Mathemagic Read online

  ROHINI CHOWDHURY

  Mathemagic

  Numbers

  Numbers

  Everywhere

  Illustrated by Anil K.S.

  PUFFIN BOOKS

  Contents

  About the Author

  1. An Unexpected Visitor

  2. What’s in a Name?

  3. How Many Beans?

  4. How Far to the Moon?

  5. Numbers Everywhere!

  6. Share and Share Alike

  7. Parts and the Whole

  8. Nothing and Goodbye!

  Acknowledgements

  Copyright Page

  PUFFIN BOOKS

  NUMBERS NUMBERS EVERYWHERE

  Rohini Chowdhury writes for both children and adults. She has more than twenty books and several short stories to her credit, and has published in both Hindi and English. Her writing covers various literary genres including translations, novels, short fiction, comics, and non-fiction. Her most recent publication for children is Gautam Buddha: The Lord of Wisdom, published by Puffin India. Her most recent translation is that of the widely acclaimed Hindi novel Tyagpatra by Jainendra, into English. Her literary interests include translation, mythology, folklore, mathematics and history.

  Rohini also runs a story website for children at www.longlongtimeago.com.

  Before moving into writing Rohini was a strategy consultant for five years. She holds a PGDM from the Indian Institute of Management, Ahmedabad, and a First Class Honours degree in Economics from Jadavpur University, Kolkata.

  Read More in This Series

  The Most Powerful Number of Them All (forthcoming)

  1

  An Unexpected Visitor

  Mehul woke up with a start. What was that noise? He rubbed his eyes sleepily and sat up. The moon was shining straight into the room. Mehul looked around. But he could not see anyone or anything except his twin Megha fast asleep in bed.

  But—there it was again, the same noise—scrabble, scrabble, scrabble! It seemed to be coming from the large wooden wardrobe that stood against the far wall of the room.

  Mehul leaned over and shook Megha awake. Megha sat up, her hair tangled into tight curls, her eyes wide with worry. ‘What’s the matter?’ she began.

  ‘Shhh,’ whispered Mehul. ‘Listen!’

  Scrabble, scrabble, scrabble—came the noise again.

  Megha frowned. What could it be? A mouse perhaps? She threw off her covers, and tiptoed softly across the room.

  Mehul picked up the torch he always kept handy under his pillow, and followed her silently.

  Taking a deep breath, the twins pulled open the wardrobe doors and saw … nothing. The shelves looked as innocent as ever. They were neatly stacked with Mehul’s clothes on one side, and Megha’s on the other.

  ‘What could it be?’ wondered Mehul. He clicked on his torch and shone the powerful beam across the shelves.

  ‘Oi! Could you switch that off? It hurts my eyes!’ cried a voice.

  Mehul jumped and nearly dropped the torch in fright.

  ‘Who … who said that?’ asked Megha bravely.

  ‘I did!’ replied the voice.

  The air shimmered and there, in front of the astonished children’s eyes, appeared a tiny old man. He was as tall as a pencil, almost as thin, and could stand comfortably on the wardrobe shelf. He was quite bald, though his curly white beard reached almost to his knees. He was wearing a flowing, old-fashioned robe, and a very cross look on his face.

  ‘Who are you?’ asked Mehul, who was so surprised that he quite forgot to be polite.

  ‘Hmmpph! Rude as well as ignorant!’ replied the old man, frowning. ‘I am Tzyphyr, the greatest Wizard and Mathemagician of the Universe. You may call me Sir Tzyphyr.’

  The twins looked disbelievingly at each other.

  ‘A Wizard? We must be dreaming!’ cried Mehul.

  ‘You can’t both have the same dream at the same time,’ replied the Wizard matter-of-factly. He hopped down from the wardrobe shelf and on to the bookshelf, where he began to busily rearrange the books. ‘I am here to teach you Numbers, by the way,’ he added.

  ‘To teach us numbers? But we already know all about numbers,’ declared Megha.

  ‘Oh, do you?’ said the Wizard, looking surprised. ‘Tell me then, what is a number?’ He had by now arranged the books to form a little armchair. He settled himself comfortably into his book-chair and smiled brightly at Megha.

