The Cinderella Theorem Read online

  “Oh yes,” Mom agreed. “They released a new album just last week.”

  “Not that. What ball?”

  “Your presentation ball, of course.”

  “I have a presentation ball?”

  “Yes, of course,” my mother explained. “After you spend the afternoon receiving your subjects, there will a ball in your honor. Everyone is very excited about you coming home. The ball is really just a normal formality.”

  Normal? Does she know what my friends are doing right now? What the entire world does normally on a weekend?

  No, of course.

  7

  Prime Number Presentation

  We ate supper at Once Upon A Tine. Another clever Smythian play on words. Forks have three tines, the sharp, pointy parts. “Once upon a time” is a common beginning phrase for fairy tales, so, clearly, the name of the most popular Fire Land restaurant has to be–Once Upon a Tine.

  I was more than ready for bed when our pumpkin carriage brought us back to the castle. After all, in just one afternoon, I’d entered an alternate world and eaten in a restaurant owned and operated by the talking cat from Puss-in-Shoes or something. I actually didn’t know the story, but the talking cat introduced himself when he brought over the menus.

  As we returned to our castle, the guard shouted a salute from the gate.

  My dad squeezed my shoulder, in a gesture of good will and fatherly affection. “Everyone is just so glad you’ve finally arrived, Lily. I’ll be surprised if your ball ends before three in the morning.”

  I yawned. Lovely. A ball, that I didn’t want in the first place, lasting until the wee morning hours. Won’t everyone turn into pumpkins or something at midnight?

  We were met in the courtyard by the in-charge person I had seen earlier in the Arrivhall.

  “Your Majesty,” he said, quickly bowing and addressing my father. “Do you have some time available to discuss the schedule for tomorrow?” He nodded a quick bow to my mother and me.

  “Of course, Macon.” My father turned to us. “This won’t take long, Ginnie; I’ll be up later, but I’ll go ahead and say good night to you, Lily. You look pretty tired.”

  I nodded back at him. I was tired, but, more than that, I needed time alone to process this world where cats are not kept out of eating establishments for sanitary reasons.

  My mother offered to show me to my room. “Your fairy godmother and I had the best time decorating your room. I’m sure you’ll love it.”

  “I have a fairy godmother?” I should have known.

  “Of course.” Mom chuckled.

  Why was she laughing? Should I have just known I have a fairy godmother? I don’t even have a normal godmother.

  I had my doubts about how my mother (constantly in a world of her own creation full of princes, curses, and everlasting love) and a fairy person (not known for matters of logical or rational thinking) would decorate my bedroom. I prepared myself for the worst–pink, wispy material everywhere, little ballerina figurines dancing (maybe literally, through magic), lace, a vanity dressing table full of jewelry, and a pink diary on the bedside table, which would be covered with more pink lacey business.

  Apparently, my mother had paid some attention to what I like over the years, but it was easy to determine where my fairy godmother had added her own touch. There was no pink, thankfully, and no lace. There were, however, books. Shelves and shelves of books.

  “Those shelves,” my mother pointed out, “are boring math books, but those,” (more pointing), “are the stories of every citizen of Smythe’s SFL.”

  A huge chalkboard hung on one wall. (“For solving your math problems.”) But I liked the ceiling best. Floating (actually floating) near it, were all sorts of famous math equations. The quadratic formula, the Pythagorean theorem, e = mc². They floated around up there, like literal math heaven. (“That was Glenni’s idea.” Glenni, I suppose, is my fairy godmother.)

  “Do you like it?” Mom asked.

  I nodded, noticing the right angles made by the bookshelves, the symmetry of the windows, and the perpendicular lines made by the walls and floor.

  “Good,” Mom smiled. “Your bathroom is through that door, and your closet is over there.” (Pointing.) “Breakfast will be around nine tomorrow. Someone will show you the way.” Mom spoke quickly. “If you need anything, pull the cord beside your bed. Your father and I are at the end of the hallway. Do you have any questions?”

  “I don’t think so,” I managed, trying to remember everything she had said.

