“Now you’ll be able to appreciate the genius of this method.” Glaucus was unaware that his hand was trembling over the parchments. He radiated so much enthusiasm he looked like a madman. “Pay attention, because this is the key to everything: the side of the duplicated polygon is the hypotenuse of a triangle whose long side is half the length of the side of the original polygon, and whose short side is the difference between the radius and the long side of another triangle whose short side is half the length of the side of the original polygon, and its hypotenuse is the radius.”
Complete silence descended on the banquet hall, as if these words had stopped time.
I got lost from the beginning, thought Akenon, slightly embarrassed. From the corner of his eye, he observed his companions who were as still as statues, staring intently at the parchments. He concentrated on the drawings as well, trying to extract some conclusion.
Ariadne contemplated the geometric figures, trying to recreate Glaucus’ explanations. She concentrated on obtaining the eight-sided polygon from the four-sided one. After a while, she managed to do it, impressed with the process, and then immersed herself again in the diagram to see if the method could also be used to obtain the sixteen-sided polygon from the eight-sided one.
“It works,” she whispered in amazement after a while.
She turned to Evander, who had just finished checking it for himself. The grand master had the same astonished expression as Ariadne. If they hadn’t been standing next to their potential enemy, they would happily have stayed for days, exploring the geometric world they had just discovered.
Akenon continued looking at the diagram, frowning, and finally gave up. Maybe he would be able to understand it by analyzing it in his own time in a relaxed, safe environment, but he certainly couldn’t do it there. His priority was the investigation, and everything else was very much secondary. However, he respected the importance it had for the Pythagoreans, and could sense the enormous magnitude of that geometric discovery.
Glaucus stood there in expectant silence, giving them time to assimilate the method. When he saw that Ariadne and Evander had understood it, he was disappointed they didn’t get as carried away with euphoria as he had.
Evander spoke in an absent tone, without taking his eyes off the parchments.
“How many sides have been obtained by doubling?”
“Two hundred fifty-six,” replied Glaucus proudly, as if the merit were all his. “He’s done the doubling six times, starting from the square. The operations are cumbersome, but the discoverer has a superhuman ability to do numerical calculations. Besides, he uses numbers in a strange way, different than what I had seen up to now. As you can see from the parchments, it's an ingenious and very efficient method.”
Ariadne turned to Glaucus, almost afraid to ask.
“What approximation did he obtain?”
“3.1415. But don’t be in such a hurry, my dear brothers. I’m going to order a copy of all the parchments to be made so you can take it back to Croton with you.”
“You’re very kind, Glaucus.” Ariadne smiled in gratitude, but she feared that a new change of heart in the Sybarite would make him retract his offer. Because of that, she continued trying to memorize as much as she could of the parchments, as did Evander, while she continued asking questions. “How do you know the approximation is correct?”
“The method is correct, as you can see. As for the calculations, I’ve spent days poring over them, trying to understand the ingenious way of using numbers which makes it possible. Besides…there’s still something I haven’t told you.”
His tone made Ariadne and Evander look up.
“The discoverer of the method realized something else. Much more, actually.” Glaucus paused. His eyes shone feverishly. “Every time we double the number of sides of the polygons, the figure obtained for the quotient increases. The increment tends to be four times less with each doubling. The inventor of the method didn’t show me the reason for this, and I’m still working on it, but if we start at a particular point and follow this rule instead of duplicating the polygons, the calculations are much simpler and we can make quicker progress. The person who discovered this applied the rule starting with the two hundred fifty-six-sided polygon. In eight steps you can obtain an approximation to eight decimal places: 3.14159265. [6]
Both Ariadne and Evander were completely dumbfounded. That went beyond everything imaginable. When they finally managed to react, they immersed themselves avidly in the parchments, trying to corroborate what they had just heard.
Right, they’ve gotten what they were looking for, thought Akenon impatiently. From the folds of his tunic, he pulled out the gold coins he had taken from the Council secretary. The same coins Eritrius had confirmed were minted by Glaucus.
“Glaucus, do you recognize these coins?”
The Sybarite took one, studied it for a few moments, and nodded with a frown.
“Of course. They’re the coins I used to pay for all this,” he waved his hand over the parchments.
“Who did you pay?” asked Akenon, elated.
“I can’t tell you his name, as I don’t know it.” Glaucus’ satisfied expression darkened slightly as he thought back. “His face was hidden behind a black metal mask and he wore a hood which he kept pulled up all the time. He was slightly stooped, though sometimes he stretched and seemed as tall as I am. His voice was deep, the deepest I’ve ever heard, but it was also strange, broken… Though now that I think of it, I only heard him whisper.”
“Could he have been disguising his real voice?” enquired Akenon, after discreetly looking in Ariadne’s direction. She was supposed to analyze Glaucus while he was being questioned, to determine if he was telling the truth.
“Maybe, but I doubt it. I can’t see how it would be possible to simulate that voice.” Glaucus’ large body shivered suddenly and his face paled. “The truth is everything about him seemed unsettling and sinister. I never got to see his eyes, but when he looked at me I felt he was reading my mind in a way I’ve only ever experienced with Pythagoras. And inside him…” he turned to Ariadne, as if apologizing, “I sensed even greater power than I perceived in Pythagoras.”
