The Golden Rectangle

by Gillian Neimark

  “Show me Puddleville,” said Lucy. “Where is it in comparison to here?”

  He pushed a button, and the screen zoomed in on trees and rolling land dotted with small houses. He pushed another button and zoomed in on one house.

  “There’s your home. You’re nine hundred eighty-three miles away from it right now.”

  He zoomed in on the pond.

  “There’s your baby alligator.”

  He zoomed up.

  “That’s your tree fort. Another golden rectangle.”

  “I built it for her,” said Buddy.

  “Naturally,” said Square Man. He seemed to be enjoying himself.

  “You should see my tree fort sometime,” Lucy said to Flor. “I’ve been meaning to have a slumber party there. Maybe you’ll come.”

  Square Man zoomed over a few blocks.

  “And there’s your ice plant.”

  Square Man zoomed in on the plant. Past a KEEP OUT sign. His galactic camera peered inside an enormous room. The floor was made of many rubberlike blocks covering steel containers with ice.

  “That ice plant makes how many blocks of ice a day, Mr. Moon?”

  “Each steel container has four containers inside it. There are two hundred fifty containers. So that’s a thousand blocks. Once we take the ice out, fresh water is poured into the containers, and they’re lowered back down and frozen into ice again, over and over, day after day, year after year.”

  “The proportions are perfect,” said Square Man. “A thousand blocks of ice a day—all perfectly rectangular!”

  “Zoom in on the other room, the one with tons of bags of crushed ice,” said Lucy. “It’s over to the right, there. See that, everybody? That’s where I go every day after school. And even when it’s hot enough to fry an egg on the sidewalk, I wear a winter jacket in there. It’s so cold! I’m a super ice-bagger. I put the crushed ice in ten-pound bags and seal ’em. I can bag ice faster than anybody.”

  “There’s something wrong with this picture,” said Flor suddenly.

  Everybody turned to look at her.

  “Mr. Moon,” said Flor, “where is Lucy’s mom?”

  Lucy frowned. “I don’t have a mom.”

  “Everybody has a mom.”

  “My mom died,” Lucy said shortly. “I was two months old. I don’t remember. Don’t play no violins for me. I have the best dad and sister.”

  “Wow, I’m sorry.” Flor hesitated, then said bravely, “Until recently, I basically didn’t have a dad.”

  Lucy tilted her head and waited. Flor could tell she was curious but didn’t want to show it. And then it all came rushing out, how her father had moved to France, about his new family and her new sister, Aimée, about her adventure to meet him.

  “That sounds awful,” Lucy said.

  “Sometimes people just avoid things that are too painful,” said Dr. Pi. “I think Flor’s father didn’t know how to make it right. But she inspired him to start being a real father to her.”

  “Now he calls me once a week,” said Flor. “And they’re going to visit later this summer.”

  Square Man, who had followed both stories closely, was strangely silent, almost brooding.

  “I have no idea who my mother or father is,” he finally announced. And then he thrust his tiny shoulders back. “Nor do I care! Put on your golden seatbelts. You four are my prisoners, and I am taking you to Planet Square, where we will begin our grand task of turning spirals into rectangles.”

  BE THERE, OR BE SQUARE

  I never realized how many things in the world are curved,” said Flor. She had just stepped out of the golden rocket ship onto Planet Square. The ride had taken only ten minutes, and the wormholes had been no trouble at all. Each time the ship went through one, Flor felt like she was disappearing into nothingness, almost as if she had fallen asleep, but then she reappeared fully awake a few seconds later, and all of her was still there.

  Planet Square was brown and gray. The sky was a faded white, like a dirty sheet. Everywhere the eye could see was an endless expanse of rock, made of small squares. It was as if nature had decided to tile the entire planet, and forgot about soil and grass. Every so often a patch of long columns of rock pushed out of the tile, clustered in groups like organ pipes.

  Square Man was tapping and folding up the rocket ship. He slipped it into his pocket.

  “Lines and angles everywhere,” said Buddy. “Amazing.”

  “A planet without a single curve that I can see,” said Dr. Pi thoughtfully.

