Once, long ago, there were two nation...

The nation called Archimedal was in the west, with rich resources and beautiful forests and rivers and mountains. The nation of Newtonia, in the east, was much more industrialized. They had factories and cities, and all their forests had been razed for lumber. They were at war with each. Archimedal wished to learn the industrial techniques of Newtonia, and Newtonia longed to acquire the vast resources of Archimedal. Unfortunately, between the two nations was the vast Sea of Hyperbola. The only possible way to get from one nation to the other was by boat. Archimedal couldn’t create good enough boats to get to all the way to the other side, and Newtonia had to few resources to use its industry to construct warships. Fortunately for both, right in the middle of the Sea of Hyperbola, was the large island Pythag. It was miles wide, with rivers and lakes and forests and beaches and even a mountain. The mountain was on the northern end of the island, and, growing at the very tippy-top, was the tallest oak tree anyone had ever seen. It was so tall it could be seen from the shores of both Archimedal and Newtonia, as far away as they were. Both nations wanted the island as a base, so as to be able to sail from there and then onto the other nation. The two kings of Archimedal and Newtonia rallied their forces and sent them off the claim the island. Archimedal sent 15,000 knights, with all their squires and cooks and armorers off to fight, while Newtonia sent their entire army of 25,000 Knights, with all their retainers and wives and squires and even the peasantry that lived in the lands held by the knights. All in all, Archimedal sent a total of 100,000 people off to conquer the island, and Newtonia sent 300,000. Meanwhile, as the two nations were filling their ships with food and drink and livestock, the knight of the island of Pythag, was watching the two massing armies. Unbeknownst to either nation, the Island of Pythag was a sacred place, as designated by the Great Spirit Hoken. The Knight of Pythag had been stationed on the island to help protect it from invaders. This noble knight was all alone on the island, except for his single squire, a young lad, barely having reached the age of 16. It was this boy that had first seen the rallying troops, as he patrolled the edges of the island on his daily route. As soon as he saw them, he rushed to the knight. “Sir!” he exclaimed, “The two surrounding nations are preparing for war, with us in between. I fear they may try to claim the island as a means of providing support.” The old knight, having known for some time this would happen, simply said to his squire, “It need not concern you, if you but do what I ask. You must take our cooking pot, and this rope, and put them in your traveling pack. Take care you do not lose either one, for if you do, all hope is lost.” The squire took the rope and the pot and placed them gently in his pack. “What will this accomplish, sir?” he asked. “By themselves, nothing,” said the knight, “Which is why that was merely the first step in the journey of protecting this island. Next, you must take the rope and the pot up to the northern part of the island, where you will find the island mountain. Up to the top you must climb, and what a perilous climb it will be. Howling winds and wild wolves and paths blocked by rocks and ice could all try to prevent you from reaching the summit. You must not let them. For once you reach the top, you will find the tallest oak tree you have ever seen. You must climb to the top of that tree, with the pot and rope and tie the pot to the very top branch using a noose. You must be very sure to tie it very tight, and it has to be a noose, no square knots or bowline knots. Once you have done that, look to the east, then look to the west. You should see a large eagle flying about the tree. Grab onto one of his legs, and use it to descend swiftly to the bottom of the mountain. Then, quickly make your way back to our camp so we can prepare to defend the island.” The squire had no idea how this would help, but knowing how wise the old knight was, he started on his journey. It was a long journey. He climbed hills and forded rivers. He felled trees and hunted deer for food. Many days past. Luckily, both the Nation of Archimedal and the Nation of Newtonia had very slow moving ships, and they were very far away. On his way to the bottom of the great hill, the young squire saw an owl flying overhead. When he finally made it to the bottom of the great mountain, he saw a long, winding path leading up to the top. He climbed and he climbed and he climbed all day. But in the end, he had made little progress up the side of the mountain. As he was laying down to sleep that night, he heard a rumbling noise. He looked up. There was an avalanche headed down the mountain side, right for him! He quickly scrambled to gather up his things, taking particular care to grab the cooking pot and rope before dashing back down the hill. Mid-way down, he stumbled and began rolling. Down and down he rolled, until he hit the bottom of the hill. As he stumbled up and began running away from the avalanche, a single tear rolled down his cheek. He would have cried more, but he knew that he had to be strong. He had to find a new way up the mountain, now that the path was covered. Instead of letting himself get some sleep that night, he made his way wearily around the mountain, searching for another path. By the time the sun had risen, he still had found no such path and was forced to conclude that he would have to make his own. So, he set on up the mountain, trying to take the easiest path possible, for he knew it would be a long journey. Up and up he climbed, day after day. Once, he thought he saw the eagle the old knight had spoken of, circling high above his head. But when a tried to look closer, he saw nothing at all. The night he finally made it to a spot half way up the mountain, as he was lying down to go to sleep, he noticed a strange rock on the ground next to him. It was in the shape of a nearly perfect 'H'. For reasons unknown to him, his eyes began to brim. The second tear of the journey fell from the corner of his eye. Maybe it won't be here in the morning, he thought. He told himself to hold it together, and promptly fell asleep. The next morning when he awoke the 'H' stone was still there, not having moved from the night before. Feeling ashamed at having been so dimwitted as to