A Midsummer's Equation

FORTY

Yukawa had placed three paper triangles on the table. He’d stacked three sheets of paper and cut them out at the same time, so they would be identical. First, he stuck two of the triangles together to make a parallelogram, then he added the third to form a trapezoid.

“See? Put the three inside angles together, and you get a straight line. In other words, 180 degrees. This is the basis for the rest of our calculations. You can make a square by putting two triangles together, which means that the sum of its inside angles is two times 180, so 360 degrees. Similarly, with a pentagram…”

Yukawa was going out of his way to make everything clear, but to no avail. Kyohei’s mind was off in a different place. Last night, before he went up to bed, he wandered down to check in with his uncle and aunt and heard hushed voices spilling out into the hallway by their apartment. He couldn’t catch everything they said, but one thing he heard crystal clear:

“He knows. That professor knows.”

It was Uncle Shigehiro’s voice.

Kyohei had crouched, frozen in place. Gradually, he forced himself to turn around and walk quietly back down the hallway, straining to step quietly across the old floorboards.

He’d gone straight up to his room and crawled into his futon. A horrible, black premonition pushed down on his chest, and it felt like his heart would never stop racing. He was being kept in the dark, but he wasn’t stupid. Something was happening, something bad. Why else would his uncle talk like that, in a voice that made him sound like a horrible person saying horrible things?

At some point, Yukawa had stopped talking. Kyohei looked up. The physicist was resting his chin on his hands, staring at him as though observing some experimental test subject.

Kyohei scratched his head and looked down at the table. Yukawa had drawn several diagrams in a notebook spread out on the table. The most recent one was a shape with nine sides.

“I asked you how many triangles you can divide a nonagon into, but from that look on your face, I don’t have my hopes up for an answer.”

“Uh … right…” Kyohei hurriedly picked up his mechanical pencil, but he wasn’t even sure where to begin.

“Pick one corner, then draw lines from that corner to every other corner, except the ones right next to it. That means you can only draw six lines, giving you seven triangles. The sum of their inside angles is seven times 180 degrees, so 1,260 degrees.” Yukawa reached across the table and wrote the calculation in the notebook. He wrote upside down so Kyohei could read it, the pencil moving even faster than Kyohei could have written it right side up.

“What’s the matter?” The physicist raised an inquisitive eyebrow. “You aren’t focusing at all today. Something on your mind?”

“No,” Kyohei said, unable to come up with a good excuse. When his phone began to ring, he reached for it, thinking, Saved by the bell. But he didn’t recognize the number on the display.

“Aren’t you going to answer that?” Yukawa asked.

“My mom told me never to answer the phone if I don’t recognize the number.”

“The number wouldn’t happen to be…” Yukawa said, rattling off ten digits in rapid succession, “… would it?”

Kyohei jerked in his seat. “Yeah. How’d you know?” He held up the phone to Yukawa.

“It’s for me,” Yukawa said, snatching the phone from Kyohei’s hand and answering it as though he’d done nothing out of the ordinary at all. “Yeah,” he said. “No problem. You find anything out after that?” He stood and left the room, still talking.

Hey, that’s my phone, Kyohei thought, standing with a scowl. He went over to the door and opened it a little. He could see Yukawa standing with his back to the room, phone pressed to his ear.

“I see. Ogikubo? Yes, that’s probably it, then. I knew it had something to do with the family. Right, good idea.”

Kyohei slid the door shut and stepped quietly back to his spot at the table. His knees were trembling, just like they had the night before. His uncle’s voice echoed in his ears.

“He knows. That professor knows.”