Akenon looked at Ariadne. She nodded almost imperceptibly, confirming that Glaucus wasn’t lying.
“So then,” continued Akenon, “you can’t tell us anything about his physical appearance?”
Glaucus looked vaguely ahead of him and nodded slowly.
“On one occasion, the hood loosened a bit. I got a glimpse of some skin on his neck and head. It was wrinkled and aged. I’d say he’s at least sixty, maybe seventy…though from his hands and the way he moves he doesn’t seem that old.”
He certainly can’t be an invalid, thought Akenon. He was sure the masked man Glaucus was talking about was the hooded man who had left him out cold beside the stables at the inn after killing Atma. He must have been wearing the black mask then, which explains why we couldn’t see anything under the hood.
“Did he come on his own to your palace?” Akenon continued questioning.
Glaucus’ face lit up, happy to be able to give more precise information.
“One servant accompanied him. Greek, tall, about forty years old. By the way he behaved, I’d say he was a soldier.”
Crisipo!
Akenon clenched his jaw. The pieces kept falling into place.
“More or less my height, thin, intelligent looking?”
“Yes, yes. That’s right. Do you know him?”
“I have my suspicions. But let’s go back to the gold. Did the masked man ask you to mint it?”
“Yes. It was a surprising request. He said he wanted it all in coins, as if he intended to spend it all quickly in many small payments. I told him it would take at least a month before it was ready. I had to ask the authorities for permission, create a suitable stamp, and then cut all the gold into pieces of the right size and weight. Lastly, the minting process itself would take at least a week.” He frowned as
he remembered. “The masked man didn’t speak or move a single muscle while I explained this to him. When I was finished, he whispered slowly in his strange voice: ‘I’ll come back for it in three days.’” Glaucus shook his head. “By Cerberus’ three heads, you had to have heard his voice! It was impossible to refuse him!”
The Sybarite exhaled noisily, discomfited by the memory, and continued.
“The first thing I had to do was forget about permits or administrative procedures. I paid a little here and there to bypass the legal obstacles, and we began minting that same day. As we had no time to make a new stamp, we used others which had been used for minting silver. Neither the mint workers nor I slept a wink in three days. Some spent the whole time cutting and weighing the gold while others minted it.”
“Why did you put your name on the coins?”
“Normally it’s an honor for your name to appear on a coin. However, in this case I had it put on to try and minimize any problems I might encounter as a result of issuing currency with the Sybaris stamp without having sought prior approval from the authorities.”
Ariadne had been dividing her attention between the questioning and the discovery. Now she peeled herself away from the parchments, leaving Evander alone to absorb their contents. Keeping abreast of the investigation was very important to her.
“Did you manage to mint all the gold?” Akenon was asking Glaucus.
“Practically all of it. We still had a little over two hundred pounds left to do, but the masked man returned on the third day and said he couldn’t wait. He took the three thousand pounds as it was.”
“How did they transport it?” asked Ariadne.
“The prize included transportation of the gold to wherever the winner wished it delivered. I couldn’t imagine what he would ask of me, but I’ve already told you it’s very hard to say no to anything the masked man asks. He told me to take the gold to the port and make a ship available to him with enough crew and provisions to sail for a week, unload the prize and transport it by land for a day.” Glaucus shrugged. “I did everything he asked, and they set sail immediately. I stayed in the port, watching the boat sail eastward until it disappeared beyond the horizon. I thought it might be headed for Corinth or Athens.”
The masked man was probably trying to throw us off his scent, thought Akenon.
“Has the crew returned? I’d like to talk to them.”
“Not yet, but I expect them back in two or three days. I’ll let you know when they arrive.”
Ariadne remained silent, reflecting. The enemy leaves more and more clues. Through the crew, they’d probably be able to get a bit closer to the mysterious masked man. She glanced at the parchments, in which Evander was still absorbed, and shook her head. The mind of that enemy seemed capable of anything.
And now he has an enormous amount of gold. A bad combination, she worried.
Glaucus suddenly called Ariadne and Akenon’s attention.
“There’s still something I haven’t told you.”
He paused, and Akenon sensed he wasn’t going to like what was coming.
“In exchange for the prize, the masked man explained the method for duplicating polygons and gave me the approximation to four decimal places I had asked for. But, as I told you, he also showed me a faster way to approximate the quotient, and gave me an approximation to eight decimal places. He didn’t share the last part with me out of generosity. He did it in exchange for something I had that he was very interested in taking with him.”
Akenon held his breath as Glaucus finished.
“The masked man is now Boreas’ master.”
CHAPTER 82
July 4th, 510 B.C.
The masked man took a handful of coins from a large earthenware jar full of gold. He put them into a bag and went out, keeping his head down. Then he locked the small vault, which was part of a much larger underground storeroom. He was in his latest acquisition, a villa set some distance away from the most frequented roads. He had bought it through Crisipo, using the remainder of Daaruk’s gold, counting on the fact that he would soon claim Glaucus’ prize.
He smiled in satisfaction. Now he had two lairs, and had distributed half the gold from the prize in each.
