Alice In NumberlandAlice In Numberland

Alice was a normal girl with Alice was a normal girl with a normal life, except for a normal life, except for

the fact she had traveled to the fact she had traveled to a mystical place called a mystical place called

Wonderland no less than a Wonderland no less than a week ago, but other than week ago, but other than

that, she was normal. that, she was normal. She even goes to school.She even goes to school.

Although Alice goes to school, Although Alice goes to school, she wasn’t doing terribly well. she wasn’t doing terribly well. Her worst subject of all was Her worst subject of all was math, and she always found math, and she always found herself confused; especially in herself confused; especially in transformations.transformations.

One day, after being dismissed from math One day, after being dismissed from math class by her tutor, Alice spotted the prettiest class by her tutor, Alice spotted the prettiest white rabbit she had ever seen out the white rabbit she had ever seen out the window, and, disregarding the warning bells window, and, disregarding the warning bells going off in her head, followed the rabbit…going off in her head, followed the rabbit…

……right to a giant gaping hole…right to a giant gaping hole…

When Alice awoke, she realized she was When Alice awoke, she realized she was back in Wonderland; except it was back in Wonderland; except it was different. It was covered in flowers with different. It was covered in flowers with petals shaped like numbers, and the birds petals shaped like numbers, and the birds called out math problems. To her, it called out math problems. To her, it looked more like, well, Numberland.looked more like, well, Numberland.

““The side of the web I’m on right now is the The side of the web I’m on right now is the mean spider’s side, he will eat me, the other mean spider’s side, he will eat me, the other side is the nice spider’s side, she will keep side is the nice spider’s side, she will keep me safe. I can use my magic to flip my self me safe. I can use my magic to flip my self from one side to the other, but I need to know from one side to the other, but I need to know my coordinates first! my coordinates first!

““Will you please tell me my coordinates?”Will you please tell me my coordinates?”

The first creature that Alice stumbled The first creature that Alice stumbled upon was the Blue Caterpillar. It upon was the Blue Caterpillar. It appeared to be stuck in a web.appeared to be stuck in a web.

““Alice,” the Blue Caterpillar called Alice,” the Blue Caterpillar called out, “I appear to be stuck in a spider’s out, “I appear to be stuck in a spider’s web!”web!”

Though Alice only got the gist of what just Though Alice only got the gist of what just happened, she knew she had to move on if happened, she knew she had to move on if she had any hope of finding her way home, she had any hope of finding her way home, so she walked away.so she walked away.

Alice counted the Blue Alice counted the Blue Catperpillar’s Catperpillar’s coordinates, which were coordinates, which were (-1, 1).(-1, 1).

““You are at (-1, 1),” she You are at (-1, 1),” she said, and the caterpillar said, and the caterpillar cried out in joy.cried out in joy.

““Thank you my dear! Thank you my dear! Now I can Reflect –flip Now I can Reflect –flip that is- to the other side that is- to the other side of the web!”of the web!”

And he did just that.And he did just that.

““Because I am flipping Because I am flipping myself from left to right, I myself from left to right, I need to change the first need to change the first number in my number in my coordinates to it’s coordinates to it’s opposite value, but leave opposite value, but leave the second coordinate’s the second coordinate’s value alone. If I were to value alone. If I were to have been flipping from have been flipping from up to down, would have up to down, would have changed the second changed the second coordinates value.”coordinates value.”

The second –or rather- the second third The second –or rather- the second third and fourth creatures Alice came upon and fourth creatures Alice came upon were Tweedle Dee, Tweedle Dum, and were Tweedle Dee, Tweedle Dum, and the Mad Hatter. The Mad Hatter was the Mad Hatter. The Mad Hatter was laughing gleefully, while he spun laughing gleefully, while he spun Tweetle Dee and Tweedle Dum on Tweetle Dee and Tweedle Dum on boards.boards.

HA HA HA HEE HEE!

““Why, what are you doing?” Alice asked the Hatter, who Why, what are you doing?” Alice asked the Hatter, who was laughing madly at the turning twins.was laughing madly at the turning twins.

““I am rotating –turning that is- Tweetle this and Tweetle I am rotating –turning that is- Tweetle this and Tweetle That!That!

““I can turn them once clockwise, in the way the clock I can turn them once clockwise, in the way the clock moves, or even counterclockwise, opposite the way the moves, or even counterclockwise, opposite the way the clock turns. One turn is 90°, two turns are 180°, three are clock turns. One turn is 90°, two turns are 180°, three are 270°.”270°.”

““Really?” said Alice, “How interesting, but Really?” said Alice, “How interesting, but can you turn me the way home?”can you turn me the way home?”

The Hatter laughed and turned her 90° The Hatter laughed and turned her 90° clockwise and sent her on her way.clockwise and sent her on her way.

After what felt like hours of walking, Alice After what felt like hours of walking, Alice was met with a delirious White Knight.was met with a delirious White Knight.

““Boo, hoo,” cried the Knight, “How shall I Boo, hoo,” cried the Knight, “How shall I get to the other side of the board where I left get to the other side of the board where I left my lunch? I need a player to tell me where to my lunch? I need a player to tell me where to go; I need someone to slide me!”go; I need someone to slide me!”

““I will help, but only if you tell me where to I will help, but only if you tell me where to go after this to get home.”go after this to get home.”