  “Alright then.” Mom smiled at me like it was the first day of kindergarten, and I was going off to ride on my first school bus. “I’m so glad you’re here, Lily. Good night.” With another smile, Mom was out the door, leaving me alone in my math heaven.

  I immediately went to the chalkboard and wrote the equation of a line in slope-intercept form.[15] The room seemed more like home. I smiled, put on my pajamas, and fell asleep reading my Newton biography.

  ~~~

  I woke the next morning to prime numbers dive bombing me from the ceiling. Apparently, Glenni had also put in an alarm clock. I swatted an 11 away, hoping that would equal a snooze button. After a seven-minute snooze, a 29 hit me on the knee, and I got out of bed, wondering how to set the alarm.

  According to the traditional clock on my bedside table, I had plenty of time to get ready before breakfast. With the remainder of time, I sat in the squishy chair, reading my wonderful Newton book, waiting for my escort.

  “Good morning, Princess Lily,” the short green lady from Thursday night said. “My name is Beryl. Her Majesty asked me to show you to the breakfast room.”

  “There’s a breakfast room?”

  “Of course. You can’t have breakfast in the dining room or the tea room.”

  “Oh.”

  “Right, then. Shall we go?”

  I nodded and followed Beryl into the hall. After a series of staircases, elevators, locked (and unlocked) doors, we arrived in a sunny room. My parents were already there.

  “Princess Lily,” Beryl announced.

  Breakfast was actually pretty normal and served by the seven short people from before. With some of the dishes my mother offered explanations. “This bacon is really a bacon substitute sent over by the Three Little Pigs.” “These eggs are from the Goose Girl. You remember that story, Lily.” (I do?) “This is gingerbread from the Little Old Woman who made the Gingerbread man.” (Isn’t that wrong somehow?) “When you eat this alphabet cereal, the letters on your spoon will spell character names, places, and important things from the stories of Smythe’s SFL.”[16]

  When we finished breakfast, my mom asked, “Do you think you can find your way back on your own? Your father and I have lots to do before your presentation at one. Beryl will come for you around twelve forty-five. Cook will send lunch to your room. Wear the blue dress in your closet. We’ll save the green one for the ball tonight.”[17]

  “Okay,” I mumbled as she left the room.

  I did have trouble finding my way back. After thirty minutes of wandering, I thought I’d finally found my room, but when I opened the door, it was a library. Exhausted and frustrated, I decided to sit for a moment and analyze the route I’d taken.

  Looking around the room, I noticed a framed map on the wall, near the door. The probability of it being a type of fire escape map seemed high to me, so I went over, hoping to find the way to my room.

  Sadly, the map was written in some sort of code. (Nothing is normal in this place!) I started looking around to see if there was a codebook, or at least a readable map of the castle. Wouldn’t a library be a great place to keep something like that?

  As I examined the room, I came across a framed portrait of a young man. He had dark hair and dark eyes. He was smiling, but his eyes were sad. I looked at the bottom of the frame to see the title, but the placard had been removed. The place where it had been was a slightly different color than the rest of the frame. I reached out to touch the spot.


  “Your Highness?”

  I sucked in a frightened breath. “Macon! You scared me.”

  “I apologize, Princess. May I ask how you came to be in this part of the castle?” His face looked a little hard; it made me feel like I was in trouble.

  “Oh. Um, I got lost on the way back from breakfast. I was looking for a map.”

  “I see.” Macon’s eyes softened a fraction. “Allow me to escort you to your chamber.”

  “Certainly.”

  Macon closed the door behind us, then pulled a ring of keys from his pocket and locked it. “This door is ordinarily locked, Your Highness. I can’t imagine how it came to be unlocked.”

  “Oh,” I mumbled, still feeling guilty for being in the library. “Why is the door kept locked?”

  Macon pursed his lips and thought a moment before answering. “It is His Majesty’s wish.”

  I didn’t think it would be wise to continue my inquiries.

