|(quoted from Aurora in Four Voices)|
"Open," he said.
He tried again. "Open."
Swirling lines and speckles appeared on the door and a holo formed, an amber rod hanging in front of the door. A curve appeared by the rod and rotated around it, sweeping out a shape. When it finished, a vase hung in the air with the rod piercing its center. Soothing pastel patterns swirled on the image.
"Solid of revolution complete," the door said. "Commence integration."
"What?" Jato asked. No door had ever asked him to "commence integration" before.
"Shall I produce a different solid?" it asked.
"I want you to open."
Silver and black swirls suffused the vase. "You must calculate the volume of the solid."
"Set up integral. Choose limits. Integrate. Computer assistance will be required."
"I have no idea how to do that."
"Then I cannot unlock."
Jato scratched his chin. "I know the volume of a box."
The vase faded and a box appeared. "Commence integration."
"Its volume is width times height times length."
Box and rod disappeared.
"Open," Jato said.
Still no response.
Jato wondered if the Innkeeper had his door vex all visitors this way. Then again, Dreamers would probably enjoy the game.