  “I told you,” said Square Man impatiently. “Why are you so surprised?”

  “But in the natural world, squares are not everywhere. It’s easier for nature to make round things. Like raindrops that fall. Or bubbles that float. Or dandelion seeds with their white puffs. Was this planet all square before you arrived? Or did you change it?”

  “I made it in my own image,” said Square Man.

  “What’s bumping against my skin?” said Lucy. “Is it square mosquitoes or something?”

  “That’s wind,” said Dr. Pi. “Wind usually flows in waves. But waves are not allowed here. So it has to form rectangles and bounce along.”

  “And the mist—is that mist?” asked Flor, squinting. “It’s not rolling over the rocks—it seems to be jumping.”

  “What is that monster coming toward us?” shrieked Lucy, pointing at the horizon.

  They all turned. Something huge was crawling over the drab landscape and galumphing toward them. Sweat dripped from its spotted armor, which on closer look was made of thousands of hard, shell-like scales. The creature had two huge claws with pincers as sharp as razors. Two long antennae twitched against the ground as the creature reached them.

  The monster stopped and lifted its claws into the air. And there it remained, unmoving.

  “Hello, Red Eye,” said Square Man. “Meet my four new friends. Dr. Pi is an evil wizard who is now in my employ. We must strip him of his power to protect spirals. Mr. Buddy Moon is a master rectangle maker, but so far he has resisted doing what he knows he must. This is his daughter, Lucy Pipsqueak. And this is her friend, Flor.”

  “This is the way we die,” whispered Flor.

  Dr. Pi walked up to the creature and nodded hello. “Extraordinary. His eyes are made of nothing but tiny squares, a thousand tiny squares.”

  Buddy followed. “They’re beautiful, actually. Precise beyond all imagining.”

  “That’s a lobster’s eye,” said Square Man. “Made of thousands of tiny square tubes, with shiny mirrors on the sides. He can practically see behind himself. When I came here and got rid of everything round, I saved him and named him Red Eye. Because of the squares in his eyes. He is my trusted assistant.”

  “A lobster,” said Flor. “Right! He looks just like the ones at the Chinese restaurant, only about a hundred times bigger.”

  “So does he talk?” asked Lucy. “Lobster, do you talk?”

  One claw slowly lifted in the air and came to rest on the ground, and a robotic voice said:

  “All four lines are equal.”

  The lobster cleared his throat.

  “A square is a special case of a rectangle, where all four lines are equal.”

  The lobster cleared his throat one more time.

  “Where shall I deliver them, sir?”

  “To the square chamber. I’ll see you there,” said Square Man.

  Without a moment’s hesitation, the lobster swept the four humans into his claws, delicately closing the pincers, and began to crawl away. Square Man followed, leaping like a grasshopper.

  “What is the square chamber?” cried Flor, wriggling and pushing against the pincers.

  Lucy piped up. “You wouldn’t just make a plain old square chamber. I already know you better than that. It’s got some special feature.”

  “Well, it does have one special feature. It has room enough for four right now. But if I don’t like the way things are going, the square is going to get smaller. And then smalle
r again.”

  “You’re going to crush us?” Flor shouted.

  “Squeeze you gently until everybody gets their priorities straight. Squares and angles, let’s unite! And is what I want so terrible? I just want to stop Dr. Pi from turning rectangles into spirals.”

  “He’s never touched a rectangle of yours,” Flor shot back.

  “Every spiral was once a golden rectangle,” said Square Man. “And besides, I hate a curve.”

  “But why?”

  “A curve thinks it’s more beautiful than a line.”

  “That’s not true.”

  “Nobody appreciates a square.”

  “I never heard that,” said Flor.

  “If you want to insult someone, you say, ‘Oh, you’re such a square.’ Did you ever hear someone say, ‘You’re just a circle’? Of course not. But squares do all the hard work. Square bricks make buildings steady. Square tables hold food. Square chairs, square rooms, square houses. Squares are the basis of everything. And still, nobody praises a square. They praise the sun and the moon and everything round.”

