There’s a fascinating little video making the rounds right now, on the relationships of 3, 6, and 9 to circles, the universe, nothing, and, well, everything:
Reminded me of Professor Tranh and his drangles. And, of course, the story.
I was ALL about words when I was a kid. Words made stories, and I was a storyteller, so it all made sense. Anything with words, I nailed.
Numbers didn’t make sense. Numbers were useful, I had nothing against them, but it certainly wasn’t like they made stories. All you could ever make out of numbers was…more numbers. I just didn’t see the point.
So what I mostly did in math class was become very good at avoiding it. I put more effort into getting out of math tests than most people put into studying it. I argued, got sick, ran errands for the teacher, even spelled my way out of quizzes.* When I finally grew breasts–apparently my math teachers were serious breast men–I did very well in calculus.
I did just enough homework, passed just enough testing to get by, but what I didn’t really do was learn math.
Since I majored in physics and electrical engineering in college,** that was kind of a handicap, and it puzzled the engineering department. The transcripts said I’d passed calculus with flying colors; the evidence said I needed to acquire core math skills, fast.
Which is how I wound up in Professor Tranh’s Trig 101.
Dr. Tranh was brought in at the last minute to handle the overflow demand for remedial math students like me, and was maybe the worst hire the university could have made. On paper, his credentials were impeccable; he was the former chairman of mathematics at a prestigious college in southeast Asia.
He was rumored to have been one of the shining lights in some abstruse branch of higher mathematics, but had barely escaped with his life when his country was invaded. The feds had temporarily parked him in our town, which is how he wound up teaching remedial math.
The gurus at CalTech would find him soon enough and he’d be gone, but for now he was teaching trig…and it was a disaster. The big problem: Although his written English was good enough, Professor Tranh could barely speak English.
Fifteen minutes into his first lecture, he realized we had no earthly clue what he was saying, so he took to writing key points on the board as he spoke. It became a Rosetta Stone of sorts; every time we looked puzzled, he’d simply point to the correct word on the board:
- Drangle: Triangle
- Schleeves: Isoceles
- Road angles: Right triangles
- Cussing: Cosine
- Shy: Sine
- Treenotree: Trigonometry
- Danger: Tangent
Another big problem: Dr. Tranh really didn’t understand the average American college student culture, or at least not at the level in this class. A college trig class doesn’t exactly attract the best and brightest math students; most were simply trying to check off a box on a requirements list.
Dr. Tranh didn’t have much patience with people who didn’t love math, and he sure as hell didn’t get the lack of appreciation for little things like life, liberty, and the pursuit of boredom.
The idea that a whole classroom of semi-adults could float into his class, settle into suspended animation and absorb absolutely nothing of his beloved mathematics three days each week for an entire semester absolutely astounded him.
“This is your education,” he’d plead, almost in tears. “Your money. Your life. You don’t even care?”
Me? I cared. For the first time in a math class I was really trying to learn this stuff, but the numbers were staying numbers. I was flunking tests and not understanding the homework. No longer trying to just float past on good-enough-to-get-by, I needed to understand.
I’d never had to study for anything until now, and now that I was studying, it wasn’t working. So I looked up his office hours and went to ask for help.
“What are YOU doing here?” he asked, obviously astonished, “Nobody ever comes, you don’t care.”
Apparently I was the only student who’d ever shown up. It took 30 minutes to convince him that I really did want coaching.
“You need calculus for physics (which, oddly enough, I was mostly acing, don’t ask me why), how can you not know treenotree? Your tests are very bad.”
This, I knew. But at last he agreed to coach me. We mostly worked at cross purposes. He’d explain a concept, I’d try to explain it back. He’d explode, “NO! NO! NO!!!!!”
Once he threw the chalk across the room.
Finally, he buried his head in his hands. “So stupid, so stupid!!!” He moved his hand and I saw there, on the side of his neck, jagged, melted skin.
The scar was time-worn and softened now, running from just behind his ear all jagged across his neck and down into the back of his collar. Whatever made it must have screamed fire across his back.
He caught me looking, and gestured with a hand that, I noticed, had a matching half-melted pinkie finger.
“Burn,” he said briefly, “The soldiers, when I’m a little kid, from a bomb. My friends died. My daddy sent me away to school and I learned math.”
“You’re very lucky. It’s good you are taking advantage…” and then he stopped, deep in thought. He’s given up on me, I thought, and started to gather my books to leave.
“Thanks for trying, ” I said, “I think I’m just not cut out for trig…”
“Wait…” he said, grabbing my arm, suddenly excited, “Okay, maybe we try something I learned at school when I was a boy. Look! We should make a deal, like in my country.”
“In my country we don’t have quizzes and tests. We have just one test, at the end.”
He ran to the board, started erasing. “I will make you a deal. You watch this now. You watch this first!”
“OK…” I said, cautiously.
“Now, you look, and try this, and I will erase all your test results to now. At the end of class I will give you the final. What score you get on that test, that score is your grade for the whole class, just like it happens in my country for math classes.”
“We do it that way because it is a comprehensive test, it shows everything you have learned all year. Or maybe what you didn’t learn, either way. OK?”
He gestured for me to join him at the board, picked up the chalk, and started to draw. “You don’t see the beauty! See why the circle lives with the drangle inside. You don’t understand that. That’s why you don’t understand treenotree. Look! See the beauty!”
He drew a big circle. Inside the circle, to the right, he drew a triangle that engraved contrails within and without, and as it did, he pointed out how it left an indelible record of its presence within the circle.
And I realized suddenly what he was doing: He was charting relationships. He was telling the story of numbers.
The triangle lived within the circle, moved purposefully. Its actions had measured effects, and it was telling its own story. I suddenly understood.
How come no one had ever told it this way before?
There it was, the mathematics unfolding from Dr. Tranh’s excited fingers, the story of the relationship between a circle and a triangle. The tale of how they shaped rhythms and periodicities and music and engines and computers and all the technologies I’ve grown to love.
We spent the next hour playing with the shapes on the board–for those of you who haven’t twigged to this yet, this is called the unit circle–and Dr. Tranh quickly led me through a half-dozen exercises in the back of the chapters. Now that I could SEE how the triangle moved inside the circle it was pretty obvious how to solve the problems.
And Dr. Tranh smiled. “You don’t need to come back, just study for the final.”
I got an A.
I still see the beauty of the circle that lives with the drangle inside.
Thank you, Dr. Tranh.
*Not kidding. My high school algebra teacher couldn’t spell to save his life and was fascinated by the fact that I could, so he cut me a deal: For every test I wanted to skip, all I had to do was spell any ten words he gave me correctly and I’d get an A on the test. I aced every test that year except the final (he wouldn’t let me spell my way out of that one). Of course, I couldn’t solve a quadratic equation to save my life, but hey…
**ADDENDUM: Once this post was published, I got a puzzled note from my sister, “I thought you majored in journalism?” so I should probably explain: Majoring is not the same as GRADUATING. By the time I actually graduated with a gen-u-wine degree I’d majored in agriculture, art, genetics, public relations, botany, physics, journalism, electrical engineering…and even math.
Mostly, I stayed with electrical engineering, but toward the end of my lengthy college career I started planning a wedding (mine), and knew I’d be the breadwinner while my husband finished his degree. I had only one more semester to go in EE…I thought.
Then it turned out the courses I needed were spread out over the next three semesters. I already had enough credits for a degree in journalism, so that’s what it reads on the diploma. By the time I considered going back to finish the EE I was already writing about computers for my first magazine and never really felt the need.