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opportunity to finish the next three problems of his assignment. Then he glanced at the board.
    “Two hundred one point one centimeters,” Joel said before Layton even finished writing. Joel looked back down at his paper, figuring the last problem. “You need to practice your sketches, Professor. The proportions on that cylinder are way off.”
    “Excuse me?” Layton said.
    Joel joined Layton at the board. “The slant length is supposed to be twelve centimeters, right?”
    Layton nodded.
    “Then proportionately,” Joel said, reaching up and redrawing the cone, “the radius of the bottom circle needs to be this long, if you want it to accurately reflect a proportionate measurement of four centimeters.”
    Layton stood for a moment, looking at the corrected diagram. Then he pulled out a ruler and made the measurements. He paled slightly. “You could tell by eye that my drawing was off by a couple centimeters?”
    Joel shrugged.
    “Draw me a line one third the length of the slant length,” Layton ordered.
    Joel drew a line. Layton measured it. “Accurate,” he said, “to the millimeter! Can you do a circle with that radius?”
    Joel did so, drawing a wide circle on the board. Layton measured the circle by getting out a string. He whistled. “Joel, these proportions are perfect ! The arc on your circle is almost as exact as if it were drawn by a compass! You should have been a Rithmatist!”
    Joel glanced away, shoving his hands in his pockets. “About eight years too late for that,” he muttered.
    Layton hesitated, then glanced at him. “Yes,” he said. “I guess it is. But, well, you mean to tell me you sat there in class all this time knowing how to do this ?”
    Joel shrugged.
    “You must have been bored out of your mind!”
    Joel shrugged again.
    “I can’t believe it,” Layton said. “Look, how about we do your summer elective as a trigonometry study?”
    “I know trig already,” Joel said.
    “Oh,” Layton said. “Algebra?”
    “Know it,” Joel said.
    Layton rubbed his chin.
    “Look,” Joel said. “Can I please just pass geometry? I have plans for summer elective. If I can’t make them work … well, I’ll do calculus or something with you.”
    “Well,” Layton said, still regarding the board. “Really is a shame you’re not a Rithmatist.…”
    You’re telling me.
    “Did you learn this from your father?” Layton asked. “I understand he was something of an armchair mathematician himself.”
    “Kind of,” Joel said. Layton was new to the campus, having arrived at the academy just a few months back. He hadn’t known Joel’s father.
    “All right,” Layton said, throwing up his hands. “You can pass. I can’t imagine spending three months trying to train you in something you already know so well.”
    Joel let out a deep sigh of relief.
    “Joel, just try to do your assignments, all right?”
    Joel nodded eagerly, rushing back to get his books from his desk. On top of them were the two books that belonged to Professor Fitch.
    Maybe the day wasn’t a loss quite yet.



CHAPTER

    Joel left Professor Layton’s lecture hall, stepping out onto the grass. A girl in a white skirt and a grey sweater sat outside, back to the brick wall of the building, sketching idly in her notebook. She looked up, curly red hair bouncing as she inspected Joel. It was Melody, one of the Rithmatists in the class.
    “Oh, is he done with you?” she asked.
    Joel nodded.
    “Well, you’re still in one piece,” Melody said. “I guess that’s a good sign. No bite marks, no broken bones…”
    “You were waiting for me?” Joel asked, frowning.
    “No, silly,” she said. “Professor Boring asked me to stay and talk to him once he was finished with you. Probably means I’m failing. Again.”

    Joel glanced at her notebook. He’d watched her all semester, imagining the complex Rithmatic defensive circles she was drawing. On the pages, however, he didn’t see Lines of Warding, Forbiddance, or even