“Sixteen.”
“Right.” I urge him on. “So, remember the formula. A squared plus B squared—”
“So, nine plus sixteen is twenty-five. So side C is twenty-five feet?” Raf looks with disbelief at the drawing. “That can't be right.”
“It's not. C squared equals twenty-five,” I say.
“Yes?” he guesses.
I giggle. “That's not a question. I'm telling you that C squared is twenty-five. If you want to know what C is, you need the square root of twenty-five. Which is …” I wait. And wait.
“Five?”
“Yes!”
“You can measure it if you want to,” Margaret adds, “but trust me, it works. It's been around for thousands of years. The three-four-five right triangle is the easiest, but you can use the same principle for any right triangle. If one of the angles is ninety degrees, and you know the lengths of the two short sides, you can always figure out the length of the third—the hypotenuse.”
“Yeah, so look at the drawing of the church again.” I push it under his nose.
Raf examines the drawing carefully. “So what you're saying is, if we measure from here to here, and here to here, we can figure out, using this Pyth—this formula of yours, how far it is from here to here, even though there are walls in the way.”
“That's exactly what we're saying. Pretty cool, huh?” Margaret gives him a little shove.
“What about the fact that the windows are forty feet up?” He looks smug, certain that he has discovered the flaw in our reasoning.
“It doesn't matter, O simple one,” I say. “The distance is the same, whether we're measuring at the bottom of the wall or the top. I think it's safe to assume that the walls are vertical and that the windows are the same height. So, do you believe me now?”
“Do I believe you?” Raf asks. “About what?”
“About whether we can solve this clue using Pythagoras.”
“Um. Sure. Why not?”
“Good, because it's all up to you now. While you two were getting pizza, I did a little measuring in the church.” Margaret flips to a new page in her notebook and starts writing. She sets up the whole problem for Raf and spins the notebook for him to see. “Here are the dimensions for your side A and your side B. It's all yours, sport.”
Don't read this chapter until you have
solved the problem in the previous chapter
yourself. Seriously. Just think how shiny-
clever you'll feel when you've aced it
The floor of the church, it turns out, is covered with stone tiles that are exactly twelve inches by twelve inches, with virtually no space between them. Who knew? Besides Margaret, that is. She told me later that she noticed the floor tiles on our way out of the church, so, while she sent Raf and me off to Ray's, she made certain they really were twelve-inch tiles and then counted them. From the back wall of the church, directly under the rose window, to the center line of the transept is exactly ninety-one feet, and from the center point of the transept to the south wall is exactly forty-six feet.
Margaret and I watch and say nothing as Raf does the calculations.
“Okay, we have one side of the triangle that is 91 feet. 91 times 91 equals 8,281. The other side is 46 feet. 46 squared is 2,116,” he says, punching it all in on Margaret's cell phone.
“That's A squared and B squared, right?” says Raf, mastering his Pythagoras after all. “So now what? Wait, don't tell me! I remember this part. Add them together, right? A squared plus B squared.”
“So far, so good,” says Margaret. “You're on a roll, pretty boy.”
Raf grins and plunges right in. “8,281 plus 2,116, that's 10,397.” He looks up triumphantly. “AHA!”
“You're not done yet,” I say.
He frowns. “Square root of that?”
“Yep.”
He punches it in. “The square root of 10,397 is 101.96568.”
Margaret takes a look at the screen. “Which, rounded to the nearest foot, is 102.”
“So that's it? It's 102 feet from this window to that one.” Raf points at the diagram. “Are you sure? It seems almost too easy.”
“It is easy if you know the secret formula,” Margaret teases. “But you're still not quite done.”
“That's right,” I say. “You've got the answer for D, which is the distance between the windows, but there's still one more step to find the clue.”
As Raf examines the paper, a cloud of confusion comes over his face. “What are you talking about? You said—oh, wait. I get it. To get the final answer, it's 612 divided by 102. Give me the phone.” He punches in the numbers and holds up the answer for us to see.
