Good Luck

Good luck to those taking the AMCs tomorrow! I hope I do well so I won’t have to stress about 10B/12B, whichever I decide to take in the end.

Edit: I did not do well.


Website Updates

I’ve updated the website so that it contains a sample of Exploring Euclidean Geometry.

The section included is F4 – Inversion. Take a look here.

Projected release: Those of you who read my last post know this is mid-April, but I am not exactly sure when it will be.

Also, the entire website will be rebranded as “EEG+other stuff.” This process starts today.

The New Year

With the New Year that has just arrived, I have an opportunity to revise the dates for documents for the next four months when I inevitably forget it is 2019. While I’m at it, I might want to revise my life as well.

  • Exploring Euclidean Geometry – Those who know me in person have already heard about this project. For those of you who don’t know, EEG is a geometry book leaned more towards those who are interested in learning something new in geometry instead of competition math. I have a couple of things I need to do for the book.
  1. First and foremost, finish all of the theory. Write a couple of problems for each section.
  2. Grind out geometry problems in general, adding them to whichever section is most fitting.
  3. When I feel there are enough problems to release this as a book, I will write a preface. (Note to self: Don’t go too overboard. Last time, I wrote 4 or 5 pages worth of introductions… during a standardized test.)
  4. Branding, website preparations, etc. (In particular, the home page of the website will advertise the book, so I actually have a use for my home page. In general, homepages are useless – but I digress.) Instead of having this website be known as “Dennis Chen’s website + book,” I will have this be known as “Book (also see some handouts).”

General notes on the geometry book:

Three sections on transformations to write. One currently written section (homothety) desperately needs more problems. Three sections on 3D Geo to write (I really do NOT want to do Analytic or Conics, because I’ve done enough of them in 2D Geo). 4 more miscellaneous (and short) sections to write, and I will probably pad the end of the book with some parting shots. 3+3+4=10, so 10 sections left to write.

The last section took me 13 days to write, but I think I can do better – churning out a section every 3 days should be possible for the shorter ones, because I’ve been busy with USAMTS and a “challenge.” Projective and 3D Analytic will probably take a week each. 3*8+2*7=38, so 38 more days of work and the book should be out. Since I have no school, I’ll subtract a couple of days and estimate 35. The problems will probably take me 2 months at most (I already have a couple in mind for some sections), preface/branding will take a week. I hope I can release the book by April.

(Of course, unless I have more content to add. Though I’m already writing stuff like Projective and by the time I’m done, I’ll probably be tired of geometry.)

  • Exercise Book to accompany EEG – as self-explanatory as it gets. I have a couple of nice problems in mind (USAMTS #5 from Round 2 in particular) to put on there, and I have some problems which I’m pretty sure I’ll forget on there. However, this isn’t very high priority with the actual book (with problems from yours truly) and the MPP Summer Camp (see below) coming up, which I care about a little more. Estimated release date: Probably 2020 at earliest.


  • MPP Summer Camp – This one really is in the works. I have to hope I’ll be done with the Geometry book (minus branding) by early March. Currently planned topics: Root Analysis, Factoring, Complex Numbers. I wanted to teach some Algebra (MPP was mostly about Geometry to this point), so that’s what’s planned. However, none of the handouts are written – though doing some old AIME’s has gotten the Root Analysis part pretty much done. I just have to write stuff.


  • Smash Ultimate – Get good at the game. I realized I have never blogged about this, ever. I gave up on my old main Kirby (who I religiously stuck by in Smash 4), and picked up some better characters. This is my character lineup:
  1. Pikachu – NEW MAIN NEW MAIN NEW MAIN! I used him in Smash 4 and boy is he much faster, stronger, and F-Smash is safe on shield! Thunder is ridiculous (which Pichu will bring to new heights), the new N-air lends so well into combos, and D-Tilt is plain stupid. There’s a reason some top players call him #1.
  2. Pichu – Despite Pikachu being my proclaimed main, I probably use Pichu more. Why? Because of his N-air and Up-air! I can run around the whole stage and spam those aerials to control the flow of the game. Yes – he hurts himself, but his best moves (N-air, U-air, U-tilt) don’t hurt himself. Also, the 1 percent he deals on Thunder is well worth the reduced lag. Pichu can still reasonably control stage with Thunderjolt, you can probably just charge Skull Bash and it’ll work, and F-Tilt, a move that you can spam, is a kill tool. The only complaints I have are that his F-Smash has awful range, and his Up-B does too much self damage and has no hitbox.
  3. Mewtwo – Two words: Forward. Aerial. (Also, Shadow Ball has so much stage control.) I was secretly hoping Mewtwo’s float from PM would come, but I’ll take an OP F-air over nothing any day.
  4. Meta Knight – His Up-B felt nice initially, but it’s too hard to connect. His ‘Nado being a kill tool though is welcome. The Rufio from Brawl returns (kind of) as he can kill with his ‘Nado (through the side, but details don’t matter). However, he’d go into my Pockets category.

