mathguyzero ii ISBN provided by: Createspace.com All Rights Reserved Worldwide Content from this book and/or e-book cannot be reproduced in whole or part, or stored in any retrieval system, or transmitted in any form by any means, electronic, mechanical, photocopying, recording or any other manner of reproduction not yet invented, without written consent from the author or the copyright holder. Mathguyzero is a registered trademark. Please visit our website at http://mathguyzero.com for contact information. ISBN-10: 146375664X ISBN-13: 978-1463756642 Copyright © 2011 mathguyzero All rights reserved. This book was written for today’s young Math student, so that by the time they reach college they won’t be terrified of Mathematics… mgz. Where am I? Into Fraction Valley Doing Time Decimal City Doing Time Again Escape from Decimal City, or Chapter Pi The Triangle Mountains The Wizard A Battle Engaged In the Heat of Battle Oona the Brave This is a free preview chapter from The Adventures of Oona. 7 8 The trio sped down the steep sloping path and headed into Decimal City. The path turned into a paved road and within five minutes, thanks to the giant stepping, they were through the outskirts of the city and were approaching the suburbs. The streets were dark and empty along with the houses that lined them. This was not a good sign. 17 asked of Oona, “Do you think that the Irrationals will be having another parade tonight?” “I doubt it,” said Oona, “Irrational numbers are nearly impossible to predict.” Archie said, “Well put. Irrational numbers do not behave like other numbers… that is why we call them “irrational”… and they have parades here?!?... Wow! I would love to see that!” 17 described the Irrational parade for him, about the funny hats that some of them wore, about the shiny musical instruments and the irrational music that came out of them, and other details. Archie listened in fascination. Oona had to break up this lively learning moment and suggested that they check the map again. Archie pulled out his computer and projector and turned it on. After a few minutes they were again looking at the map that 3.14 had supplied them with earlier. Oona studied the map and memorized the way back to the Irrationals. After Archie shut down his equipment and put it back into his giant bag, the three companions continued down the hill with Oona giving directions. They made a few right turns, a few left turns, a few mid-block street crossings, all without seeing another number. Oona led them down a familiar dark alley to the staircase that led down to the Irrational numbers enclave. Almost there, but there was a slight problem: Archie was too big! He would never fit through the door thought Oona. So, she made a decision and said, “Archie, you wait here while 17 and I go find Pi and bring her back… and don’t talk to any strange numbers while we are gone, okay?” she said with a smile and a wink. Archie smiled back. “I don’t think that will be a problem,” he said making a point about the streets being empty. “The only two numbers that I have ever spoken with are you two… and now that I know you… you guys are not that strange.” Oona and 17 took to the stairs and began their descent. They soon saw the light at the bottom of the long staircase. 17 was first to the door with Oona right behind her. Together they pushed the mighty door inward and went inside. They were stunned by what they saw. There were no numbers! It was as deserted as the streets above. 17 said, “But, where is everynumber? This place was a happening scene the last time we were here… I don’t get it.” Oona too was confused. Where had all of the Irrationals gone? She thought for sure that they would be here and willing to help. 17 hollered, “Heeelllloooooo…. Any number here?” and the echoes bounced back and forth in the big empty hall. “This is spooky!” she yelled. “This is spooky!... This is spooky! ... This is spooky!”” answered the echoes. The two young numbers did not know what to do. They were looking at each other for ideas when they heard a door open with a whooshing sound. They turned to see Pi running through a door on the far side of the hall, her unending trail of Decimals following her like a train. She ran up to them and asked, “Were you successful? Did you deliver the letter to my good friend Archie?” 17 nodded and said, “He is outside… at the top of the stairs. He is way too big to come in here… In fact, I don’t think that his head would even….” Pi cut her off. “We must hurry! This war is going to start at dawn… which is in just a few minutes!” Pi said as she headed for the staircase that led to Archie. Oona and 17 had difficulty keeping up with her. 10 Oona asked, “Where are all of the other Irrationals?” Pi replied, “They are all in hiding… they fear that this war will escalate to more than just a dispute between the Decimals and the Fractions… these are indeed dark times when numbers fight against numbers.” Pi stopped talking as she pulled open the big door and started racing up the steps that would lead her to Archie. Oona and 17 tried to keep up with Pi’s leading digit, but quickly fell behind. Pi’s trailing Decimals were whizzing by them at a furious pace when they suddenly stopped moving and stood still. “Pi must be at the top of the stairs,” Oona said. Oona and 17 hurried but stopped suddenly when Pi’s trailing Decimals disappeared! The two