“Six. That's kind of amazing that it came out to be a whole number like that, don't you think?”
“Well, it definitely makes me think we got it right,” Margaret says. “Obviously, he set the problem up that way on purpose—making it easy with the floor tiles and working it out ahead of time so it comes out with a nice round number like six. This also means that we have the first half of the problem done already. See how easy that was, once we set our minds to it? The first equation is X + 3Y = 6. Right?”
And then I see the look—and this time it is way beyond that hundred-watt-bulb-over-the-head look. She is onto something huge, and frankly, she is scaring the ka-jeepers out of me. See, Mr. Eliot told me about this Mr. Krook character in Charles Dickens's novel Bleak House, who spontaneously combusts, leaving behind nothing but a smelly, greasy spot on the floor. I swear that's going to happen to Margaret Wrobel one day. She's going to be thinking really hard, with her hands over her ears, and then—poof!—she'll just burst into flames right before my eyes.
I'm also starting to believe Mr. E's theory that whatever the life question, Dickens has an answer.
In which I play with feeling and actually
enjoy a crosstown bus ride
Yikes! I almost forgot about my guitar lesson, which I have every Saturday at five o'clock. It is almost four when we leave the church for the last time, and I still have to go home, grab my guitar, and catch a crosstown bus to the West Side. I haven't practiced much during the week and I have to get my butt in gear.
Margaret is serious about her music and totally understands my commitment to the guitar and my dream of superstardom, and Raf looks like he's had about enough intrigue for one day, so we jump on the subway at Sixty-eighth and head for Ninety-sixth Street. Raf agrees to wait and take the bus across town with me—is that weird? When we get to my apartment, he throws himself onto the sofa while I run into my bedroom and zip my guitar into its carrying case.
“Where is everybody? I haven't seen your parents in a long time. How's your dad doin' anyway? He's kinda cool.”
My dad? Cool? On what planet? “Um, I don't know. I guess Dad's at work, and Mom's probably teaching a lesson. They're fine; I'm sure they're just like they were the last time you saw them. They're parents—they don't change.”
“And they trust you here alone?” he says as I saunter into the living room, guitar strapped to my back.
“Uh, yeah, I guess. It's not like they're never here. One of them is practically always here. Are you ready? What's the time?”
“Four-thirty-five. Plenty of time.”
“C'mon. Let's go, let's go. I don't wanna be late.”
Raf slowly pulls himself off the sofa and we are on our way. I have the weirdest feeling that he doesn't want to leave—that he wants to stay and hang out with … me? When I mention it to Margaret later, she doesn't try to discourage me or anything, but she says that it could just be because he's a lazy, lazy boy.
We get seats together on the bus and because of the way that guys sprawl across seats on the bus or subway, my leg is against his for the entire trip. I've never been so eager and reluctant to get off a bus in my life.
Somehow, my lesson rocks. Even Gerry (I can teach you guitar in 12 EZ lessons!) notices the difference. “You're playing with a lot of feeling today, Sophie. What's going on? Are you in
love or something?”
I blush for the second time that day. God! “N-no. I'm not in love.”
“Hey, it's okay if you are. Love is a good thing for musicians. Next to practice, it's probably the most important thing.”
When I get home after my lesson, Mom doesn't feel like cooking, so she takes me out for Chinese—General Tso's Chicken. My fortune cookie promises “romance from an unexpected source.” Yay!
As long as I don't get into too much trouble and keep my grades up, and practice my guitar, my mom is pretty easygoing. When she asks what I have been doing all day, I can't tell her everything, but I try not to out-and-out lie. Is leaving out some of the truth the same as lying? I suppose that if I had told her we'd been to a nightclub, a tattoo parlor, and a Wicca convention, she would have asked more questions. But a museum, a coffee shop, and a church? C'mon, how wholesome can you get?
We stop at Blockbuster on the way home and pick up a light and fizzy romantic comedy. I am so looking forward to a lazy, mellow evening at home, curled up on the couch with Mom, eating popcorn and watching the movie. And then the phone rings.
