# The Beauty Of Geometry

# Preface

Now Coral, you might be asking, why did you write a math book!? For goodness sakes!

Calm down, this isn't your ordinary math book.

How many of you are math haters out there? Here is my story☻

When I was in second grade, math was finally becoming hard and boring it was this way for me until this year(2015), I'm good at arithmetic now, and algebra up to a point, mind you faithful reader I'm still in school you know. But I found some math videos on you tube and the way the person taught math was a whole new way of looking at math! My hate slowly dissolved.

Okay Coral, that's cool, but why geometry? And why a book about it?

Ah, yes, I was coming to that. =)

Then one day I was on a cool website with lots of educational videos and I found one about a phenomenal novella called Flatland: A Romance of Many Dimensions, written by Edwin A. Abbot in 1884.

❖In the hierarchal two dimensional world known as Flatland, the Polygon class rules but this isn’t their story. Rather A. Square adventures out from his two dimensional home to other lands with varying number of dimensions in his exploration of Spaceland, Lineland and Pointland. But his radical thoughts on a land with four dimensions get him thrown out of the freest thinking land in this satirical novella by Edwin Abott Abott. - Summary from bookrags.com

My mind was blown so I read the book and my mind was blown again! The thing is, I have always been good at geometry. So, I decided to make a math book on my own... or I should say math *adventure*. As Flatland was an adventure as well. Of course this wont be exactly like Flatland, I was inspired by other math books similar to Flatland which were made as well. Now, some of this is fiction, but please have an open mind for the math.

With that being said I challenge you to journey with Indigo Ann White on this adventure.

For math lovers, haters, and future lovers alike...

# Chapter 1

Indigo was very happy. School was done. Homework was done, and best of all, no more math. Oh the joy!

She was a copper colored haired and green eyed fifteen year old, she loved to wear purple tops and dark jeans. Her brother, Desmond, was the same age and in the same grade, they were both freshmen. Algebra 1 and Psychical Science was cinch. Though her and her brother were both great in school they had one big difference. Indigo was *not *a math lover and *anything* that had to do with math. It was a stale, drab, flat, irksome subject.

Indigo's eyes payed close attention to her game on her PSP. Just a few more homing attacks then a quick run to the finish and then the level would be finally done.

"Hey Ind."

Three bad guys left.

"Yo Ind."

One more.

"Indigoooo!"

Pause game. Indigo turned around in a huff to meet her brother Desmond, he had dark auburn hair and her same eye color. He was holding a few papers, and pencils.

"Come on dude, I was like five seconds from reaching the goal!" She responded frowning, then she let her frown disappear. She remembered when her deceased mother told her not to argue over the little things.

"Well, I would like your help with two things, first I'm stuck on three algebra problems, and I'm working on a building I want built someday. I'll need an extra smart brain to help me with the math involved in the architecture." He declared.

Their father, who was still alive, was an architect. He had taught the two the lots of the math that was involved in the job, her brother wanted to follow in his footsteps. Indigo sighed defeatedly it seemed that she couldn't get away from things like these happening. Math wouldn't go away.

"Fine. Homework first." She put down her PSP and put out her hand for brother to hand her his homework. He handed it to her and he sat down next to his disgruntled sister.

"Aw Ind... I didn't mean to upset you." Desmond said with a softer voice. Their sibling relationship changed after their mother died now they were closer together. They still had their disagreements though.

"Its okay. Multiplying and dividing polynomials..." Indigo did the three problems then showed her brother how they were done.

Desmond grinned, "Thanks! So-- hey! Look at this Ind. You know when you rise a number to the second power that is known as squared, and the third power is cubed... those are dimensions!"

Indigo raised an eyebrow. "So... where are you going with this?"

"What about to the fourth power? We know that a four dimensional cube is known as a tesseract so why don't we call it tesseracted in algebra?"

Indigo tapped her PSP. "Well it sounds weird... I mean seriously. A cube has 8 vertices, 12 edges, and 6 sides. Most rooms are cube shaped, it would be ridiculous and weird to be in a room with 16 vertices! Besides there is *no* fourth dimension."

"Another euclidean plane!"

"Its only X, Y, and Z bro. Sorry about that."

"How about X, Y, Z, and W? How about that sis?"

"I'm telling ya bro its only--"

The door opened and their father came through, he and Desmond looked really similar. Their father was very loving.

"Indigo! Desmond! One of my buildings I designed is finished today!"

Their step-mother ran out of the kitchen to meet Mr. White with the kids, She had dishwater-blonde hair, and gray blue eyes, she was a bank teller.

"That's great Brian!" She said.