young numbers shook off the surprise and raced to the top of the stairs. When they reached the top of the staircase they saw Archie talking with what looked like a circle wearing a belt. Where was Pi? 17 was first to speak interrupting their conversation. “Where did Pi go?” she asked of Archie. Archie was speaking to the circle with a belt, “Excuse me for a moment, won’t you?” He turned to Oona and 17 and introduced the circle with a belt, “This is Pi.” Before he could say another syllable 17 said, “Oh no it’s not! We know Pi. She starts out with a 3.1415… and she has a tail that goes on and on… like forever… well, at least as far as we can see.” The circle with a belt said, “Girls, girls… It is all right. It is me…Pi. I am just in a different representation of who, or what, I am.” 17 did not understand and said so. “I don’t understand.” Archie explained, “Pi is a number… an Irrational number… when she is represented in a number system founded on the powers of the number 10, she has no last digit… but in all simplicity, Pi is the ratio of a circle’s 11 circumference to its diameter.” 17 nodded as if she understood what Archie was saying, but in reality, did not. Pi broke in and said, “We can discuss that later. Now, we must get down to the river and stop this war!” As if on cue, a loud boom shook the very ground upon which they were standing. “Too late!” said Oona. “The war has begun!” Oona, 17 and Archie tried to keep up with Pi as she sped off like a wheel, rolling towards the bridge and the battling numbers. The sun was just showing the top of his shiny head above the horizon, but it gave off enough light for them to see both massive armies clearly. Pi had stopped in a safe spot behind a small building where she could see what was happening. The others caught up with her, and together the foursome crept up to the back of the Decimal army, which wasn’t easy considering Archie’s giant-ness, just in time to see the first rush of Fractions attempting to take the bridge that connected the two warring factions. It was a frightening thing to watch. The bridge spanning the River Curve and connecting Fraction Valley and Decimal City was starting to catch the first rays of the morning sun. On either side of the bridge were thousands of angry and armed numbers. The Fraction standard could be seen waving over the Fraction army, as could the Decimal flag over the Decimals. 12 A loud roar rose up from the hundreds of charging screaming Fractions as they clogged their side of the bridge rushing to meet their foe. The scene was repeated on the Decimal side of the bridge. Hundreds of screaming charging Decimals jammed together as they charged towards their supposed enemies. The two factions smashed into each other in the middle of the bridge. Pi turned and said matter-of-factly, “We have to get to that bridge.” 17 quipped, “Are you crazy? Look at what is going on over there.” But Pi already knew what was going on over there, and that was why they had to be there. Oona shared 17’s uneasiness. She saw the standards of both sides fall as their bearers were struck down, but then rise again as they were grabbed by other brave Decimals and Fractions. Oona had no idea how they would reach the bridge. The side that they were on, the Decimal side, was jammed pack full of angry Decimals waiting their turn to charge their enemies. Pi took charge and said to Archie, “Stay here until I signal you… and if something happens to me, I think that you will know what to do… if and when the time comes…” Her voice trailed off. She gestured to Oona and 17 to follow her. Pi slowly rolled towards the battlefield and soon they were among the vanguard of the Decimal army. Oona and 17 were shoulder to shoulder with Decimal soldiers as they struggled to get through the angry throng. Somehow Pi had made her way through much faster and was soon out of Oona’s sight. Something flew overhead with a whizzing sound and hit its target with a dull thud, then another and another. 17 shouted, “Look out!” but it was too late. Right in front of Oona and 17, the Decimal 2.43 was hit by one of the flying weapons: an Additive Inverse bomb. Time slowed down to a crawl as the two young numbers watched the neutralization of this unlucky Decimal. When the bomb hit 2.43 it froze him. He was struggling to move, to escape his destiny, but could not. Instantly a duplicate 2.43 appeared out 13 of nowhere, but it carried a small horizontal line in front of it, then an Addition symbol appeared… and then the unspeakable happened. 2.43 was Added to the -2.43…and both of them were… gone… simply vanished... right in front of Oona and 17! Oh the innumerality of it all! 17 said, “I think that I’m going to be sick.” Oona grabbed 17 and they pressed on through the pressing crowd. More and more Additive Inverse bombs were raining deadly neutrality from the sky, but the Decimal soldiers were a brave lot, and made no attempt to take cover. As they made their way towards the bridge, the two young numbers tragically witnessed hundreds of brave Decimals being turned into nothingness. They saw 6.41 Added to – 6.41, 7.5 Added to -7.5… and so many others. Somehow, Oona and 17 had made it to the foot of the bridge on the Decimal City side. It was a much better vantage point. Oona could see the hundreds of Additive Inverse cannons lining the Fraction Valley side of the river, all pointed in the direction of the Decimal army. Boom…boom…boom… the cannons rung out in a horrible numberneutralizing rhythm. 