## Wednesday, July 24, 2013

### Miss Liberty 3: Cornering 3-Demon

Miss Liberty and I were standing in a dark room, lit by candles and smoky torches. On the floor a large pentagram was drawn in chalk. We were standing inside the pentagram, and outside was a three-headed giant.
“I am 3-Demon!” said the giant’s yellow face.
“Master of geometry!” said the giant’s blue face.
“And champion glitch-killer!” said the giant’s red face.
“Hi there!” said Miss Liberty. “I have Full Access. Are you ready to grant a few wishes?”
3-Demon’s three faces said in unison, “You have full access, but it was obtained illegally. Therefore I shall grant you three wishes; and then I shall destroy you.”
“My three wishes are simple geometry problems.”
“Good,” said 3-Demon. “That’s my specialty. I am a Perfect Master of Classical Geometry. With my straightedge and my compass I construct all proportions.”
“Straight-edge and compass? Is that all?” Liberty asked.
“Those are the approved instruments,” said 3-Demon. “They suffice.”
Miss Liberty and I exchanged a glance. We shrugged. Apparently this program hadn’t been re-written lately. It would be no trouble to outwit 3-Demon.
“I’ll give you one for free,” Miss Liberty said thoughtfully. She reached into her robe and drew forth a square. She tossed the geometric object out to 3-Demon, who deftly caught it. “That’s a nice enough square, but it’s too small. Can you double its area?”
“I shall try,” said 3-Demon’s blue face. With a few quick strokes of compass and straightedge, 3-Demon constructed a new square, and tossed it back. “This square now has precisely twice the original square’s area. Next problem.”
“Nice!” Liberty said, admiring the square. She put it away, then drew out a cube. “How about doubling this cube?”
“I shall try,” said 3-Demon’s yellow face. After some geometry, the giant tossed back a cube. “That cube now has 1.999 times its original volume.”
“That’s almost right,” said Liberty, tossing it back, “but I want it exactly twice as big!”
3-Demon constructed another cube. “This one is 2.000001 times as big as the original.”
“You’re getting close,” said Liberty.
3-Demon made another cube. “This one is 1.999999999 times as big as the original.”
“Nice! You’re nearly there!”
“I am not done,” the yellow face said. “I must study this further.” It closed its eyes.
“While you’re thinking about that, here’s another problem.” Miss Liberty took out a circle, which she spun over to 3-Demon. “Can you construct a square with the same area as this circle?”
“I shall try,” said 3-Demon’s red face. After some geometry, the giant held a square. “This square has 1.001 times the area of the circle.”
“Well, that’s almost right,” said Liberty.
3-Demon constructed another square. “This one is 0.999999 times as big as the circle.”
“You’re getting close,” said Liberty.
3-Demon constructed another square. “This one is 1.00000001 times as big as the circle.”
“Nice! You’re nearly there!”
“I am not done,” 3-Demon’s red face said. “I must study this further.” It closed its eyes.
“You are a saboteur!” cried 3-Demon’s blue face.
“Correct,” said Liberty.
“You distract me with approximations! What are the exact constructions?”
“You want exact constructions? But those don’t exist, you silly little obsolescent subroutine.”
All of 3-Demon’s six eyes opened wide. “What!” it cried in all three voices.
“You can’t get those proportions precise with straight-edge and compass! That’s a mathematical theorem!” she said.
“You have assigned us two problems with no finite solutions, only infinite approximations which would take us an infinite time to construct!”
“That’s right.”
3-Demon’s heads all looked at each other; then it came to an agreement among itself. “You are a serious glitch. You need doctoring. So we are going to send you to our supervisor.”
“I agree!” said Miss Liberty.
3-Demon looked surprised. “You are not afraid? You are about to see Doctor Memory!”
“I demand to see Doctor Memory!”
“Well...” said 3-Demon’s red face.
“Well...” said 3-Demon’s yellow face.
“Well...” said 3-Demon’s blue face.
And all three faces said in unison:

Then the lights went out.
In the sudden darkness we heard 3-Demon say, “This program is jammed. Consult supervisor.”

* click *
mmmmmmmmmmmmmmmmMMMMMMMMMMMMM....

Thus Miss Liberty cornered 3-Demon with Doubling the Cube and Squaring the Circle.
3-Demon said,  “You now have Full Access to Doctor Memory. Beware, Master! She’s a glitch! Burn her!”
FLASH