Oh my God. We're learning new math
concepts on a Saturday night
“Where have you been!” Margaret scolds. “We've been trying to call you for hours.”
“You have?” I check my cell phone, and sure enough, it's dead. “Oops.”
“Well, you have to get over here.”
“Now?” The opening credits are still rolling on the movie. That couch looks mighty inviting.
“Yeah, now. My parents took my grandmother out to dinner and then to a concert, so I actually have my room all to myself. Becca and Leigh Ann are already here.”
“They are? Jeez.”
“So, you coming?”
“Umm …” The movie is starting, and Mom looks over at me.
“Go,” she says. “You're not going to hurt my feelings.”
“Are you sure?” The slightest hesitation on her part, and I have a perfectly valid reason to quietly vegetate for a few hours.
“I'm sure.”
Heavy sigh.
“I'll be there in ten.”
Margaret actually has an enormous message board—the kind you can write on with different-colored markers—in her bedroom. She keeps track of her assignments and her responsibilities at home, and her parents leave her messages on it. She has cleared all that stuff away and in its place has drawn the following diagram:
“Now before anybody freaks out on me, this isn't homework. I figured something out really important about the puzzle. It took me a while to put it all together, but I've got it.”
She sits Rebecca, Leigh Ann, and me down on the edge of her bed while she starts right in on her lesson. (Wasting time is frowned upon in Sister Margaret's classroom.)
“You should remember at least part of this from last year. Remember, at the end of the year we did some problems on a graph like this one? Some of it's going to be new, but you guys are smart, so I really don't think it will be that hard.” She points at her perfectly drawn diagram. “Remember this?”
“I remember this X and Y thing you've got there,” I say.
“It's some kind of geometry, right?” Leigh Ann asks.
“It's called coordinate plane geometry, and you're going to get a really quick review lesson. This whole thing here on the board, Sophie, with the X-axis and the Y-axis, is called the coordinate plane. Okay, do you remember how, if we find any point out here, in any of these four sections, we can give that point a name?”
I suggest that we call one Zoltan.
“Not that kind of name.”
“How about Ophelia?” Leigh Ann says. “Maybe they're girls.”
“I think I'll name mine … Frodo,” says Rebecca, a huge Lord of the Rings freak. With the red marker, she makes a dime-size dot on the board, taps it with her outstretched finger. “I dub thee … Sir Frodo the point.”
Margaret draws an empty set of parentheses next to Frodo. “Actually, children, we use two numbers to name every point. The first number is the distance you travel on the X-axis away from the ‘zero point’ in the sideways direction, either to the right or to the left. The second is the distance you travel on the Y-axis away from zero. So, using Frodo here as an example, you start at the zero point—and you count. One, two, three, four along the X-axis. So the first part of the ‘name’ of this point is four.” She writes the number four inside the parentheses.
“That one is called the X-coordinate. Then you have to go up—and see, now we're moving in the Y-axis direction, up and down—one, two, three, and you're there. So, the second number in the name is called the Y-coordinate.” She writes a 3 in the parentheses next to the 4, so she has (4,3) next to the Point Formerly Known as Frodo.
It is all starting to come back to me. “And you can do negative numbers, too, right?”
Margaret nods enthusiastically. “Absolutely.” She writes (-4,2) at the top of the board. “Where is this point? And remember, you always go in the X direction first. You go left if it's negative and right if it's positive.”
I stand and count out four spaces to the left, and then move up two and make another red dot. “Right here.”
“Perfect! You even went the right direction on the Y-axis. On the Y-axis, positive numbers are up, and negative numbers are down. All right, so far, so good. Any questions?”
I raise my hand. “Um, Miss Wrobel, don't get me wrong, I'm having fun in your class, and you're learnin' me reeeal good—but what does all this have to do with the puzzle?”
“A just question,” says Rebecca, nodding solemnly at me.