And now I also have two servants.
The first time he crossed the courtyard in Glaucus’ palace, he had felt an intense presence behind him, watching him. When he turned around, he had seen nothing. Boreas was spying on him through a gap in the curtains, hidden in the shadows of some room on the upper floor. The masked man had kept walking until he reached the great hall where Glaucus was, explained the method of calculating the quotient by duplicating polygons, and then asked him to show him the slave he was hiding.
“What slave?” replied Glaucus, tensing.
“The one who’s lurking in the shadows,” answered the masked man, though he hadn’t actually seen Boreas. “The one who is stronger than any other man.” Glaucus shifted uncomfortably, and the masked man came closer to him so he could whisper in his ear, “The one who enjoys killing.”
A minute later, Boreas was standing in front of them, escorted by two guards it seemed he could have flattened with one hand. Glaucus avoided looking at him, as if the sight of him brought back very unpleasant memories. The masked man, on the other hand, fixed the giant with an intense look and discovered that, in many ways, they were kindred spirits. He also detected that Boreas would be happier having him as master. He asked Glaucus to add Boreas to the prize. If he did, he’d not only give him an approximation to four decimal places, but another to eight. Glaucus hesitated longer than the masked man expected, but finally agreed.
Now Boreas was his, and the masked man was overjoyed to have had the good fortune to find him. Not only had he been an unexpected discovery, Boreas was also, as he would shortly demonstrate, a tremendously efficient acquisition.
Boreas was strolling through the woods around the villa, enjoying the novelty of not having to spend all day cooped up indoors. After two months in hiding from Glaucus, he now found the fresh air especially enjoyable. However, his greatest source of satisfaction was having changed masters.
They had arrived at the villa a week ago. The first thing they had done was to transfer the gold from the mules to the storeroom under the house. There were seven men in total: four crew members from Glaucus’ ship, the masked man, Crisipo, and him.
When they were all in the storeroom, putting away the gold, the masked man asked Crisipo to come to him. Boreas paid no attention and continued carrying sacks of gold. Then the masked man addressed him.
“Boreas,” he whispered in his guttural voice, “show me what you’re capable of.”
The giant looked at the masked man to confirm what he was asking. He couldn’t see his eyes, but didn’t need to. Instantly, he felt his senses becoming more acute while his heart rate increased. He crept up behind the ship’s captain and with one swift movement took his sword. When the captain turned around, surprised, Boreas struck with all his strength. He wanted to impress his new master. The sword sliced into the captain’s body between shoulder and neck, continued diagonally through his torso, and exited at his opposite hip. Before he could utter a single word, the captain’s body fell to the ground in two pieces.
Panic erupted.
Although the dead man’s companions tried to save themselves, they were too slow for Boreas and too stunned. The giant wielded the captain’s sword in a vertiginous arc and decapitated the man closest to him, hearing cries of hysterical terror when the head separated from the body. Next he took two steps and thrust the weapon into another man’s abdomen. He lifted the unfortunate skewered man, twisted the hilt of the sword ninety degrees and jerked it upwards, pulling it out at the man’s collarbone.
Then he turned calmly toward his final target.
The sailor walked backwards, trembling, until the wall impeded his movement. He made no attempt to pull out his knife. Boreas was about to use the sword again, but thought better of it. The master
said “show me what you’re capable of.” He dropped the weapon, gripped the man by the throat, and lifted him with his left arm. Then he walked over to the masked man.
Beside the master stood Crisipo, white with terror, surely fearing he’d be next.
That depends on our master’s wishes, thought Boreas.
When he was a couple of steps away, he extended the arm from which the man dangled, kicking frantically. He pulled back his other arm, curled his fist, and let fly with a brutal punch.
The man’s dead body slithered from his hand to the ground.
Boreas was covered in blood. He had destroyed all four crew members in a minute.
Maybe too fast, he thought, looking at the black mask.
The masked man was intently focused on him. Boreas sensed that under the unchanging metal features, a pair of eyes were looking within him, and a pair of lips were curving in a wide smile.
The master was satisfied.
CHAPTER 83
July 4th, 510 B.C.
Theano went to the house where she lived with Pythagoras to get a parchment for that evening’s reading with her disciples. With her usual elegant gait, she crossed the inner courtyard and went into her room, lighting the way with an oil lamp. As she crossed the courtyard, she didn’t notice that the door to the pantry was ajar.
Behind her, a pair of eyes anxiously followed her every move.
A minute later, she emerged from the room, made her way back across the courtyard, and out into the balmy night of the compound. The person hiding in the pantry waited a while before coming out of hiding. Out in the open, the rays of the waning moon revealed that it was Ariadne.
Almost on tiptoe, Ariadne hurried to her mother’s room. She looked behind her, took a deep breath, and went in, closing the door. Inside, the room was illuminated only by the moonlight that filtered through the window. It was enough for her purposes.
She knew her mother’s room well. It was furnished with a wooden-framed bed, a beautiful chest with delicate carvings that had belonged to her family, a chair, and a table that was always covered with parchments.
Killing Pythagoras (Mediterranean Prize Winner 2015) Page 37
