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

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestWhat a great effort!

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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".

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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.

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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 :)

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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?

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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.

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

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

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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?

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

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Wow! Hats Off Man. Keep it up!

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

Brilliant WIKI's are waiting for your contributions

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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.

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

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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.

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

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