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Proving the Pythagorean Theorem


Alec awoke uncharacteristically late in the morning, feeling refreshed and excited by what the day would hold. He jumped from bed and listened to his phone messages. The first one, from his mother, expressed concern about a news report she heard about a "terrorist situation" at the café on the late news.

She'd heard that "…no one had been injured due to the fast action of the anti-terrorist squad." Would he please call her first thing to let her know everything was OK? 

Two more messages were from Lenore and Jake. They had heard similar reports in the local media. Would he call them soon too? The last message was from Monty: "Forget the shenanigans last night. I want to see you when you come in this afternoon on your regular schedule. Stop by my office first thing."

Alec was more excited than he could remember feeling for a long time. He was beginning to feel engaged in something that was real and important. Quickly, he returned the phone messages with new recorded messages, then dressed for class that afternoon. If he hustled, he figured he would make it there just before Dr. Catania charged into the room to begin another assault on fuzzy thinking.

But Just before he could get onto Highway 12, the only route to the college, traffic came to a fitful creep. Fifteen minutes later, he was slowly passing a State Police checkpoint. Arriving late, he ran down the long halls and then burst into the Ancient Philosophy class.

"Well, I will try and explain to you what figure is. What do you say to this answer?—Figure is the only thing which always follows color." Dr. Max was reading from a book as he paced furiously across the room. The almost frenetic professor usually paced back and forth and around the room as he lectured and questioned. But as luck would have it, at this moment he was heading directly toward Alec as he entered.

"Mr. Booner," Dr. Catania said with a dour owl face, "our class starts promptly at two o'clock-every time. Please see me in my office after class."

Socrates directs Meno's slave boy, Anytus, to construct squares on the sides of a right triangle. Then, Socrates  leads the youth to deduce that the sum of (areas of) the two small squares equals (the area of) the large one. In algebraic terms, a2+b2=c2 where c is the hypotenuse while a and b are the legs of the triangle.

"Oh yes, back to the Meno, wherein Socrates directs Meno's slave boy, Anytus, to demonstrate the Pythagorean Theorem," Dr. Catania fairly shouted as he spun like a solider on his heels. He resumed his fast-paced, interpretative reading in English and Alec quickly found a desk in the back of the room. 

He sat, feeling like a mouse that must go unnoticed if it is to survive. Alec had intended to seek out Dr. Max after class. Now he had been summoned—not the best way to start, he thought glumly.

Like most students at Sundance, Alec knew of Dr. Max' reputation: the mad doctor façade in the class room; a gentle and understanding man outside of class. He had planned to talk to the professor about…generally, without blabbing, some of the big questions that he suddenly had about the ethics of promises to generals. Then, if there was time, he hoped that Dr. Max might have some pointers on the logic systems used in cryptography. Instead, it looked like their after-class meeting was going to have a different agenda. Alec slunk into a brown study for the rest of the class, only reviving briefly for Plato's account of how an unlettered slave boy came to discover the Pythagorean theorem—with only a bit of coaching from Socrates.





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