Chapter 4

The sun was now much lower than it had been before. Stella became slightly worried-suppose she would have to stay in Geomno overnight? Where would she find shelter? Stella had brought no money with her, and for all she knew, the currency in this land was something totally different from America.

Stella became distracted from her thoughts as she spied a very odd sight: there was the top of a ship's mast, complete with a crow's nest, peering over the crest of the next hill. How in the world did something that bizarre turn up in the middle of a plane? Stella hadn't seen any signs of water, except for a few small streams that wouldn't be able to allow a whole ship to pass through. She came over the crest of the hill and the sight she met with was very hard to believe. There was an entire wooden ship, set up in the middle of the plain. It's hull was buried half-way in the ground, and the sails were unfurled and snapped in the breeze. Upon closer inspection, Stella spied that the name of the ship was the Santa Maria. That sounded slightly familiar…

"Ahoy there!" A voice resounded from the ship. Stella looked up, to try to catch a glimpse of the caller. A man peered over the ship's railing. He had fuzzy blonde hair covered by an outrageously plumed hat, and a ruddy face. The rest of his clothing was just as extravagant, which looked rather foppish next to the background of a weathered ship.

"Hello!" She called, waving her hand. "Are you a friend of Santiago's?"

"Indeed I am, lass. Why do you ask?"

"I need to find a solution to a problem, and Santiago referred me to you."

"Ah! In need of assistance? I'll be glad to help! Here, come up on deck." The mad dropped a rope ladder over the side of the ship and Stella promptly climbed up. By the time she had reached the top and managed to drop somewhat ungracefully on the rough wooden deck. The man helped Stella to her feet.

"Thank you," said Stella.

"Ah! That is not a problem. So tell me, lass, what is your name?"

"I'm called Stella. Who are you?"

"My name is Christopher Columbus. I prefer it if you would call me Columbus." The man introduced himself somewhat brashly, with an air of superiority.

"Wow, I've read about you in my history book! It's very nice to be of acquaintance with you."

The man beamed, his ego sated. "Now, Stella, what is this problem of yours?" Columbus sat down on a small barrel, and gestured for Stella to do the same.

Stella told the man of her experiences from the time she left her geometry classroom to the present. "I am looking for a way home. Can you help me?" She pleaded.

Columbus mused for a moment. "Yes, I might be able to find some sort of safe passage for you…but first: why don't I teach you what I know? Oh, and it is getting quite near to suppertime. Would you like to join me?"

"Oh yes, thank you. That would be excellent." Stella could feel her belly rumble at the mention of food.

"Alright then! How does plum duff sound?"

"What is plum duff?"

"Ah! It is a traveler's dish worthy of the King's halls. You will be pleased, I assure you." Columbus led her to a closed hatch, and proceeded to open it and venture down into the darkness. Stella squinted in order to see, until he lighted a match. "You may come down, Stella. I keep a very clean ship!"

Stella nodded and followed after him, down through the hatch and through a narrow passageway. She came out to a room filled with cookware, an oven, stove, refrigerator, and a sink. Against one wall was a massive table with equally massive chairs. A delicious smell emanated from the oven. Columbus had been busy checking on whatever was baking when Stella came in. He peeled off his oven mitts (in the shape of lobsters) and drew out two of the large chairs. He sat down in one and gestured Stella to do the same. She sat down in the chair and Columbus lounged back, stretching his legs before him.

"What do you know about parallel and perpendicular lines?" He asked.

"Well, parallel lines are coplanar and don't intersect. Perpendicular lines intersect once and form right angles at their points of intersection."

"Skew lines are another form of lines. They do not intersect and aren't coplanar. A transversal is a line that intersects two or more coplanar lines at different points." Columbus strode over to a kitchen cabinet and took from it a piece of paper and a pencil. He came back to the table and plopped gracefully down into the chair, laying the paper out on the table. He grasped the pencil and drew three lines, labeling them and their angles:

"T is a transversal. The angles formed by the transversal have been appointed special names."

"What are they called?"

"Two angles (one and five) are corresponding angles, because they occupy corresponding positions. Alternate interior angles lie outside the two lines on opposite sides of the transversal, like angle one and angle eight. Angle three and angle six are alternate interior angles because they lie between the two lines on opposite sides of the transversal. Consecutive interior angles, like angle three and angle five, lie between the two lines on the same side of the transversal. Consecutive interior angles are sometimes known as same side interior angles.

"I see."

"Good. Now, these can become very important if you want to prove that lines l and m are parallel, or if you want to prove that, say, angle one and angle five are congruent. Before you learn how to prove them, however, you must learn a few postulates and theorems. The first is the Corresponding Angles Postulate, or the CAP as I like to call it. The theorem states that if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. The converse of that postulate is called the Corresponding Angles Converse. It says that if two lines are cut by a transversal so that corresponding angles are congruent, then the two lines are parallel."

"Ok."

"The next theorem is called the Alternate Interior Angles Theorem, or the AIA, which states that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. The converse states that If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. Ready for the next one?"

"There are more?"

"I'll give them to you in a nutshell; they are all the same except for the differences in angles."

"Ok," said Stella, relieved.

"The Consecutive Interior Angles Theorem (CIA) states that if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. The Alternate Exterior Angles Theorem (AEA) states that if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. There are converses for both of these. Now we must cover the Perpendicular Transversal (PT), which is slightly different from the others. It says that if a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other. Do you understand those?"

"Yes. They are crystal clear!"

"Very good. Now, do you know about slopes?"

"Yes! It's rise over run. Is that important in geometry, too?"

"Yes. There are a few basics you must always remember about perpendicular and parallel lines in a coordinate plane. If two nonvertical lines are parallel, then they will most definitely have the same slope."

"Why only nonvertical lines?"

"Because all vertical lines are always parallel."

"Oh! I see! What about perpendicular lines?"

"In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slope is -1. Vertical and horizontal lines are always perpendicular."

"Ah-ha! I understand."

"That is very good! My lesson is now over. Would you like some plum duff?"

"Oh, yes, please."

"Very good." Columbus took the meal from out of the oven and cut two helpings with a kitchen knife. He scooped the food out on two plates. He also fetched silverware and two small tankards which he filled with cider. He handed a plate and tankard to Stella. "Here we are!" Columbus exclaimed happily, digging in to his meal with an enthusiastic gusto. Stella took an experimental bite and chews for a moment with a skeptical look on her face, which quickly turned into surprise. The food was delicious!

After they had finished the meal, Stella turned to Columbus. "Have you given any thought to my question?"

Columbus leaned back in his chair. "Yes. I think that you must find the book that you came through-The Geomno, you say it was called? Yes, you must find it. It will be somewhere in this world-of this I have no doubt. When you find the book, I think you will know what to do."

Stella could have jumped for joy. "Thank you very much, Columbus! I am indebted to you! Only one thing: where is the book?"

"That is a question I do not know. I have some friends over yonder, however. They might be able to help you along."

"Oh, ok then." Stella jumped up from her chair. "I am afraid I cannot delay, so thank you again for the meal-it was delicious! Goodbye, Columbus!"

"May lady luck be with you, Stella! Farewell!" Columbus waved with his plumed hat. Stella nodded one last time and made her way up through the hatch. She climbed down the rope ladder with much more ease than before, and made her way down the road. By now, the setting sun had stained the sky a blood red. Stella cast a worried glance over her shoulder. Who knew what things could lurk in the wilds at night in this strange land?