  Square Man waited for the girls to agree with him, but they seemed unconvinced.

  “Everyone should live in a square world. Maybe people will appreciate me then.”

  Red Eye stopped before a tall building. It towered into the sky, constructed entirely of brilliantly shiny black marble.

  “Is this your tree fort?” Lucy joked.

  “Ha ha. Red Eye, proceed,” he said as a door slid open and they moved inside. Red Eye clattered across the marble floor and through a door, where he finally opened his claws.

  “Thank you for being gentle with us, Red Eye,” said Dr. Pi. “Those pincers look very sharp, but you didn’t hurt us at all.”

  A lobster can’t smile, but Flor could feel a smile coming from the creature.

  “What does the world look like to you, Red Eye?” asked Buddy now.

  Red Eye seemed to think for a moment. “It was different down in the ocean depths, where it was so dark. My eyes are good for the dark, and I could see well. But on a bright day I am nearly blind sometimes.”

  Square Man shut the door to the room. Now he turned to Lucy.

  “First, I have a few questions.”

  “Shoot,” said Lucy.

  “So how did you learn that trick back in the barn when you escaped me?”

  “My great-great-granddaddy taught me,” she lied, thinking back to what Dr. Pi had said.

  Square Man looked nervous. “How is that? Isn’t your great-great-granddaddy dead?”

  “He came to me in a dream and taught me. The night before you arrived.”

  Square Man looked at Buddy. “Is this true?”

  “Quite possibly,” said Buddy.

  “Then the famous Buster Moon, the fierce guardian of the Golden Rectangle that everybody talks about, is somehow still around,” Square Man muttered to himself. “Not good. Not good.” He looked back at Lucy. “What else did he teach you? I’ll need to know everything.”

  “He taught me what the Southern saying really means, when you tell someone you’re finer than a frog hair split four ways,” Lucy blurted out. Oh sheesh, she thought, why did I just say that? Now he’s going to ask me what I meant, and I have no clue. My mouth is bigger than my imagination sometimes.

  “Go on,” said Square Man.

  “You split a frog hair four ways, and you line up the hairs to form a golden rectangle that is practically invisible. Because, I mean, a frog hair is so fine in the first place, who can see it when it’s split? And you can carry the power of the golden rectangle with you wherever you go, right in your pocket.”

  She could tell Square Man not only believed her, but he was both fascinated and uneasy. Out of the corner of her eye she could see her dad smiling, and Dr. Pi nodding, as if to say, “Well done!”

  “When I came to this planet,” said Square Man, “half of it was covered with oceans and rivers and lakes. Not unlike your planet Earth. I saw frogs. I got rid of all the water and all the frogs, with their loathsome flowing curves. I never saw a hairy frog in my life.”

  “The frogs in our pond are disgustingly hairy,” said Lucy. “They are covered with slimy hair. It’s actually quite gross.”

  “Is that so?”

  “Absolutely,” said Lucy.

  “Mmm-hmmm. We’ll go back there one day, then, and you’ll catch me some?”

  “I’m not too keen on helping you right now,” Lucy said.

  “Is that a refusal?”

  “For now, yeah.”

  “I have another question.”

  “What?”

  “How did you manage to teleport yourself to Brooklyn?”

  “That part I have no answer to. I have no clue how I ended up in Flor’s closet tangled up in all those clothes. I don’t even know how Dad followed me there. I’d love to know.”

  “I’ll tell you how,” he said. “You and Flor didn’t just meet tonight. You have been friends for years. You went straight to Flor and Dr. Pi because you know, and have always known, just as your father knows, that spirals come from rectangles. It’s no coincidence that you ran to the two people I came across galaxies to find and stop their spiral-spinning.” He shook his head. “You four have been working together for years. How dumb do you think I am?”

  “It sounds reasonable, Square Man,” said Buddy, “but I can swear to you that Pip never met Flor until an hour ago. And I never laid eyes on Dr. Pi until tonight, though, of course, I’ve known of him all my life. The force of the universe itself sent my daughter to Brooklyn. Which,” Buddy concluded, “presents a far more troubling situation for you. Doesn’t it?”