"Pop!" Indigo and Desmond exclaimed unanimously

"Hey!" Mr. White gave his two kids and wife a hug. "Good smells are coming from the kitchen!"

Mrs. White grinned, "Thanks Brian, your favorite is in the oven. I'll get some salad ready." She walked back into the kitchen.

Indigo and Desmond both felt neutral about their stepmother. "Sounds cool." Indigo nodded. "a nice meal."

Mr. White turned to Indigo and her brother. "Now you two, did you finish all your homework? Study?"

"Yes." They answered at the same time.

"Good, well another one of my houses were finished." He showed them a picture of a mid-century modern house. Their house was the same style, just a little different, Mr. White designed it himself.

"Like our house... just some changes in where you placed some angles. Still a very good house that an architect can make." Indigo affirmed.

"That's my girl. You still hate math though don't you." He breathed sadly.

Indigo frowned a little, "Honestly pop, yes, no matter what I do math moments keep coming I might as well have said that anyway. It wouldn't have mattered."

Then she heard Desmond snicker, "Well good that means your available to help me with my building. After all it is allowed."

Much to Indigo's disgust her dad added jokingly. "Desmond is right!"

# Chapter 2

Indigo and Desmond worked on Desmond's future building blueprint during lunch. Mrs. White liked math up to a point, not as much as stepson and husband though.

The next day was Wednesday, school again. Her first subject's in order were American History, English, Algebra 1, Psychical Science, Health. Indigo was not particularly happy at the moment because English class was almost done. On to more polynomials... how wonderful...

Her friend, Cherry who sat besides her in almost every class was humored at Indigo's reaction when they were dismissed to Algebra. Mrs. Taylor greeted her students.

"Today we'll go over what we know about multiplying and dividing polynomials." Several sounds of disappointment were heard, Indigo kept her unsatisfaction to herself. Mrs. Taylor taught for 20 minutes then Desmond raised his hand.

Mrs. Taylor stopped. "Yes Desmond?"

"Yesterday I was speculating. If the raising a number to a power, like the second power, is squared, and the third power is a cubed, which are dimensions right? So... what about raising a number to the fourth dimension? When *supposedly* there is no fourth dimension."

"You know Desmond," Their math teacher sat down at her desk, "I don't know."

Another student chimed in. "What would a 4D cube look like anyway?" he asked.

The wealthiest student in class took out her smartphone. "Kinda like this." she held it out for the class to see. The class got up from their seats, and took a look at the computer generated image. Indigo was near the front of the group. Ooh's and Ah's filled the classroom.

"It's... a cube of cubes?" Indigo thought aloud.

"Right." Mrs. Taylor's voice interjected. "Sit down please. I do know a little about the fourth dimension." Mrs. Taylor was easily distracted.

"A dimension is a direction. We live in a three dimensional world, on the planes X, Y, and Z. The fourth dimension is known as W. A 4D cube is called a hyper-cube, or tesseract."

Then Indigo spoke up, "But how can there be any other directions that left, right, back, forth, up, and down? It's crazy to believe in that."

Most of the students nodded in agreement with Indigo.

"But what if there is?" Desmond said.

Indigo huffed. "Alright then bro, where is this other plane. Huh?"

"I don't know but there must be sis, we just can't see it."

"Yeah, sure, in a two dimensional world up is a direction you can't see. But the two dimensional world is not our concern. Lets say we have a point in space, which is zero dimensions, then a line which is one dimension, a square is two dimensional, a cube is three dimensional. You have *all possible* directions now, left, right, side to side, up, and down. There is nothing else, this is it bro. There is *no* fourth dimension!" Indigo denied indignantly.

Mrs. Taylor raised her voice. "Hey! You guys can stop now." The class had become very quiet during the small but powerful debate the other students were secretly taking sides. Mrs. Taylor continued, "I'm glad you're talking over math, and considering things, but I won't let any debates get too heated. Class dismissed."

Indigo and Desmond did not talk for the rest of the school day.

When their stepmother picked them up they finally started talking again.

"Ind... I'm sorry." Desmond said quietly.

"I'm sorry, I started the argument, but I *still* *don't* agree with you." This was not something little, so Indigo openly disagreed.

Mrs. White made a sound of disapproval, "Kids... what's going on."

"Basically, in so many words, we had a multi-dimensional quarrel." Indigo answered.

"Hmm... Is that what I overheard you two talking about yesterday?" Mrs. White asked.

"Yes Mam." the two replied.

looking at the rear-view mirror Indigo could tell that Mrs. White still didn't look happy. "Do I need to tell your father?"

"Nope, everything is good, me and Indigo are happy people to the third power." Desmond grinned and nudged his sister with his elbow.

Mrs. White shook her head as she heard her step children laugh together in the back.