Tuesday, August 29, 2017

The Matho-Dungeon Settlement Sphere, Part 6

The next day I went into the Geometry common room, and went right through into the Door room, disregarding any commentary or bs.

I was ready to keep moving, working my way through this stuff.

It was trolls at the white boards in the first dungeon that day. Trolls with huge stone rulers.

The first troll's first question was about the center of a dilation, I still wasn't totally familiar with the term and I bombed that one.

The troll's second question was also about dilations and centers. I was starting to get an inkling of maybe what it all meant.

I got it right. So it meant a scaling of a point or many points relative to their distance from some other point, called the center of the dilation. I had messed up and thought it was just a fancy name for scaling.

The first troll's last question was about a triangle's dilation, and I defeated that troll after taking that first whack from his ruler!

The next troll asked me about an angle after rotating a triangle about a point. But all angles stay the same before and after rotation. Easy!

That troll next asked me about a quadrilateral under reflection and what properties are preserved. It looked like all were right except for None of the above. That was right.

The troll's last question was about a line segment length under dilation.

The next dungeon troll had another choose the answers that apply question about dilation, and it looked like none applied, and that was correct.

I was getting familiar in the dungeon, instead of the practice rooms. I knew that wouldn't last forever, once I moved up to the more advanced geometric dungeons I might have to put in some practice.

I had come into this dungeoneering career hyper-cocky, but now I had to at least engaged in and think about the problems. Maybe I wasn't so much of a hot shot.

The third troll had an interesting question about changing one figure to another by using all of the transformations they had been asking about.

So I finished that first dungeon with three trolls, only getting whacked in the head by the first troll, and getting 88% overall.

I took a second to catch my breath, noticing I was now considered a Dolphin in Initiate - Geometry. It was more trolls, this time with spectacles in the next dungeon.

The first bespectacled troll asked me to take one figure to another using rigid transformations. Done. Coordinates of a point translated left and up. Done. Question about reflecting across y axis, done!

The next troll was bespectacled, wearing a pocketed shirt with pocket protectors. The pocket protector troll's first question was about the area of a triangle under reflection. Under reflection the area of a triangle stays the same. 1/2 base times height. Done. The next one was about the dilation of a point. Done. The next one was a dilation question but done in reverse.

The next troll had a slide rule as well. He asked about what type of rigid motion a motion up and to the left was. Translation, duh and done! Then there was a reflection line problem. DOne. Then another question about what type of motion, translation! Done.

I was getting these transformations down cold.

The next troll had a fancy scientific slide rule. The trolls first question was about an angle of rotation. Done.

Then there was a question about what symmetries apply to a rhombus. This required me to think about it. It looked like the first two symmetries were correct, but the 180 deg rotational symmetry was not sure. I looked at it some more and guessed all three were symmetries, and I got it right.

The next one was about a point after being rotated 135 degrees, and it looked like 2 answers could be right.  It looked like B was the same length from the center as P. So I guessed B. Right!

The last troll was holding a bunch of mechanical pencils. IT was a question about properties of a quadrilateral under dilation. None of the Above I guessed.

I got my first one wrong in the dungeon, but I wasn't sure which of the three possibilities was right.

The next one was about a reflection and coordinates. Done. The last one was a rotation and I got the rotation direction wrong again. Dangit I was on a roll too.

The troll stabbed me with a mechanical pencil. It stung, a lot. So I ended up with 87% on the dungeon. I had been hoping to get to another bonus combat section.

Onto the next one:

The little kobold with a little whiteboard was asking whether two quadrilaterals were congruent. It was easy to see they were.

Then there was a new type of question about an angle x in a diagram. The angle should be 55, the same as the one diagonally opposite. Done.

Then there was an angle x on the narrow part of an Isoceles triangles.

The next kobold had a question about whether two triangles that looked similar were congruent. They had two sides with the same lengths but the third side could be different, so I said there's not enough info to know. Done.

Then another isoceles question. Another parallelogram angle question. A triangle congruence question. I couldn't see how they could be congruent.

The next one was about two triangles with different angles were congruent, I said definitely not. Done. Another Isosceles, Done.  Another triangle congruence. Done.

Gotta perfect, with a combat bonus.

Some Kobolds came swarming out of wall that suddenly opened up.

"The sum of the angles of a triangle are 180."

pop! went one Kobold.

"The sum of the angles of a quadrilateral are 360."

popop! went one Kobold, exploding into the next.

"The sum of the angles of an n-gon is 180 * n - 360"

BOOM. Went maybe a dozen Kobolds in a nice fiery explosion.

It was time to get serious. I was getting comfortable in a geometric setting.

"The hyper-volume of an n-dimensional unit hyper-sphere is Pi to the n/2 power divided by the gamma function of n / 2 + 1."
 
BABOOM AWOOOOMM!

I couldn't hear anything, I was flat on the hard floor of the dungeon. I felt my face. My eyebrows were burnt. My sight was fuzzy. There was a gong, from nowhere.

"Super Surprise Award! Your spell just caused a 6.3 Richter scale earthquake in region 104. You have been placed in Initiate - Case Delta 9 track. Please return to the common room for processing."

This didn't sound like an award.

It must have been obvious to the others that I was the culprit as the crowd, some standing and some laying on the ground, all glared at me.

"Whose the perp?" asked the cops as they came in.

They pointed at me.

I was dumbfounded. How could math cause something that big in the greater world, when I had been inside a dungeon at the time? I mean, I wouldn't call the volume of a hyper-sphere something super-advanced.

How do they even handle the unknown dungeons if even these sorts of problems cause an earthquake.

I didn't say anything, but cooperated as the hauled me off to the local jail.

My dreams, snapped into two, by my dumbness. I didn't know about this world. And I knew math up to about an undergraduate level.

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