So now I need to practice the Dash-Attack cancel tech. Goodbye. (For those of you who don’t know what I’m referring to, My Smash Corner made a video about it.)

(Notes to self: Reference AoPS V2 for Conics. V2 is a good start for Projective but research will probably need to be done on my own. Analytic = Vectors [mostly] as 3D neq 4D. Remember La Hire’s exists.)


After not posting something for long, I’ll post something a little bit underwhelming. The inactivity wasn’t because I had something really good right now (the only thing I have on the back burner is satire), but it’s because I’ve been busy with school work. With winter break, I’ve gotten more time to work on the things I care about (i.e. NOT school).  I hope you find this interesting, despite this post having no substance.

Remembering that all your students exist

I have 6 wonderful students and one not so wonderful student (screw you, Steven). When I need to list them all or take mental attendance, I have to get out the roster. I realize that I have 5 or 6 people listed and blankly wonder who I forgot, despite all 7 of them being in front of me. I pull up the roster and look for 10 minutes before I realize who is missing, and it seems very obvious to me after I find it.

Then we have teachers whose classes have 30 people a period, and have around 90 to 150 people in total. They can remember who exists without batting an eye; often attendance is done without looking at the seating chart and just by memory of seating arrangement. It truly amazes me how teachers can do that, when I can’t remember 7 people who I converse with often outside of class.

And we don’t understand why seating changes aren’t more frequent.

(I am very sorry, class, but it really is hard to list all of you guys. This probably speaks volumes about my teaching method, which is to make the lecture not tailored to anyone at all, so that the kids will think I am tailoring it to everyone.)

Trying to make problems

Boy, this is going to piss my class off. As if I didn’t already last time.

Whenever I make a conscious effort to make problems (i.e. flip through pages of study guides and textbooks to find an idea I can use), they usually turn out to be crap. (Around 5-10% of my problems are going to make it on, say, the final version of our entrance exam.) In contrast, my shower problems (usually brought on because of a combination of fascination for some idea, stupid flavortext ideas, and guilt that nothing I made in the last hour was remotely salvageable), I have a success rate of around 30-40%, and that is a very stingy estimate. At worst this is an improvement of x3, which I have no idea why.

Obvious Observations

Recently I was given the trivial line $$\angle HBC=90^{\circ}-\angle C.$$ The reasoning took me 10 minutes to realize. For those of you as lazy as me, this is because extending HB makes a right triangle. Oops.

I’m sure I have other idiocies, like $$\angle AOB=2\angle ACB,$$ but I don’t remember any of them as of the moment.


Disclaimer: I usually claim to be knowledgeable in what I blog about, but this time I do not claim to be. If you’re an expert, feel free to correct me, since I’ll probably be wrong most of the time.

Generally, when I write a handout on something, I’ll have two things: theorems, and problems. Theorems used were usually proved very long ago, and problems can easily be sourced as “2018/AMC 10A/25,” though (unfortunately) people don’t do the best job at citing and leave it as “2018 AMC 10,” which makes it take a while to find the problem.

Let’s take a look at what MLA has to say about citing your sources.

So, MLA, there’s this very helpful book for aspiring mathematicians. It is called, “the Art of Problem Solving: Volume 2.” Those of you who don’t know this are probably going on and searching it up, in which case it would be a good citation, since I made it easy to find.

Take for example, this imaginary quote from an imaginary chapter of my imaginary book.

A History of Logarithms

Chapter 1 – What is a Logarithm?

To understand the history of logarithms and their uses, we must first understand what exactly a logarithm is. For this task, I turn to Chapter 1 of “the Art of Problem Solving: Volume 2” for the definition of the logarithm and the six most important properties.

[insert definition]

[insert properties]

Now let’s let the MLA do this for us!

A History of Logarithms

Chapter 1 – What is a Logarithm?

To understand the history of logarithms and their uses, we must first understand what exactly a logarithm is.

[insert definition]

[insert properties]

Then, you get to flip to the end of the book, find the bibliography (this is much more annoying the further in you get), and it will say this following:

Works Cited

Rusczyk, Richard, and Sandor Lehoczky. The Art of Problem Solving. AoPS Inc., 2013.

Insert source here.

Hanging indents suck.

Here’s my initial reaction to this:

When did you use this source? Which AoPS book is this? What counts as a citation? What section did you use? What is wrong with you?

After I calm down, my thought-out and reasonable response would be this: “You can go screw yourself.”

(Note: The original draft of this post had an endnote, and a rant on why footnotes are far superior. Then I remembered that many people will simply put “Bibliography” and have no reasonable way aside from guessing to know where each reference fits in, making it even more annoying.)