17 pointed to the Decimal City banks of the river. There too, were hundreds of Additive Inverse cannons aimed and firing at the Fraction army. The air was full of booming and whizzing and zipping. Oona and 17 were scared and confused. They could not see Pi. They could not see Archie… and he was over 200 units tall! But they did see 3.14! She was running towards an old fortified building not far from the foot of the bridge where Oona and 17 were perched. And 3.14 saw them too! She dashed over to them and blurted out, “Quickly…I need your help to stop some of these Decimal generals! Some of them are long-time Fraction-haters… they have gone crazy… off the deep end… totally insane in the membrane… you get the picture. They 14 will do anything it takes to win this war, even if means that the only survivors will be zeros!” 3.14 caught her breath and continued, “These whacko military guys are chanting “Zero the Hero” and we have to find out what they are planning. I am afraid that it will be the undoing of us all. Not just the Decimals and Fractions, but of all numbers everywhere.” 17 asked timorously, “What kind of nut cases do you guys put in charge anyway?” Oona said, “It is too late to lay blame, we need to stop them. Where are they?” “Follow me,” 3.14 ordered. She turned and ran off with Oona and 17 in tow. The three scared but determined numbers made their way through the throng of still-charging-up-the-bridge Decimal soldiers and made it to the outside of the fortress. The walls were far too tall for any of them to see over by themselves, so they made a numerical ladder with 17 at the base supporting Oona, who was standing on her shoulders, and 3.14 standing on top of Oona’s shoulders. “What is it? What do you see?” asked 17 as she tried to ignore the growing weight of her two companions. 3.14 let out a gasp and said, “Oh My Log! They will destroy us all!” 15 3.14 jumped down from her position as top wrung and Oona jumped down from 17’s shoulders. “What is it?” demanded Oona and 17 simultaneously. 3.14 replied with dismay in her voice, “It is what I feared most… a ZP Bomb!” Before Oona could ask for clarification, 3.14 continued, “And it is ready to be launched!” 3.14 fell silent so Oona asked, “What is a ZP Bomb?” Slowly 3.14 looked at Oona and 17 and answered, “A Zero Product Bomb…” “Oh My Dear Log, no” someone behind the trio said. They turned to see the speaker. It was Pi and she had reverted back to her Decimal form. “We must get word to Archie! Now is his time!” 3.14, Oona and 17 waited patiently as Pi thought things out. Pi turned to 17 and said, “You and I will go bring Archie back here while Oona and 3.14 try to find a way inside…” Pi paused, and then said sincerely, “And be careful of the neutrality from above.” Just as Pi finished her last syllable, an Additive Inverse shell exploded directly over 17! Before Oona could react, an identical twin of 17 appeared before them. There, standing next to Oona’s best friend, with her dreaded negative sign. And out of nowhere came the dreaded Math symbol for Addition which instantly wiggled its way between 17 and her evil twin… -17… and poof!...17 was no more! “Noooo!” screamed Oona. She fell to her knees. “Seventeeeeeeeen,” she cried. 3.14 and Pi were also in shock of seeing the neutralization of such a young and innocent number. Pi reached down and touched Oona’s shoulder. Softly she said, “I will go fetch Archie… You and 3.14 do what you can.” And Pi was off to find Archie. 16 Oona’s thinking processes came to a complete halt. All of them. Her eyes did not see. Her ears did not hear. When 3.14 tugged on her arm she followed numbly without question. 3.14 led poor Oona back to where they had made their number ladder to spy the ZP Bomb, just a few moments earlier. 3.14 had Oona sit down with her back against the wall of the fortress. 3.14 said something to Oona, who did not hear it, and sped off. 3.14 was carefully creeping around the walls of the fortress looking for another way in. She had left Oona, poor poor Oona, sitting where Pi and Archie would find her. If something wasn’t done soon to stop the ZP Bomb, every-number would share poor 17’s fate. As she was practicing her stealth, she heard shouts and cries coming from the Decimal army. She stopped to listen. She heard shouts of “Giant! Giant!” and “The Fractions have loosed a monster upon us!” 3.14 knew who they were referring to. It had to be Archie! She turned around and headed back to where she had left Oona. 17 This story was written by a Mathematics Learning Specialist with over thirteen years teaching experience with middle school, high school, undergraduate and graduate college students. In 2008 mathguyzero presented at the Society for Applied Learning Technologies (SALT) convention in Orlando, Fl., the TechEd convention in Ontario, Ca., and the Hispanic Association of Colleges and Universities HACU) in Denver, Co. Mathguyzero also presented his work at the National Council of Teachers of Mathematics (NCTM) in San Diego, Ca. in 2010. Mathguyzero has also written Homegrown Statistics, an introductory statistics textbook (and e-book) and created an aligned website with over 100 video tutorials. Free previews available at http://mathguyzero.com. 19

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