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Chapter 2
The woods were cool and dense. As Stella walked, she was shaded by the canopy of leaves overhead. A breeze played with her long, dark hair and yellow sundress. Goldbach had been very pleasant, and Stella hoped his friends would be just as nice. It was also good to have a friend in Geomno. By now, Stella didn't have a doubt that she was inside the book she had found on her teacher's podium. The question still remained of how she got there, and how she would travel back.
Presently, she came upon another clearing. To her surprise, she spotted a miniature version of an ancient Greek building she had once seen in her history book. What was it called again…? Ah yes, The Pantheon! What was a replica of it doing in the middle of a forest in a book?
Stella's curiosity overcame her and she ventured towards the stone structure. Did Goldbach's friends live here? He must be of a very odd sort, Stella thought, to live in such a house.
"γειά σας! (Hello there!)" A pleasant voice called out. Stella turned, to find an old, bearded man dressed in a toga.
"Who are you?" She asked, now thoroughly confused. Did the man speak English?
"Oh, you speak English! Pardon me, but Greek is my native language. My name is Euclid."
"Oh! I know who you are! We learned about you in history! You wrote The Elements!"
"Right, my girl! Now, what is your name?"
"I'm Stella."
"Well met, then. What brings you to my humble abode?" The man gestured at the miniature Greek building.
"I am trying to find out how I came to this place. Geomno, I mean. Do you know a man by the name of Goldbach?"
"Ah, yes of course! Jolly old chap…"
"He told me I might be able to find an answer with his friends."
"He did, did he?"
"Yes. Do you think he was referring to you?"
"Maybe, maybe. Tell me your story."
Stella explained the odd circumstances by which she came to Geomno. When she was done, Euclid wore a contemplative expression.
"Well, do you think you could help me?"
"I might be able to…but first! I like you, girl, because your quest for knowledge amuses me. So I will help you in this quest! Do you know what a definition is?"
"Yes of course! But what does this have to do with-"
"What is a definition, then?"
"It uses known facts to describe a new word."
"Precisely! And how about undefined terms, eh?"
"No. I really don't see what this has to do with helping me-"
"Patience, my dear girl, patience. Terms such as point, line and plane are classified as such. Do those words sound familiar to you?"
"Yes. A point is a small dot on a plane (think up a better definition!)"
"And what of the others?"
"A line extends in one dimension, and is represented by a straight line with two arrowheads. It extends without end in two directions. A plane extends in two dimensions and is commonly represented by a shape which resembles a tabletop, although planes extend into infinity, also."
"Quite right. And how does a line differ from a line segment?"
"A line segment consists of two endpoints and a lone between."
"What about rays?"
"A ray has an initial point, and a line that extends into infinity in only one direction."
"Good. Can you define collinear points?"
"They are points that lie on the same line."
"And coplanar points?"
"Points that lie on the same plane."
"Bravo! It seems that you already know quite a bit, so I do not have much to teach you." Euclid paused for a moment, thinking. "Do you remember intersections?"
"Yes. Two or more geometric figures intersect when they share one or more points, and the point where they intersect is called the intersection."
"Very good. Now, I suppose Goldbach told you about reasoning and such?"
"Yes, he did."
"In the future, you will use those terms to help you prove statements. Another helpful tool you must learn is the usage of postulates and theorems."
"What are those?"
"Postulates, or axioms as they are sometimes called, are rules that are accepted without proof. Rules that are proved are called theorems."
"I see."
"You will be given those later on, but I wanted you to understand what they are first. Postulates and theorems also have names, such as the Pythagorean Theorem, which is very famous and, not to mention, useful."
"Ok."
"Now, getting back to what we were talking about before: points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is called the coordinate of a point."
"Oh yes! I learned this before!"
"Good! Well, I'm afraid that that's all I can teach you."
"Really? But…I still don't know the answer to my question!"
"What was your question? I apologize if you told me; my memory is failing in old age. I am 2,330 years old, you know."
"That's amazing! I didn't know people could live that long!"
"They can in Geomno!" Euclid winked. "Now what was your question?"
"How did I get into Geomno?"
"Ah! Well, you must have found some sort of enchanted book. I assume it serves as a portal between your world and this one."
"So Geomno is a different world?"
"Either that, or a different plane of your world."
"That's quite confusing."
"I suppose…have you ever heard of Quantum Mechanics?"
"No."
"Well, we'll save that for another time, then."
"Sure, but how do I get back home?"
"I don't know. I have a few friends down the road aways-maybe they can help you."
"Thank you, I will. Goodbye, Euclid!"
The Greek smiled. "Goodbye, Stella. I hope you are successful in your quest."
Stella smiled and waved as she headed off down the road again