think a rock could move by itself, he began again on his long ascent up the mountain. He passed many dangers going up; snakes and scorpions and wolves and bears. But he wouldn't let any of them frighten him. Until finally, he reached the top of the mountain. There, just as the old knight had said, was the tallest oak tree the squire had ever seen. The young lad wept a third tear as the longest part of his journey was over. Now all he had to do was climb to the top of the tree. He soon found that that was more easily said than done. For while the bark of the tree provided adequate hand and footholds, the sap and branches seemed to cling to him as he climbed, and poked at him and held him back. As he was whipped in the face by a branch for the fifth time, he made up his mind. He was going to finish this climb today, or never. He fought his way boldly through the thick branches on the lower part of the tree, then began to carefully climb the rest of the way, with narrower branches. About half way up, he saw a sparrow resting on a branch on the opposite side of the tree as him. As he watched it, it began to call out in tis song. He listened, then, without so much as a noise, crept over to it to watch it more closely. It sensed his presence, however, and quickly took flight as he neared it. It swooped low down over the trees in the forest, and the squire watched it go. He began to shed his fourth and what would hopefully be final tear of the long hard journey. He was swept with a sense of awe as he gazed at the island he called home. There was so much beauty. He couldn't let it get destroyed by invaders. With renewed strength, he began climbing again. As he reached the top of the tree, he looked out, over the island once again, knowing that he would probably never see this view again. However, knowing that he didn't have all that much time, he quickly slipped the rope and pot out of his pack and tied the rope into a noose around the top most branch of the tree. He hung the pot from the noose, high above the rest of the island. Just as he was checking to make sure the pot was secure, he spotted the eagle the old knight had told him about. Using the old bird languages he had learned form the knight, the young squire called the bird over and grabbed its leg. The bird barely even dipped in the air as the squire clung to it, for it was old and incredibly strong. It knew right were to go. The squire was overjoyed to not have to make his way back across the island as the bird carried him back to the campsite the knight was using. They descended a little rough, but nothing the squire couldn't handle. "Your back." said the knight. "Good. For tomorrow the armies of Archimedal and Newtonia wll land on the island. Did you succeed in your task?" The squire told him that he had, but he still had no idea how that was suppose to help. The knight did not answer. He merely set about preparing for them a modest dinner of bread and cheese. That night, the squire stirred in his sleep, worrying about the coming battle. When they awoke, it was to the sound of war horns. The time had come to fight. Now, this wasn't exactly the most important battle ever, and knights were of royal blood, which nobody wanted to spill. So the knights sent out their squires to battle for them. The squires of Newtonia rushed forward onto the island near where the old knight and his squire stood, just as the squires of Archimedal did the same on the other side. The old knight quickly got out of the way, leaving his squire to himself. But not before telling him, "Remember: when things seems darkest, go to the mountain. Look up to the pot." Still unsure as to how this would help, the squire assured the old knight he would, and told him to stay safe. Then the tides of battle reached the young squire, and he found himself swept up. Both armies were fighting to gain an advantage on the other, and to do that, they had to take the area he was standing on. He couldn't let them do that. He drew his sword and began to try to drive them back, both sides. He quickly grew nearly exhausted from the effort, and yet both armies seemed to limitless. They pushed into the island, far and wide, long into the day. By about 5:00 at night, the squire realized they were on almost the same path he had taken to the mountain. They were driving him there! He couldn't let them get there. If the did, they would win. He could not hold them off ot the entire mountain. With this thought, he felt some of his strength come back and he began fighting anew. He manage to drive the armies back a few feet, but seemed that for every five feet he drove them back, they drove him another 12, or 13 feet the other way. As dusk fell, he nearly stumbled to ground, knowing how difficult his fight would be in the dark. But he held his strength, for he knew he must not lose this battle. They fought all through the night, long and hard. Then, just before dawn, the squire stepped back and felt a rise under his foot. The mountain. They had driven him all the way there. He nearly lost all courage then and there. But then he remembered the old knights words: "When things seem darkest, go to the mountain. Look up to the pot." Well, didn't people always say it was darkest before the dawn? He chanced a look up the mountain. Just as he did so, the sun broke over the top of it. It shined in all its glory. The two armies were both blinded by the light as the young squire looked up at the pot he had hung from the noose, way up high. He found himself filled with a new strength, a stronger strength. Suddenly his sword didn't seem so heavy, and his eyes not quite so tired. And the legends of Newtonia and Archimedal say he fought with the strength of 10,000 men, holding both of the armies at by all by himself. So ferociously did he fight that the opposing armies fled and sailed back to there own lands, never attempting to take the island again. When the battle was over, the young squire returned to the old knight, who as sitting in there camp. "What happened to me?" he asked, for he was beyond a clue. "Think it through," said the knight, "think it through and it will come to you." The squire sat and thought, and sat and thought some more. Until finally, he jumped to his feet, one last tear in his eye, as he said, "I've got it! I know what happened." The old Knight smiled at him, and said, "So now you know it is true that the squire of the hypotenuse is equal to the sum of the squire of the other two sides.