  Macon deposited me back at my room and wished me a pleasant morning. I spent the rest of it reading, wondering why the library was forbidden, and getting a little nervous about what to do at my presentation. Lunch came and since my mother was not there to provide the inside information, I wasn’t able to enjoy the soup as much as I would have if I’d known exactly how it fit into Smythian society.[18]

  Beryl (the amazingly prompt little green person), arrived at precisely twelve forty-five to lead me to the throne room. It seemed a great deal less confusing this time, but that was probably because we were able to take the elevator marked Throne Room. When we got off the elevator, Beryl ushered me through a doorway into another library. My parents were already there, and they looked surprisingly royal.

  Surprisingly royal = crowns, ermine fur lined capes, and scepters.

  “You look lovely, Lily,” my father beamed.

  “Thanks,” I murmured. As irrational as it sounds, I was starting to be excited about being presented.

  “Alright, Lily. This is what’s going to happen.” Mom placed a sparkling tiara on my head. “Your father and I will go in first. The gathered populace will shout ‘Long live King Matthew! Long live Queen Virginia!’ as we walk to our thrones. When the cheering stops, your father will make a speech and end with, ‘I give you Princess Lily!’ Then, you come in and walk to your throne, while the gathered populace shouts ‘Long live Princess Lily!’ Do you understand?”

  I nodded.

  And that was exactly what happened.

  Right up until the part where I tripped on my dress and knocked over some candles that Mom didn’t mention which–briefly–set the floor on fire.

  Following my amazing display of grace and agility, several Smythian men rushed in to save the damsel in distress (me) by putting out the floor fire. My father (who I may decide to call “Your Majesty” since “Dad” seems weird) did an excellent job of thanking “the brave men who, forsaking personal safety, chose to save the Princess.”[19]

  I think I regrouped well after the fire incident. I advanced to my throne, sat gracefully, and listened to my father’s speech, which in addition to gratitude for the volunteer firemen contained a lot of words that all seemed to be taking the longest possible way to say, “Hey, aren’t we all glad Lily is here?”

  He said, “When we look back across the chasms of time that have led us to this glorious day,” and “Surely, our hearts contain fountains of joy that know no lack of purest water,” and “Her arrival heralds a new dawn of bright hope and promise for all in this great and abundant land.”

  This was all long, boring, and annoying.

  Finally, after using all the words in the English language, King Daddy said, “Now, people of this land, come forward and meet your Princess.”

  This dramatic statement was followed by more cheering. When the cheering stopped, Macon came forward.

  “Warmest greetings, Princess,” he bowed. “Allow me to present, Lady Potio Bane of Hemlock.”

  As he spoke, the main doors of the room opened, and a positively scary woman entered. She wore a deep purple cape, and after she bowed low, she removed her hood to reveal jet-black hair. I realize, mathematically speaking, a deep purple cape plus jet-black hair do not necessarily equal positively scary, but I was afraid of that woman.

  “Welcome to the Salty Fire Land, my princess,” she said in a sickly sweet voice. “In honor of your arrival, I have brought gifts.” (My mother hadn’t said anything about gifts!) She clapped her hands twice, and the doors opened again for a young servant boy. He carried a box wrapped in paper of the same deep purple as her cape. On top of the box sat a bright, shiny red apple. Even though I just ate lunch, my mouth watered for a taste of that apple.

  The boy advanced and bowed before me, while uplifting the gift. Not really sure what I was supposed to do, I stood and took the box from his hands. The apple was mine! I would have taken a bite right then if my father had not spoken.

  “We thank you kindly for your attentions, Lady Potio. But, of course, we shall have the apple tested for poison before we allow the princess to taste it.” He made a motion, and a castle servant whisked the apple away. My beautiful, shiny, red apple taken away to be tested and destroyed!

  Lady Potio spoke again, interrupting any plans I had for protesting. “Does Your Majesty mean to insult?” She asked in a voice even more sickly, sugary sweet than before and with a smile that showed she was not insulted.

