed in Deadpool, or really any movie with Ryan Reynolds, which no matter what the supposed plot is are mostly just movies about how much Ryan Reynolds is in love with Ryan Reynolds. Every single part of a Ryan Reynolds movie always circles back to the fact that Ryan Reynolds would very much like to marry and raise children and grow old with Ryan Reynolds, where he can offer up self-satisfied smirks and sarcasm from now until eternity.

There is the ever-so-rare love square (sometimes rectangle) films, a tricky shape to build because it often requires siblings or parents and it always gets, or at least feels messy to include a family member in any game of romantic connect the dots. The square is unusual, though not impossible to build. A love square is essentially a connection between two love carets, in which the points diagonally across from one another are not in love but are otherwise linked, by their hearts, to the remaining points. It seems complicated. It’s not. Take Wedding Crashers for example. You take two best friends who love each other who are separately in love with two sisters who of course love one another and you’ve formed a neat, tidy square of love to help guide you through an otherwise tangled, knotty romantic scenario.

There are the obelus movie loves, also known as “division sign love” in which the main romance is sort of circled about or observed by two parties who may be in love with the main players, though that love is unreciprocated, leaving them unconnected and floating around the periphery of true love. The most obvious obelus film is Titanic. Here you have a tragic line-segment movie love between Jack and Rose, robbed of their chance of an infinity love line by an iceberg and the hubris of a smug nautical engineer. Above them floats Billy Zane’s Cal, who loves Rose but is not connected to her, evidenced by the fact that Rose once tried to kill herself rather than spend even one more meal sitting next to him. Below them, drifting in romantic loneliness, is Fabrizio, who is very much in love with Jack, evidenced by the fact that he left everything he ever knew and loved behind to travel with Jack to America. Sadly, his love remains unconnected, as Jack, by leaving Fabrizio to die below deck, illustrates that he considers them to be nothing more than travel companions.

Those are the shapes of our movie romances. Now, does love geometry help in the same way that regular old boring math geometry can help you determine how much carpet you need to purchase? No, sadly no. Finding the shapes of our romance won’t make love any easier, but it is always nice to know where you stand, which plane you lay upon. Wherever that is, hopefully you remain far, far away from The Goose.