Goals

   As it is almost halfway through the school year, our instructors have decided it is time for us to decide on some concrete goals for what we wish to do with our blogs. Here are my three goals-- one for this blog, one for CWatKPCN (with Jasmine, Nate, and Andy), and one for AFaiG (also with the three aforementioned group members).

Concerning Triangles

Triangles, as with lines, vary between types of geometry.  This is merely an overview of their behavior on different planes. A more detailed analysis of triangle similarity and non-Euclidean trigonometry is in store as soon as I figure out how, exactly, non-Euclidean trigonometry works.

People...

   I have not yet contacted any experts on my topic. For research purposes, I honestly prefer to learn from reading than from people. I do, however, have some ideas on people to contact once I have developed a concrete direction to point a potential conversation in.

Sources

 This is a list of the books and sites that I have been using for my research. Most information presented in other blog posts comes from one of the following sources.

Fake Spheres?

   Just as the sphere models elliptic geometry, the "pseudosphere" is the model of hyperbolic geometry. It is, however, a bit less well-known than its elliptic counterpart.

It's All Greek at Heart

The first great mathematicians were all Greek. As Leonard Mlodinow said of the Egyptians and Babylonians that came before the Greek, "like our political leaders, they sometimes accomplished astonishing feats with surprisingly little comprehension of what they were doing. Nor did they care." The Greeks, on the other hand, did care. And so while the Egyptians built pyramids with their knowledge, the Greek mathematicians-- Euclid, Pythagoras, Thales, Eratosthenes, Archimedes, Hypatia, and many more-- are immortalized through their work in the creation of the system of mathematics and logic called geometry.

The Line In Its Natural Habitat(s)

   The line is defined, by Euclid, as "that which lies evenly with the points on itself." This is utterly useless as a definition, as it seems complete nonsense unless one already knows what a line is.
   One common alternative way of describing a line is as the shortest distance between two points, or a geodensic. Now, as explained earlier, the shortest distance between two points on a sphere is along a great circle. While lines on flat planes appear straight, on elliptic and hyperbolic planes they are curves. It follows that while parallel lines on flat planes will remain the same distance from each other for their entirety, on curved planes they will curve towards or away from each other.

More Conundrums

The riddle from the last "conundrums" post: a man comes out of his house and walks one league south, then one league east, then one league north, then finds himself back at his front door.
Aaaand, the explanation...

Risk: Takes 2 and 3

Take 2:
     As our Risk board was cleared off since we last played and we didn't take any pictures of it, we had to start over. Jasmine was absent, so I played for her, managing to get the entirety of South America and Africa for her (then having her squander it by putting all her little soldierpeople in Madagascar, but never mind about that). However, we didn't save the board again, so on to take 3.

The Problems with Problems (old)

Yeah, I probably should've posted this when it was still relevant... Our problem ended up being a people-problem with people's troubles assimilating into high school at the start of freshman year, which I don't personally think is one, but the supermajority of survey answers from our class overran my veto attempt. Anyways, the post:

A Fellow Lily

"This is not intended to be
free verse.
Writing each phrase on a separate line
facilitates rapid reading,
and everyone
is in a hurry
nowadays."
-Lillian Rosanoff Lieber 

Circles, Great and Small

  Oftentimes the paths that airplanes take to travel long distances don't look straight when drawn on a map. But the fastest path from point A to point B is a straight line, right? The only problem is, that a straight line from, for instance, Chicago to Beijing, would have to go through the center of the earth. 

Fellow Inventors

     A look at some of our more-successful fellow board game designers; also posted on the CWatKPCN group site.

Math Joke (10/22)

     I'ma try to post a math joke at least once every week or so, just to make me remember to keep posting stuff. We'll start off with an easy one, and since Halloween's right around the corner...

Q: What do you get if you divide the circumference of a jack-o-lantern by its diameter?

Conundrums

 Murdered cricketers. Who ever knew there so many, and why on earth are they important enough to have an entire Wikipedia page? That, indeed, is a conundrum.
 Speaking of conundrums, I have one for you. Consider this: a man comes out of his house and walks one league south, then one league east, then one league north, then finds himself back at his front door.
Able to explain? Please do. It is indeed related to non-Euclidean geometry, in case you're wondering.

Perhaps...

     I've been looking around at potential books for the class for second quarter, because while The Talent Code seems perfectly interesting, it also seems to be almost exactly the same as Outliers. Of course, that's kind of what the teachers want us to read, but I figured we could at least get a book with a better title. 

Bounce: Mozart, Federer, Picasso, Beckham, and the Science of Success by Matthew Syed

The Wisdom of Psychopaths: What Saints, Spies, and Serial Killers Can Teach Us About Success by Kevin Dutton

Quarter 1: Outliers

In-class analysis and applications of the concepts addressed in our first quarter required reading book, Outliers by Malcolm Gladwell.

Elementary, my dear self.

     Non-Euclidean geometry is defined as any geometry in which the parallel postulate is not true, which tends to occur in elliptical and hyperbolic planes (as opposed to flat ones, of course), hence the two main geometries within the non-Euclidean ones (geometry-ception, eh?), aptly named elliptical and hyperbolic geometry. The parallel postulate can refer to Euclid's fifth postulate (If a straight line falls on two straight lines in such a manner that the interior angles on the same side are together less than two right angles, then the straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles) or Playfair's axiom (Through any point in a plane, there is at most one straight line parallel to a given straight line).

Book, books galore!

     Some potentially interesting material in varying degrees of relevance. The general trend is from most to least relevant, but there are some stragglers. As you may be able to tell, there are many books I find potentially interesting. Format in parentheses for books that I actually have.

Colonel White and the Kung Pau Chicken Nuggets

Our group name is Colonel White and the Kung Pau Chicken Nuggets, KWatKPCN for short.

Group member name- Personality Type- Topic of Interest
Lily- INTJ- Non-Euclidean Geometry
Nate- INFP- Psychology of Child Trauma
Jasmine- ESFJ- Social Psychology
Andy- ENFJ- Neuropsychology and Memory

Colonel White and the Kung Pau Chicken Nuggets- The GeoPsych Ward (site)

Euclid

Euclid of Alexandria (see Fig. 1) lived a long, long time ago. Almost as long ago as Pythagoras, though not quite, unless he was born over 200 years before he "flourished."

What I Know...

...about non-Euclidean geometry: absolutely nothing, other than that it's hopefully confusing. My book is Introduction to Non-Euclidean Geometry by Harold Wolfe.

Mission Statement?

The mission of my blog is to get me A's in Critical Thinking Gifted this year. It will accomplish this by allowing me to record my experiences in teaching myself to process and retain new and confusing information beyond its current comprehension capabilities through the learning of non-Euclidean geometry.

About Flowers

     First off, my project isn't about flowers, despite the slightly misleading blog address. Though I'm guessing nobody actually knew what a chincherinchee was before now, so I shall inform you. It's a white, star-shaped flower in the lily family, native to the Cape of Good Hope, with the scientific name ornithogalum thyrsoides. Anywho, the project (and, consequently, this blog) is about non-Euclidean geometry, which I'm sure everybody finds quite fascinating, eh?