  “Or perhaps,” murmured Dr. Pi, “Square Man is himself part of a bigger . . . ”

  He paused. Everybody looked at him and waited.

  “A bigger test,” concluded Dr. Pi.

  “I’ve never had it easy,” said Square Man. “From the moment I was created, I was an outsider. And look at all I’ve achieved. So I’m not going to worry about that now. Do you girls know the story of Rumplestiltskin?”

  “The fairy tale,” Lucy said. “Everybody knows that story.”

  “And what happens in the beginning of that story?”

  “A father brags that his daughter can spin straw into gold, and the king hears the rumor and shuts her up in a tower room with a lot of straw and a spinning wheel. He tells her to spin the straw into gold by morning or she’ll be executed.”

  “Right. So. Dr. Pi. I don’t suppose you’re willing to give up your obsession with spirals, and let me guide them back to their original form, the golden rectangle?”

  Dr. Pi sighed. “You know the answer to that.”

  “Right. And, Mr. Moon, are you still determined to refuse my offer?”

  “I couldn’t make you golden rectangles, even if I wanted to,” said Buddy. “My task in life is to make sure they are safe and protected. By universal decree I am allowed to make my thousand blocks of ice daily. That’s it.”

  “What about Lucy’s hayloft?” demanded Square Man.

  “She made it. I just spruced it up.”

  “Lucy doesn’t have to follow those rules, does she?”

  Buddy shook his head.

  “All right, then, if you won’t make me rectangles, your daughter can. The talent runs in the family. And the future lies with our children, so they say.”

  “That’s true,” said Dr. Pi. “I could fight you, and Mr. Moon could fight you, and we’d probably win, but that is not our role. It’s up to the girls. We can only do our best to support them as they tackle this challenge.”

  “Well, then. Lucy, I have a proposal.”

  “Shoot.”

  “Make me a thousand golden rectangles by tomorrow.”

  “You only need a thousand?” she said sarcastically.

  “One thousand. If you can make a thousand, you can make ten thousand. I’ll employ you. Remember, I pay well. You’ll be rich.” He leaned forward and stared at her in
tently. “Isn’t there something you’d really like to buy?”

  “I can’t think of anything.”

  “Of course you can. There is something you’re saving up for.”

  Lucy gulped. “My ranch.”

  He leaned back. “Right. Your ranch. There you go. You’ll be able to buy a very big ranch.”

  “And a pen for my wild horses,” she added.

  “Done.”

  “Really?”

  “Really.”

  “And a lot of cowboy boots,” she added.

  He waved his hand impatiently. “Anything you want. The money is there. See?”

  He snapped his fingers, and dollar bills wafted through the air like snow in a paperweight.

  “Hmmm,” said Lucy. ““What am I gonna make these rectangles with?”

  “Whatever you choose. All I ask is that they are the right proportion. Divina sectia.”

  “Okay. I’ll do it.”

  He was taken aback. “You really will?”

  “Yes, no problem. I will do it as long as I can make them out of water.”

  She might as well have said she’d make them out of air, or wind.

  “Water!” he spluttered.

  “Water?” echoed Flor. “How the heck can anybody make a rectangle out of water? The water will just run across the floor.”

  Square Man grew angry. “There is no extra water here. Water flows in waves. Waves have curves. Planet Square does not allow curves.”

  “Then what do you drink?”

  He looked even madder. “You are a very frustrating child. From frog hairs to water, I never know what you’ll say next. I can’t let you have water for rectangles. That’s final.”

  Lucy looked around the marble room.

  “That’s the only deal I can make.”

  “Ridiculous.”

  “It’s a simple request.”

  “Impossible.”

  “If you can’t get me water for my rectangles, why, I’m going to be madder than a hen tied up in a burlap sack all night long. And I’m not gonna make you anything at all.”

  ROUND PEGS IN SQUARE HOLES

  Lucy and Flor were trapped. Square Man had decided that with a bit of time Lucy would change her mind and choose a more appropriate substance to manufacture rectangles.