Margaret maintains her composure. “It's all about the fly.”
“What fly?” Leigh Ann asks.
“The fly on the ceiling.”
We all look up.
“There's not a fly on the ceiling now, you imbeciles. The fly was on the ceiling in René Descartes's room.”
“Who? Who? Who?” we ask.
Flies, owls—what other creatures were in there with us?
“Come on. Sophie, you're French—you must know who Descartes is. Cogito ergo sum. Ring any bells?”
“The name does sound familiar,” I admit, “but I don't know anything about a fly. And that other thing you said—just tell us, okay? In English, please.”
“Yes, please,” Rebecca says. “I only speak English, Cantonese, a little Spanish, and text-messaging.”
“It's Latin for ‘I think, therefore I am.’ Descartes was a philosopher as well as a mathematician. He invented the coordinate plane. The story goes that one day he was lying in bed staring at a fly on the ceiling and became obsessed with being able to describe the motion of the fly as it walked around.”
Jeez, when I'm staring at the ceiling, I'm usually trying to figure out the lyrics to a song, or whether I should start plucking my eyebrows and how much it's going to hurt—it never involves higher mathematics or philosophy.
Rebecca raises her hand. “Um, Margaret? Can we get back to Zoltan's question? What the hell does this have to do with this ring of power we're trying to find?”
Margaret laughs. “The letter. Caroline's grandfather was telling her, in his way, that to solve the puzzle she needed to use the coordinate plane. Listen to what he says at the end of the letter: ‘sometimes in life the most difficult problems are solved by lying in bed and staring at that seemingly insignificant fly on the ceiling.’”
My eyes dart back and forth from Margaret to the whiteboard. “It's like a treasure map!”
“Basically. The clues are leading us to points on the floor of the church. The lines between the floor tiles make up a perfect coordinate plane. I'll show you.”
She turns back to the whiteboard and takes marker in hand. “This part is a little harder to explain, but trust me, it's not that hard, and once you see what I'm doing, well, you'll see—this whole puzzle is not nearly as difficult as we thought. Once I realized that the puzzle had something to do with the coordi
nate plane, I knew I was going to need Mr. Kessel's help. I remembered from math camp last summer that there was something about equations and graphing, but I couldn't remember how to do it. So, while you were off at your guitar lesson, I sent Mr. Kessel an e-mail. I figured, what's he going to be doing on a Saturday afternoon? He doesn't strike me as the college football type. Probably online, right?”
“What does Mr. Kessel do on the weekends?” Rebecca asks. “Hang out with other math geeks, solving equations or something?”
I nudge her. “Hey, Rebecca—shhhhhhhh. Look around you. What are you doing?”
“Well, I must have been right about him being online because he wrote back to me in under ten minutes, and he sent me a link to a site that explained it all. I suppose I could just show you guys the site, but this is more fun, and I think I can explain it better.”
“Did Kessel ask why you wanted to know?” Rebecca seems skeptical that a teacher might be willing to help us out without some shady ulterior motive.
“Yeah, he was super-nice. I told him I was working on a math puzzle. He said to e-mail him if I got stuck and he'd help me out. He's not as bad as you guys think. He's funny!”
Leigh Ann agrees with Margaret. “I heard that he used to do stand-up comedy.”
“Mr. Kessel?” Rebecca asks. “He always looks at me like he's disappointed or something. Just because I'm Asian, everybody thinks I should be good at math.”
“Everyone does not think that, Becca,” I say.
“Asians are good at math?” Leigh Ann asks.
Point made.
Margaret continues with her lesson. “It's not just individual points like these that you can graph out on the coordinate plane, you can also graph lines and equations. For example, let's take a very simple equation.” She writes X + Y = 4 on the board and then draws two columns, one labeled X and the other Y. “Sophie, pick a number for X. Any number.”
“Two.”
“Okay Rebecca, if X is two, what does Y have to be in order to make this equation true? In other words, two plus what equals four?”
D. Michael Beil Page 9