  What game was she playing with my father?

  “The apples of Hemlock are well known in the realm for their delicious flavor.”

  “Yes,” my father shifted in his chair. “And every wise citizen uses their poison testing kit before eating those same apples. Your skilled use of poisons is equally famous in the realm. I believe your own stepdaughter would agree.”

  She laughed, actually laughed. I find nothing funny about a woman who grows poisoned apples and has apparently poisoned her own stepdaughter. My desire for the apple waned.

  “Always wise, King Matthew. You are right to test the apple.” She smiled. “But you will find no poison on it.” She turned to me. “Won’t you open the other gift, Princess? I assure you, there is no poison in that box.”

  I opened the purple present, still a little rattled by the poisoned apple (that may or may not have been poisoned). Inside the box was a mirror. This, while a little girly for me, was a normal gift. I relaxed.

  Then the mirror talked.

  “What a study is your face! Expecting danger in my place?”

  Apparently, it’s a rhyming mirror. Years of getting non-mathematical presents from my mother enabled me to look at Lady Potio, smile, and say, “Thank you very much for this mirror.”

  “I wish you great happiness.” She winked at my father. “And wisdom to equal our King.” Then she turned and left the room; the servant boy followed.

  Macon stepped forward and announced, “Allow me to present you with a gift from the whole of E. G. Smythe’s Salty Fire Land: the traditional box!”

  He pressed a wooden box into my hands. It was just like The Box I had of my father’s, but instead of “HRHMS” mine had “HRHLS” engraved on it.

  I smiled. My own Box. “But what are the letters for?”

  My father leaned over. “Her Royal Highness Lily Sparrow.”

  I reluctantly let the servant take the box and turned my attention to the next visitor.

  “Prince Harry and Princess Rapunzel of Pelo.”

  Obviously Rapunzel was the princess who had a lot of hair. So, when they gave me their gift, I totally understood: a hairbrush. Harry and Rapunzel left and were followed by Little Red Riding Hood (whose real name is Cerise) with a basket of baked goods sent over by her mother.

  “The Sphinx,” Macon announced. The doors opened for a lion with the head of a woman. This particular combination is not mathematical at all and rather puzzling. What kind of food does the Sphinx eat? She has a human’s taste buds, but a lion’s digestive system. And how does she fix her hair? Her paws don’t look very dexter
ous to me. I drew myself away from the biological/mathematical quandary in order to pay attention to what the Sphinx was saying.

  “Your Highness,” she bowed the front part of her body, touching her head to the ground. “I do not come with a gift, but I bring a riddle. Listen well, for the riddle contains a warning: Because of a gift, a name becomes a threat.”

  While I wondered how to respond to this in a proper princessly way, my mother asked, “Can you tell us more, Lady?”

  The Sphinx bowed again and looked sorrowful, “You know I cannot, Your Majesty. But heed the warning and beware.” Then she turned and left.

  What is going on? I have already received a possibly poisoned apple and now, an ominous warning from a half woman, half lion. I turned to my mother, searching for an answer, but I couldn’t catch her eye. She seemed upset.

  Macon’s voice brought me out of my wonderings. “Glenni, the fairy godmother,” he announced.

  Glenni! Creator of floating math and prime number alarm clocks. As she entered the room, I could see that she, too, was floating. Not only that, she was only about three feet tall and dressed entirely in plaid. She carried a present and a wand, with a trail of plaid sparks coming from it. (No, I do not know how to mathematically explain “plaid sparks.”)

  “Princess Lily,” she said, bowing in mid-air. The she turned her bow into a somersault, let go of the present, and used the plaid-sparking wand to float it to me.

  “Open it! Open it!” she ordered, pointing with her wand and sending plaid at me. The present was wrapped in plaid paper. I opened it and discovered (to my great delight) a pre-calculus book.

  “Thank you very much, Glenni. I love it.”

  “Of course you do, dear,” she nodded. “I’m your fairy godmother. How could I get you something you wouldn’t love?”

  I smiled as she left. Glenni’s gift added a bit of respect to my equation about fairy godmothers.