Thirteen Ways of Looking at a Parabola

with sincere apologies to Wallace Stevens,
and to all poets, everywhere


All my life
I had known only lines
so when my teacher
drew a parabola
I said,




I took all the numbers,
and squared them.
The big ones grew.
The little ones shrank.
The negative ones
became positive.
Opposites agreed.
It was kinda cool.




I watched an object falling,
tracing its arc,
the ink of time leaving curves
on the paper of space—
a perfect parabola.
(Except for air resistance.)



My teacher told us something
about beauty,
and curvature,
and the essence of number.
I took what she said
and plugged it into the quadratic formula:
No real solutions.



I was of three minds,
Like a parabola
Which is defined by three points.



I found a cone, and sliced:
a little this way,
I’d have made an ellipse;
a little that way, a hyperbola;
and a little the other way,
I’d have hacked off a finger.
But I cut true, and so,
a parabola.



An equation and a graph
are one.
An equation and a graph and a student
are confused.



If you walk a narrow path,
never too close to the house,
never too close to the road,
just the same distance from each,
then you will weird people out,
because why are you walking like that?
Nobody walks in parabolas.



The polynomials all babbled
in languages I did not speak,
like beasts, or birds,
or soccer commentators.
I could grasp no one’s words,
except the parabola,
and so I let it speak for them all.



I held a mirror to my parabola
and it simply admired itself.



I do not know which to prefer,
The beauty of constancy
Or the beauty of change,
The turn in the parabola
Or just after.



I know logarithms
and trigonometric equations;
But I know, too,
That the parabola is involved
In what I know.



I asked a cubic for its derivative.
It spoke in parabolas.
I asked a linear for its integral.
It spoke in parabolas.
I asked Jesus for a math lesson.
He spoke in parable-as.


20 thoughts on “Thirteen Ways of Looking at a Parabola

    1. This blog I have to admit, may be confusing. But it is hilarious. I guess that doesn’t make sense. I can make out about 30% of the post: Thirteen Ways of Looking at a Parabola. I especially like the part about asking Jesus for a math lesson. And the parable – as part, I got 100% clear.

        1. I’m honored, but it’s not the kind of post I tend to make! So I guess “not accepting” is my answer, although I realize what a jerk that makes me, and apologize for it.

    1. Glad to hear it! I wasn’t sure if this poem was targeted at the Venn diagram intersection of “people who like math” and “people who like Wallace Stevens,” which I feared might include precisely 0 people.

    1. I like how that book cover is a mix of genuinely weird things I say, and totally pedestrian American-isms. You’re going to be very disappointed when you meet other Americans and find out that my mannerisms aren’t that unique. (This happened with an Indian friend of mine and I was devastated; our relationship took days to recover.)

  1. I like how you drew the trig-substitution graph from behind, the side so rarely shown, with the positive u-axis pointing left.

    Also, three general points can be fitted by more than one parabola. For example, the triple {(0,0), (0,1), (½√3,½)} has three different *symmetrical* parabolas through its points, plus continuously-many others at different tilts.

  2. As a mathematician and Tolkien fan, I couldn’t resist trying to find a fourteenth way (Tokienist because, like Thorin who didn’t want 13 on his quest so Gandalf found Bilbo to make 14, and mathematicianist simply because, well, it’s what we do, don’t you know). So my suggestion for a possible fourteenth way would be about the confusion one is left hanging with like a chain around one’s neck (with the other end attached to a post of course) when a catenary is mistaken for a parabola. Just SO disturbing, sort of like how just intonation and equal temperament don’t quite match up — it’s gotta be related to the Fall somehow (didn’t God tell Adam “cursed is the temperament for thy sake; in sorrow shalt thou tune of it all the intervals of thy lyre” or something like that…

  3. I’m rather afraid this would only appeal to one person (me), but someone should figure out how to apply a quadratic function to soprano, flute, piano, and percussion and come up with a setting of this poem.

    1. they’re not necessarily involved, it just makes finding the solutions to tan theta easier. You have to sub tan theta back into the equation.

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