# Reflections: Day 1 (Seoul)

I’ve been feeling compelled to write some of the things that go through my head, and a lot of good stuff doesn’t make the blog; I hope to change that soon. There are a couple of interesting things going through my head, math and non-math alike.

As thus I feel a desire to keep a journal of some of the events that transpire and my thoughts on them, not for any real reason in particular other than fun(?) I suppose. Sentence structure will probably be more free-flow as well.

And of course, a lot of you are “here for the math,” so I will include at least one problem every day. Hopefully more. (This is mostly to force me to actually do math every day.)

# Problems

(AoPS Introduction to Geometry, Problem 3.44)

$\triangle ABC$ has a right angle at $\angle C.$ Points $D$ and $E$ are on $\overline{AB}$ such that $AD=AC$ and $BE=BC.$ find $\angle DCE.$

(Classic Problem)

Consider square $ABCD$ and point $P$ outside $ABCD$ such that $\angle APB=90^{\circ}.$ Prove that the angle bisector of $\angle APB$ cuts the area of $ABCD$ into two equal halves.

(Mandelbrot, 2000-something)

There are two possible triangles with $AB=13,BC=10,$ and $\angle A = 40^{\circ}.$ What is the sum of the two possible values of $\angle B?$

Solutions will be included as a comment to this post, as to best avoid spoilers. None of these problems are hard (though the second one will make you feel very smart when you solve it).

# The Plane Ride

Oh, boy, this was the worst part. Plane rides are half the reason I dislike travelling to different continents. On the 10 hour flight to Seoul, I decided to watch movies (and anime) the entire time, much to the chagrin of my parents. (The movies were Spiderverse, Crimes of Grindelwald, and Lego Movie 2. I also found One Punch Man on the plane’s catalogue, and watched it.)

The plane ride was boring, and it (along with actually getting to the hotel) resulted me in being so tired I walked like a drunkard. The food was also unacceptable.

As I left the plane, I saw that some of the people who sat on the plane took the liberty of taking their trash (including a really disgusting half-eaten piece of bread) and throwing it on the ground. No wonder airplanes are such a breeding ground for disease.

# Public Transportation

We did not rent a car as public transportation and taxi would pretty much get us anywhere we wanted, and the culture is much more accommodating to those who want to survive without a car. This is a good change of pace from the States, mostly because we stay in a better mood when we don’t have to actually FIND where we are going on our own.

My first impression of the subway system was that it was big. However, I soon noticed something more meaningful; the subway was very clean. Unlike pretty much every urban area in the States, there isn’t a ton of litter on the streets. I suspect this is a cultural thing at some level, because in the States even cities not so densely populated (like my hometown) suffer from litter all the time.

The view of the highways actually looks very similar to home in the SFBA, where you see a couple of billboards, non-residential buildings, and for some reason, a lot of water.

# Food

holy CRAP it’s spicy

# Jet Lag

The only type of lag that makes the input lag in Smash Ultimate seem acceptable. Fortunately, due to a LOT of luck in timing and some cooperation from my body, I don’t actually have to suffer it (I hope). I went from 6:20 AM on Sunday to something like 3:00 AM the next day (all Pacific Time) without sleeping, so I could sleep and wake up at a relatively normal time. I did wake up relatively early so I suspect I will have to power through the next day without sleeping the only way I know how – with an unhealthy dose of video games.