  ‘That’s easy,’ replied Megha. ‘Three is a number. So are four, and five, and seven, and twenty-nine, and…’

  ‘Hmm,’ frowned the Wizard. ‘I can see you know your number names—the question is, do you know your NUMBERS?’

  ‘What’s the difference?’ asked Mehul, looking puzzled.

  ‘Jelly beans. Jelly beans are the difference,’ answered the Wizard. He dug into his pocket and pulling out a handful of the tiny coloured sweets, held them out to the children. ‘Go on, take some,’ he offered. ‘Jelly beans are the best way to learn your numbers. They are easy to count.’

  2

  What’s in a Name?

  The children looked at each other. Despite themselves, they were curious. They held out their hands and let the Wizard pour some jelly beans into their palms. The sweets tingled and shimmered in the moonlight.

  ‘Magic?’ asked Mehul.

  ‘Mathemagic,’ corrected the Wizard. ‘Now then, let us count how many jelly beans we have…’

  He pulled out some more of the coloured beans from his pocket and threw them, one by one, into the air, counting in some strange language as he did so. The beans hung in a shining row in the air.

  ‘Tzaph, tzeph, tziph, tzoph, tzuph,’ counted the Wizard. ‘I have tzuph jelly beans.’

  ‘You mean you have five jelly beans,’ corrected Megha.

  ‘Well, you may call that number “five”. I call it “tzuph”. It really doesn’t matter, because it is still the same number!’ replied the Wizard.

  Megha frowned, trying to understand, and shook her head. ‘I don’t get it,’ she replied.

  ‘Well, suppose I call you, say “Mzyxph” instead of “Megha”, would it make you a different person?’

  ‘No, of course not,’ replied Megha. ‘I don’t like that name, Mzyxph or whatever, but no matter what you call me, I will still be me!’

  ‘Exactly!’ said the Wizard. ‘And so it is with numbers. We have a certain number of jelly beans—we can call that number “five” or “tzuph” or whatever else we please. No matter what name we choose to call that number by, the number itself will stay the same. Do you see?’

  The twins nodded thoughtfully. Yes, they were beginning to see…

  ‘So,’ said Mehul, ‘if a number is not the word we use for it, then is it how we write it?’ And picking up a pencil, Mehul quickly scribbled the following on a sheet of paper:

  ‘Hmm,’ said the Wizard, and pulling out a pencil from behind his ear, waved it about so that strange, glittery shapes appeared in the air:

  ‘There! That’s how I write my numerals,’ beamed the Wizard.

  ‘Numerals? You mean numbers,’ corrected Mehul.

  ‘No, I mean numerals,’ said the Wizard. ‘A numeral is a number symbol. It stands for a number but is not the number itself.’

  ‘So, just like it doesn’t matter what name we give a number, it doesn’t matter how we write them, is that it?’ asked Megha, quickly putting two and two together.

  ‘Correct,’ nodded the Wizard. ‘We can decide to use any squiggle for a number. Mehul has used the squiggle 5 to show the number that you call “five” and I call “tzuph”. I have used another squiggle, to show the same number.’

  ‘So I can use any symbol or sign to show a number?’ asked Mehul. ‘A tree, a duck, a boat? Anything?’
>
  ‘Yes,’ nodded the Wizard. ‘But as long as the rest of us understand it too!’ he added with a frown. ‘The Romans used the letters of their alphabet. For example, the letter L meant the number that you call fifty, and C meant the number you call a hundred.’

  ‘So I can call a number by any name I wish to?’ asked Megha. ‘Except rude ones, of course,’ she put in quickly.

  ‘Yes,’ answered the Wizard. ‘You can call them rude names too because numbers really don’t care what we call them!’ Sir Tzyphr yawned and stretched luxuriously in his armchair of books. ‘I’m sleepy. Teaching is tiring work, especially teaching children who don’t know anything,’ he declared.

  ‘That’s very rude of you,’ protested Megha. ‘We do know something! We know about number names and number symbols!’

  ‘Yes, thanks to me,’ muttered the Wizard sleepily. ‘But you still haven’t answered my question—what is a number?’ The Wizard yawned again. ‘You won’t find the answer before dawn anyway, so I might as well nap while you think!’ And pillowing his head comfortably on one arm, the Wizard curled up in his book-chair and fell fast asleep.