How to Fix MLA

I’m not an English/History teacher or professor. If my peers did this, I would be extremely annoyed, but they don’t. Ideally, English teachers would have other English teachers to tell them that they need to stop making their citations so lengthy, effort-requiring, yet worthless. This should mean that I don’t care about MLA citations, since it’s not my place and they don’t affect me.

However, due to the dreadful government institution that serves barely-edible food, has people stand in an orderly grid-ish fashion to take rollcall, has iron gates as a security feature, has officers that patrol the campus, is filled with zero-tolerance policies, and has a schedule strictly to the minute, this becomes my business. (And for those of you wondering whether this is school or prison, this is school. Prison inmates don’t have to write English essays, which may be the only difference.)

The true fault does not lie with the MLA. The fault lies with English and History teachers around the country. If they’d let me write my papers the way I write them, while actually demanding a satisfactory result (i.e. don’t give me 100% for sucking up in the entire essay), I wouldn’t complain about the actions of a far-off organization. When they make me adhere to the standards of a far-off organization, I expose the sheer stupidity of said standards.

TL;DR: Stop making kids do MLA citations!

Training with the Right Perspective

There’s someone who has been bugging me to post something for a while (you know who you are!), so I’ll actually post something substantial. I hope this will be worth the wait.

Studying for a Test

It’s very common in math class that the people who perform consistently well on math tests never study for those math tests specifically. Of course, they still do math often, and truly enjoy the subject. There are a couple exceptions, but in the end everyone knows that’s all there is; they’re just good at tests.

But this first class of people have a name, though this is a very uncommon description. We are known as the competition math kids, though we usually just get called “math kids.” It’s very well known that math is unique in the fact that competition math has nothing to do with school math; competition physics and school physics correlate, as does chemistry, computing, etc.

So why do the kids who do competition math perform so well on school tests, without those performing relatively well on school tests excelling at competition? What makes the difference? And why do people who study for tests for hours each day the week before usually fail, or barely “pass?”

While this is the natural order to ask the questions in for most people, the natural order to answer them in is the opposite. The way you ask your questions, in addition to the actual questions themselves, influence your answer. The reason people have been asking these questions in the wrong order while feeling that it is the right order is because they’ve been conditioned to think about it in the wrong way. The question I’m asked most often is, “How are you smart?” as opposed to “Why am I not?” which reflects the order these type of questions are asked in. (Some survivorship bias is also present when asking just the people who succeed. Often more than not, quite a couple strokes of luck are involved.)

You’ll notice that the lines of thinking for math tests go differently. Some people think, “I’ll study to get a good grade. It’d be nice to get smarter, but that’s not a priority.” Other people think, “I study to get smarter. It’s good to do well on tests, but that’s not a priority.” Surprisingly, it is often the latter type of person who ends up doing better on tests. However, most people think the former, which demonstrates a backwards thinking and a lack of understanding of math.

Most of us know people who study a week or so before every math test. Some end up only studying the night before, and others end up getting respectable grades. But even for those who believe grades are all that matter, people who study not for grades but to get smarter usually are the ones with the best grades.

But having the right mindset is not alone to succeed. I personally know some people who don’t study for grades but are still failing a particular subject. This doesn’t make their efforts worthless; this work ethic is arguably much more valuable than the specific success itself. (While I think some parents overstate the “genius” of competitive math kids, part of the reason they say this is because of the work ethic. After all, nobody gets a job doing high school math olympiads…)

The kids who do math for the sake of math become good at math, which is why they generally crush school tests, if they aren’t exceedingly stupid. (By “exceedingly stupid” I mean “show your work” or something of that sort.) The kids who do math for the sake of a grade become good at getting grades if they are really lucky, but they don’t get much better at math, meaning they have to do it again the next time there’s a test.


In general I think people understate how much they have done and overstate how much they can do. This makes sense from a motivational standpoint; the more you think you can do, the more you will try to do, and the less you feel you have gotten done, the more you feel you need to get something done.

But sometimes I feel this backfires. The feeling of “I’ve never done anything, and anything I try to do ends up sucking” can be very detrimental all the same. When no noticeable improvement occurs during the first few weeks/months of whatever you’re practicing, it can be very disconcerting. It’s very easy to beat yourself up over this, but we often forget how much we have accomplished. I’m certainly very guilty of this. Having your handouts written down somewhere though does help to give perspective, so I have it easy there.

Everything has to come with moderation, though; spending too much time thinking about what you’ve already done leads to a false sense of satisfaction and not doing anything else. Spending too much time thinking about how little you’ve done also leads to getting nothing done. I’m not sure how to quite accomplish this balance, but I’m vaguely aware it’s important.