By Katie Maier
When Mr. Newman saw a graph of two bisecting lines that a geometry student had drawn on his whiteboard, he said what anyone would say: “that’s kind of romantic.”
With my limited understanding of geometry (which I haven’t taken since eighth grade), I countered Mr. Newman’s observation, arguing that it’s not romantic because the lines only meet once and then move infinitely away from each other. Newman commented that this would be a great story for the Valentine’s Day issue.
Now, Mr. Newman has a habit of turning everything into material for the OnLion (meaning every off-topic conversation in newspaper class is punctuated by him declaring “hey, this could be an article!”). But I must say, I agreed with him as I myself was a bit curious about this particular idea. I decided to talk to the head of the Upper School Math Department Mr. Bob Amar to gain some insight into a few mathematical phenomena might apply to relationships so that I could make my own conclusions on romance math.
Perhaps it could serve as the foundation for a new math elective?
Parallel lines
“Parallel lines,” Mr. Amar explains, “have the same slope and go in the same direction, running alongside each other infinitely but never meeting.”
This is the classic case of two friends who could be something more. They met as kids in seventh-grade algebra and have been close ever since they learned how to calculate slope.
But something always got in the way of their fairytale ending. A heartfelt text that never got sent because of their lagging 3G network (but at least it didn’t intercept the control tower at Hartsfield Jackson airport). A school ban on slither.io that prevented them from bonding over multicolored worms (remember 2016?). In the end, one ended up going to AP Calculus AB, and the other to BC.
Now they’ll spend the rest of eternity as two slither.io worms never crossing paths with one another but always, it seems, within reach.
Intersecting Lines
Two lines moving in different directions meet once in a two-dimensional plane. There may be tension before they intersect, and once they meet, as Mr. Amar explains, they move infinitely further away from each other.
At one sophomore PDC, two lines intersected for a short but memorable evening (this is a true story). She had seen him in church before and became instantly fascinated with him (and his two brothers, both equally attractive). So when she saw him once again at the dance, she knew she had to make a move.
They shared a dance to a cover of “Keep Your Hands to Yourself” by legendary band Air Tight (whose apparently never-ending contract was “airtight” as they have been performing at PDC for longer than the Georgia Satellites have even existed) before parting ways.
The pair has yet to see one another since that interaction, but at least they can go about their separate lives knowing they’ll always have PDC.
Tangent of a Parabola
A tangent line intersects a parabola at just one point before they part ways forever, but their relationship is more complex than a simple, linear intersection.
“They don’t stay together,” Mr. Amar says, “but [the tangent] is a springboard for the parabola to be even greater than it was before.”
Tangent lines are like your first love…or maybe the mild crush you once had that helped you figure out your standards. One of my early tangents was a boy in my second-grade class who gave me a love letter on Valentine’s Day which he signed as my secret “atmirer” (with the last three or four letters running down the side of the paper as he obviously hadn’t spaced out his characters properly). It was a sweet gesture which helped me realize that, going forward, I probably need a boyfriend who knows how to spell.
In any case, parabola-tangent relationships can help people figure out who they are and what they want out of the future.
“Unless,” Mr. Amar counters, “the parabola has a negative slope, in which case it’s a rebound.” (aka Pete Davidson and Kim K…).
Asymptote
Two curves, one coming from the positive x-axis and the other from the negative, approach the same asymptote, infinitely drawing closer to one another.
These graphs are the Romeos and Juliets of calculus. Star-crossed lovers who never actually cross the border that divide them. Basically, think of every Hallmark-type movie, lop off the last fifteen minutes, and you’ve got an asymptote.
Two college students, one the president of Young Republicans and the other the president of Young Democrats. Two small business owners who run rival bagel shops. Asymptotes.
It can be hard to visualize the realization of these across-the-tracks relationships, but even infinity has to end somewhere. Mr. Amar assures us that “at some undetermined point in the future, they achieve unity.” (I’m blushing just thinking about it.)
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So it seems that in my interpretation of math romance, relationships have a generally low probability of Hallmark-worthy success. But even the greatest mathematician couldn’t devise a formula for romance, so you might just have to color outside of the lines to find whatever it is you are looking for.
Or, at least, get more complicated with your geometry. Consider the Mobius strip. You take a two-sided strip of paper, give it a twist, and tape the ends together. You now have an infinite loop with only one side and one boundary curve. It’s a perfect metaphor for the paradoxical nature of love. Two people…somehow become one.
You may be surprised, just as I’ve been surprised by, and grown to love, the fact that something as simple as a diagram on a whiteboard can become a (two-and-a-half-page) newspaper article.