  3

  How Many Beans?

  ‘Now what do we do?’ said Megha, looking at the sleeping Wizard in frustration.

  ‘Maybe we should sleep too?’ suggested Mehul with a yawn.

  Megha ignored Mehul. She glared at the Wizard, and at the jelly beans that hung glittering in the air. She realized she was still holding the jelly beans the Wizard had given her. ‘Ohhh,’ she said, irritated, and flung them across the room. The pretty, coloured sweets tumbled through the air, and fell into line with the other jelly beans.

  ‘What is a number? What is a number? I don’t know!’ grumbled Megha. ‘One, two, three, four, five, six, seven, eight, nine jelly beans,’ said Megha, flicking each little jelly bean as it hung in the air.

  ‘That’s it! What you just did! That’s what a number is!’ cried Mehul, sitting up, all sleep vanishing.

  ‘Huh? What did I just do?’ said Megha, puzzled.

  ‘You COUNTED. You counted the jelly beans. That’s what a number is—something we use to count with!’ exclaimed Mehul.

  ‘Yes, of course,’ cried Megha, clapping her hands. Now she was excited too. ‘Wizard! Sir Tzyphyr! Wake up! We know what a number is!’ she called loudly.

  ‘Mmph,’ muttered the Wizard, sitting up sleepily. ‘What’s the emergency? Is there a fire?’

  ‘No, of course not!’ said Megha. ‘We know what a number is!’

  ‘Oh, do you?’ said the Wizard, sitting up straight and rubbing the sleep out of his eyes. ‘That’s almost as exciting as a fire! So tell me then, what is a number?’

  ‘It is something we use to COUNT with,’ declared Megha.

  ‘Yes, like nine jelly beans, one house, five cows, seven trees…’ added Mehul.

  ‘Yes, yes, I understand,’ said the Wizard, holding up a hand. ‘You are right. Numbers are something we use to count with.’ Sir Tzyphr sat back in his armchair and looked from Megha to Mehul. He was now wide awake. ‘How else can we use numbers?’ he asked.

  The children looked blankly at the Wizard. Could numbers be used for anything else except to count?

  ‘Well, how about using numbers to put objects in sequence?’ asked the Wizard. He hopped off the bookshelf and hurried across the room to the big wide window through which the moon was still shining brightly. He jumped on to the window sill and peered out into the street. ‘Come here,’ he said. ‘Tell me who lives in that house?’

  ‘Which house?’ asked Megha, joining him at the window.

  ‘That one, the one with the green gate,’ replied the Wizard.

  ‘They all have green gates,’ said Megha impatiently. ‘Which house do you mean? The first one? The second one? Or the third one?’

  The Wizard grinned at her. ‘There you are—numbers again! First, second, third—putting the houses in sequence!’

  ‘I get it,’ said Mehul. ‘It’s like on sports day, in the obstacle race, I was number three at the finish, which means I came third!’

  ‘Yes!’ said the Wizard. ‘Just as I was number one in Wizard School—I came first!’

  ‘That’s very vain of you,’ remarked Megha. She had always been told never to compare who came first or second or fifth or last in class. It was never very nice for those who were bottom!

  ‘Hmph,’ said the Wizard, turning red. He didn’t like being called vain, but it was true, he had come first in Wizard School! He jumped off the window sill and began pacing the floor, still a little upset at Megha’s remark.

  Mehul was staring thoughtfully at the jelly beans that still hung in the air, shiny and glittery.

  ‘One, two, three, four, five, six, seven, eight, nine,’ he counted. Then, flicking each bean with his finger, he continued, ‘First, second, third, fourth, fifth, sixth, seventh, eighth, and ninth.’

  The Wizard looked approvingly at Mehul, and pulling out his pencil again, scribbled beneath the beans:

  ‘There!’ he said. ‘All put neatly in sequence!’

  ‘Hmm. How about if I eat the seventh jelly bean?’ said Mehul, who was beginning to feel a little hungry.

  ‘No, no, boy!’ cried the Wizard. ‘Those are magic jelly beans! You count them, you do not eat them!’