The Knight, so happy that someone was The Knight, so happy that someone was helping him, readily agreed.helping him, readily agreed.

““You must use the equation (x + 3 , y + 1 ) and add those amounts You must use the equation (x + 3 , y + 1 ) and add those amounts to the point I’m already on to get me to my lunch.”to the point I’m already on to get me to my lunch.”

Alice could see the Knight was placed at the coordinates (4 ,2 ) so Alice could see the Knight was placed at the coordinates (4 ,2 ) so she added 3 to the first point in his coordinates, and 1 to the she added 3 to the first point in his coordinates, and 1 to the second, which meant she had to move the knight 3 across, and 1 second, which meant she had to move the knight 3 across, and 1 up. She got (7. 3) as her answer. up. She got (7. 3) as her answer.

Alice took a stance behind the Knight, and pushed him with all her Alice took a stance behind the Knight, and pushed him with all her might to the correct point.might to the correct point.

““Thank you thank you Alice, as Thank you thank you Alice, as for my help to you, just go that for my help to you, just go that way,” the Knight pointed to the way,” the Knight pointed to the right, and Alice went on her way.right, and Alice went on her way.

Alice came upon a Alice came upon a huge red castle of huge red castle of cards. From the cards. From the outside Alice could outside Alice could hear a terrible ruckus.hear a terrible ruckus.

From the inside it was much worse. From the inside it was much worse. There, sitting on a huge red throne, was There, sitting on a huge red throne, was the Red Queen. She seemed to be the Red Queen. She seemed to be shouting her head off, so Alice, shouting her head off, so Alice, naturally, asked her to be quiet.naturally, asked her to be quiet.

““What did you say?” screamed the Red What did you say?” screamed the Red Queen, “You brat!” and before Alice’s Queen, “You brat!” and before Alice’s very eyes, the Red Queen’s head grew 3 very eyes, the Red Queen’s head grew 3 sizes!sizes!

““Now see what you made me do, you Now see what you made me do, you made my head dilate, or grow in size, made my head dilate, or grow in size, by a scale factor of three, meaning my by a scale factor of three, meaning my head grew by 3 sizes!”head grew by 3 sizes!”

““I’m sorry,” apologized Alice, “I just I’m sorry,” apologized Alice, “I just want to go home!”want to go home!”

The Queen considered this for a The Queen considered this for a moment, then offered a proposition.moment, then offered a proposition.

““Very well young Alice, I will forgive Very well young Alice, I will forgive your impudence, and I will even let you your impudence, and I will even let you go home, but first, you must answer the go home, but first, you must answer the four questions of the Cheshire Cat.”four questions of the Cheshire Cat.”

The Cheshire Cat arrived as if on command, The Cheshire Cat arrived as if on command, and immediately set to asking Alice his four and immediately set to asking Alice his four questions.questions.

““My name is the Cheshire Cat; I will ask you four My name is the Cheshire Cat; I will ask you four questions: 1questions: 1stst) if I were to flip myself from left to right ) if I were to flip myself from left to right from the points negative one, one, what points would I from the points negative one, one, what points would I be at?” be at?”

Alice, recalling her lesson with the caterpillar, Alice, recalling her lesson with the caterpillar, responded, “You would be at positive one, one, responded, “You would be at positive one, one, because when reflecting from left to right, you change because when reflecting from left to right, you change the first point’s value to opposite.”the first point’s value to opposite.”

““Good, now 2Good, now 2ndnd) if I were to turn myself once ) if I were to turn myself once clockwise, would I have turned 90°, 180°, or clockwise, would I have turned 90°, 180°, or 360°?”360°?”

““90, because one turn is 90°!”90, because one turn is 90°!”

““Excellent, 3Excellent, 3rdrd) if wanted to translate myself to (5, 5) ) if wanted to translate myself to (5, 5) and I was originally at (-5, 5), how much would have to and I was originally at (-5, 5), how much would have to slide? provide an equation.”slide? provide an equation.”

““You would have to translate yourself 10 points to the You would have to translate yourself 10 points to the right, which would have an equation of (x + 10, y + right, which would have an equation of (x + 10, y + 0).”0).”

““Splendid, but what if I were to grow my head by 2 sizes? Splendid, but what if I were to grow my head by 2 sizes? What would my scale factor be?”What would my scale factor be?”

Alice remembered what the Queen said about scale factor, so Alice remembered what the Queen said about scale factor, so she answered, “Because your head has grown 2 sizes, your she answered, “Because your head has grown 2 sizes, your scale factor is 2!”scale factor is 2!”

““Correct.”Correct.”

The Cat smiled, then disappeared. Suddenly, The Cat smiled, then disappeared. Suddenly, the Castle of Cards around Alice crumbled, the Castle of Cards around Alice crumbled, and as a card was about to fall on her, she and as a card was about to fall on her, she passed out.passed out.

Alice had awaken back in her math class, Alice had awaken back in her math class, and her tutor had scolded her for falling and her tutor had scolded her for falling asleep in his class. ‘Was it all another asleep in his class. ‘Was it all another dream?’ she thought. dream?’ she thought.

Then the tutor asked her a question on Then the tutor asked her a question on transformations, and Alice realized that transformations, and Alice realized that surprisingly, she knew the answer. Alice surprisingly, she knew the answer. Alice never had trouble in math from then on…never had trouble in math from then on…

The The

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