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:

## Comments

Sort by:

TopNewestWhat a great effort! – Chew-Seong Cheong · 2 years ago

Log in to reply

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 · 2 years ago

Log in to reply

– Steven Zheng · 2 years 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.Log in to reply

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 :) – Azhaghu Roopesh M · 1 year, 11 months ago

Log in to reply

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 · 2 years ago

Log in to reply

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 · 2 years ago

Log in to reply

– Krishna Sharma · 2 years ago

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

– Steven Zheng · 2 years ago

I will post one tonight!Log in to reply

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 · 2 years ago

Log in to reply

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 · 2 years ago

Log in to reply

– Steven Zheng · 2 years ago

I already tutor at the university level; competing against grad students.Log in to reply

– Ceesay Muhammed · 2 years ago

Wow! Hats Off Man. Keep it up!Log in to reply

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

Brilliant WIKI's are waiting for your contributions – Megh Choksi · 2 years ago

Log in to reply

Can I just create a wiki copy my notes on it? I haven't used the wikis yet. – Steven Zheng · 2 years ago

Log in to reply

– Megh Choksi · 2 years ago

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

– Steven Zheng · 2 years ago

Did you mean I should have written the documents in LaTeX?Log in to reply

– Megh Choksi · 2 years ago

No no.. , I am saying for writing mathematical texts in WIKIs LATEX is neededLog in to reply

– Steven Zheng · 2 years ago

Well, that is true everywhere on Brilliant. LaTeX is the standard.Log in to reply

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 · 2 years ago

Log in to reply

– Pranjal Jain · 2 years ago

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!Log in to reply

– Agnishom Chattopadhyay · 2 years ago

How would you use latex in email?Log in to reply

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 · 2 years ago

Log in to reply

– Steven Zheng · 2 years ago

Yeah, I never learned LaTeX before entering university.Log in to reply

– Jake Lai · 2 years ago

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.Log in to reply