  But it was too late. Mehul had already plucked the seventh jelly bean from the air and swallowed it.

  ‘Oh no!’ sighed the Wizard.

  ‘Oh no!’ cried Megha in horror.

  ‘Whoops!’ cried Mehul in surprise.

  4

  How Far to the Moon?

  Megha and the Wizard watched in horror as Mehul began to grow. He grew taller and taller, and thinner and thinner, as though he was being stretched, like a rubber band.

  ‘Sir Tzyphyr! Do something!’ cried Megha. ‘Can’t you stop him?’

  The Wizard shook his head. ‘Unfortunately not. The jelly beans are magic—they were not to be eaten. We will just have to wait for the effect to wear off.’

  ‘How long will that take?’ asked Megha in alarm. Mehul was growing longer and thinner, and even his voice had become a squeak.

  ‘It could be anything from a few minutes to a few hours,’ replied the Wizard, pulling out a large gold watch that hung on a chain around his neck. ‘Oof, this watch is heavy,’ he grumbled. ‘I wonder how much it weighs. I never did check.’

  ‘Oh, bother your watch!’ said Megha rudely. ‘Just tell me, exactly how many minutes, how many hours before my brother becomes all right?’

  ‘Maybe five minutes, maybe seven hours, I can’t say for sure,’ replied the Wizard shrugging. He nodded to himself and said smugly, ‘There we go! Numbers again!’

  ‘Oh, forget your numbers,’ cried Megha crossly. ‘This is no time for numbers!’ She stared up at Mehul who was now so tall that his head almost touched the ceiling.

  ‘Forget numbers? Impossible!’ declared the Wizard. ‘Nothing is more important than numbers. We need them all the time, especially in a jelly bean emergency!’

  ‘We do?’ asked Megha blankly. ‘Why?’

  ‘Why? Why? So that we have something to do, of course, while we wait for your brother to return to his own size again, that’s why!’ declared the Wizard.

  ‘That’s very unkind of you,’ cried Megha.

  ‘I’m just being practical,’ shrugged the Wizard. ‘Your brother is quite comfortable up there, even though he is almost three metres tall now! So instead of worrying yourself silly and boring me to tears, you might as well learn a little more about numbers.’

  Megha glared at the little old Wizard, and then despite herself began laughing. ‘Oh all right, let’s talk about numbers,’ she said, sitting down cross-legged on the floor. ‘So now we know about number names, and we know about number symbols…’

  ‘Humph,’ said the Wizard, still looking offended, but beginning to recover his temper. ‘You now also know that numbers are used to count…’

  ‘And also to put things
in sequence,’ came a high-pitched squeak from Mehul, who did not want to be left out. He knew about putting things in sequence. He had eaten the seventh jelly bean after all!

  ‘Very good,’ nodded the Wizard. ‘I wonder though, if you can think of another use for numbers?’

  Megha frowned and Mehul swayed silently in thought.

  The Wizard sighed. ‘I can give you a hint,’ he offered. ‘Think back over our conversation just now … how did we use numbers?’

  ‘We talked about how long it would take Mehul to be all right again,’ began Megha slowly, ‘how many minutes or hours…’

  ‘And we talked about how tall I had grown … how many metres…’ added Mehul.

  ‘And you grumbled about how heavy your watch was,’ said Megha.

  ‘Yes, yes, and so? We use numbers to …?’ asked the Wizard encouragingly.

  ‘To…to measure!’ cried both the children together. ‘We use numbers to measure!’

  ‘How tall Mehul is now,’ said Megha.

  ‘How much time it will take for the effects of the magic to wear off, how heavy your watch is…’ continued Mehul.

  ‘Yes!’ beamed the Wizard, delighted. ‘We use numbers to measure! How long or tall, how far or near! How much time something will take! How heavy or light an object is…For instance…’

  ‘How far to the North Pole, or to the moon…’ said Megha.

  ‘How much time it takes me to walk to school…’ added Mehul.

  ‘And how heavy our school bags are!’ finished Megha making a face.

  ‘How long is my beard, how far is my planet from yours, how much time it will take me to get there and back, how heavy is that book!’ continued the Wizard, clapping his hands and tapping his feet in rhythm to his words.