2015 New Years Collection

I posted four "books" on my blog for some time now, and I would like to share it with the Brilliant community this year. The books are a collection of problems I created and some of my personal investigations. You will notice that a lot of my problems on Brilliant.org were created around 2010 - 2012 (before I entered university). It is not surprising if many of my discoveries are just rediscoveries, but I believe my work on asymptotics is original. For ease of access, here are the links to each book:

Book 1: Patterns

Book 2: Counting Structures

Book 3: Approximation

Book 4: Physical Problems

#HappyNewYear #StevenZhengInvestigations

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
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# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

You wrote these books yourself? That is really exciting!

Can you add a brief description of what is in each of these books? E.g. "Book 1: Patterns".

Calvin Lin Staff - 6 years, 5 months ago

Sure thing. I compiled this last winter break from my notebooks. Book 1: Patterns are problems that I collected from various places, only Distinct incircles and Revival of Sangaku are original . In Book 2, my investigation of polygon networks follows from my investigation of "Combinatorial Numbers. " However, I later learned that the integral is well-known. It was a cool find because if we set $a= -1$ we get derangement, $a=0$ becomes the gamma function, $a=1$ becomes the sum of permutations. Don't know any other applications.

Steven Zheng - 6 years, 5 months ago

What a great effort!

Chew-Seong Cheong - 6 years, 5 months ago

Excellent work! I just read the book 1, sangaku problems are great (Y). I have another method for inverse square problem using telescoping series.

Krishna Sharma - 6 years, 5 months ago

Hats off to you. I've not read any of your book but I'll sure be reading them. You've really done a great job. What are your plans in the near future?

Sanjeet Raria - 6 years, 5 months ago

I'm still in university studying physics and math. Not too sure what I will be doing in the next 5 years (I don't think anybody can be absolutely certain). Aside from studying, I volunteer for the UBC Math and Physics circles, R&D for the UBC Physics Olympics and judge at the Greater Vancouver Regional science fair. I also tutor and sell textbooks for profit.

Starting yesterday, I've been attempting to come up with an original proof of the Descartes Four Circle Theorem. It is pretty hard, and there seems to be one proof online, which is short but confusing.

Steven Zheng - 6 years, 5 months ago

Hey! Sorry to disturb you, Can you post some more sangaku problems? I really like them :).

Krishna Sharma - 6 years, 5 months ago

@Krishna Sharma – I will post one tonight!

Steven Zheng - 6 years, 5 months ago

Hi @Steven Zheng , I have my JEE exam coming up and Physics is not my forte !!! Can you give me tips on studying Physics ? Any help would do .

Thanks for the same :)

A Former Brilliant Member - 6 years, 4 months ago

Very nice , great work , how did you used LATEX in PDF?

Brilliant WIKI's are waiting for your contributions

U Z - 6 years, 5 months ago

This is actually Microsoft Word equation editor. But LaTeX software (which you can download online) automatically saves PDF files when you compile documents. I actually avoid LaTeX unless I have to or if the equations look really bad because LaTeX pumps out a bunch of files for one document.

Can I just create a wiki copy my notes on it? I haven't used the wikis yet.

Steven Zheng - 6 years, 5 months ago

What I know i s - you need to use LATEX sorry , or ask for a help from brilliant staff

U Z - 6 years, 5 months ago

@U Z – Did you mean I should have written the documents in LaTeX?

Steven Zheng - 6 years, 5 months ago

@Steven Zheng – No no.. , I am saying for writing mathematical texts in WIKIs LATEX is needed

U Z - 6 years, 5 months ago

@U Z – Well, that is true everywhere on Brilliant. LaTeX is the standard.

Steven Zheng - 6 years, 5 months ago

@Steven Zheng – LaTeX is the standard tool that most mathematicians and scientists use nowadays to type up their papers. It also allows for easier communication via email, as they can read the latex command instead of trying to describe what the equation looks like.

Much like how algebra made equations much easier to write ("The number, when added to it's twice of its square, produces four" is a pain to read), I believe that LaTeX will become the norm really quickly. Currently, most people are only exposed to it in university, when they have to start writing papers with a lot of equations, and other word editors become a pain to use.

Other than formatting math, LaTeX also has many uses in terms of formatting pages, creating sections/chapters automatically, allowing for new commands, etc. It's flexibility is enhanced by the numerous packages that other people develop for it.

Calvin Lin Staff - 6 years, 5 months ago

@Calvin Lin – I didn't knew that LaTeX is so popular! Learnt so much of LaTeX on brilliant! (Maybe more than maths) Now I just start typing " $\($ " everywhere! While chatting or while searching some stuff on Google!

Pranjal Jain - 6 years, 5 months ago

@Calvin Lin – Yeah, I never learned LaTeX before entering university.

Steven Zheng - 6 years, 5 months ago

@Steven Zheng – I had the fortune of being able to learn LaTeX before even entering a high school level and I can say it's been working great for me so far.

Jake Lai - 6 years, 5 months ago

@Calvin Lin – How would you use latex in email?

Agnishom Chattopadhyay - 6 years, 5 months ago

@Agnishom Chattopadhyay – There is tex for Gmail as a chrome extension, which would convert it into an equation.

If the other person also knows Latex and can read it, then you can just type it out. For example, if I say

\sum_{n=1}^ \infty \frac{1}{ n^2 } = \pi ^ 2 / 6

then you (who know Latex) can read it as $\sum_{n=1}^ \infty \frac{1}{ n^2 } = \pi ^ 2 / 6$ .

Calvin Lin Staff - 6 years, 5 months ago

Bro the fact that you're 20 still amazes me. I understood the first page of the first book at once That doesn't happen with a lot of books for me. You're really good. Do you plan to tutor math at the university level in the future?

Ceesay Muhammed - 6 years, 5 months ago

I already tutor at the university level; competing against grad students.

Steven Zheng - 6 years, 5 months ago

Wow! Hats Off Man. Keep it up!

Ceesay Muhammed - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$