The Rithmatist

shock. “You think I’m cheating ?”
    Layton began to write on his paper. “I didn’t say that. I can’t prove anything—and at Armedius, we don’t make accusations we can’t prove. However, it is within my power to recommend you for a remedial geometry tutelage.”
    Joel felt his hopes of a free elective begin to crack—replaced with a horrifying image of spending each and every summer day studying basic geometry. Area of a cone. Area of a triangle. Radius of a circle.
    “No!” Joel said. “You can’t!”
    “I can indeed. I don’t know where you got the answers or who was helping you, but we’re going to be spending a lot of time together, you and I. You’ll come out of your summer elective class knowing geometry one way or another.”
    “I do know it,” Joel said, frantic. “Look, what if I do my homework right now? There’s still a few minutes left of class. Then I’ll have another assignment done. Will that let me pass?” He snatched a pen from its place on Layton’s desk, then opened the notebook.
    “Joel,” Layton said sufferingly.
    First problem, Joel thought. Find the area of the three highlighted sections of the cone. The figure was of a cone with two segments removed, with lengths and measurements of the various sides given at the bottom. Joel glanced at the numbers, did the calculations, and wrote a number.
    Layton put a hand on his shoulder. “Joel, that’s not going to help.…”
    He trailed off as Joel glanced at the second question. The computation was easy. Joel wrote down the answer. The next figure was of a cube with a cylinder cut out, and the problem asked for the surface area of the object. Joel scribbled down an answer for that one.
    “Joel,” Layton said. “Where did you get those answers? Who gave them to you?”
    Joel finished the next two problems.
    “If you’d already gotten the answers from someone,” Layton said, “why didn’t you just write them down earlier? You went to all the trouble of cheating, then forgot to actually do the assignment?”
    “I don’t cheat, ” Joel said, scribbling the next answer. “Why would I need to do something like that?”
    “Joel,” Layton said, folding his arms. “Those problems are supposed to take at least five minutes each. You expect me to believe you’re doing them in your head?”
    Joel shrugged. “They’re basic stuff.”
    Layton snorted. He walked to the board, drawing a quick cone, then writing some numbers on the board. Joel took the 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