Memorizing the First 100 Perfect Squares
Whether you love Number Theory, math competitions, or just have an affinity for numbers, there are many reasons why you would want to familiarize with perfec...
Posts by Category
Mathematics
Cistercian Numerals
A while ago, I came across this fascinating YouTube video by Numberphile about a number system called Cistercian Numerals. They were developed used by the Ci...
Doomsday Protocol — A Review
As Gregor Samsa awoke one morning from uneasy dreams he found himself stuck within a barren wasteland. Apparently, he has time travelled to the year 2637, an...
The Magical Hexagon of Trigonometric Identities
The magical hexagon of trigonometric identities is a handy mnemonic to help you remember a handful of the common trigonometric identities in a very straightf...
Maximizing a Trigonometric Expression: asin(x)+bcos(x).
I came across a maximization problem involving trigonometric expressions that I thought was interesting. It might be quite standard, but I have never seen it...
MSC Notes: Computing the Derivative of Cosine In Various Forms
On Wednesday, when I was tutoring at the Math Study Center at Phillips Academy, I came across the following limit. I tried to compute the former (given) limi...
Pinter Algebra Chapter 3 Summary
This is part of a series of summaries I am writing for Pinter’s A Book of Abstract Algebra. Chapter 3 is about groups. We will take the definition of binary ...
Pinter Algebra Chapter 2 Summary
This is part of a series of summaries I am writing for Pinter’s A Book of Abstract Algebra. Chapter 2 is about binary operations. When defining/verifying ope...
Two Proofs of the Irrationality of Euler’s Constant
While reading Apostol’s Mathematical Analysis, I came across a proof of the irrationality of e quite early on, in Theorem 1.11. This proof was discussed much...
Basic Definitions in Group Theory
Over the past month, I have been reading the first chapter of Dummit and Foote’s Abstract Algebra on basic group theory. The following is a summary of my not...
General Structure of Euclid’s Proofs
The following is taken from an exercise of the first section of Hartshorne’s Geometry: Euclid and Beyond.
The Principle of Induction in ZFC
I’ve always felt that the Principle of Induction was a little bit mysterious. Recently, I came across an explanation of PoI using ZFC Set Theory and Inductiv...
Puzzles
Preliminary Ideas for a Rubik’s Cube Club
Speedcubing, the act of trying to solve a Rubik’s Cube or related twisty puzzles in the shortest amount of time possible, was a hobby that I picked up years ...
Blindsolving the Rubik’s Cube: Memorizing the Speffz Lettering Scheme
A few months back I decided to challenge myself to learn how to solve the Rubik’s cube blindfolded. Recently, to speed up my blindfolded practice, I labelled...
Algorithms in Speedcubing
Speedcubing seems impossible to those who don’t know the “secret,” and that secret is the algorithms. Memorizing algorithms is definitely a tedious part of s...
Chinese
Learning Traditional Chinese (Part 2)
In the last article, we discussed the formatting of the Master List and how it could be used to aid the study of Traditional Chinese characters, assuming fam...
Learning Traditional Chinese (Part 1)
As a Chinese speaker, I want to be able to understand as much Chinese as possible, whether that is on the internet, in books, or in any other written form. W...
注音（bopomofo）入门教学
注音符号，另称“bopomofo”，是现代汉语的标音系统之一，除了可以标注普通话，也可以用来标注其他汉语方言，例如闽南话。注音创立于二十世纪初（中华民国时期），虽然现今已大致被拼音取代，但在字典中还能看到。截至目前，注音依然是台湾的首要拼写系统。
Introduction to Zhuyin (Bopomofo)
Zhuyin (注音), also known as Bopomofo, is a Chinese transcription system that is capable of transcribing all the sounds of standard Mandarin Chinese, although ...
Programming
Colemak Keyboard Layout Update
After a three weeks of trying out the Colemak layout, with 5-20 minutes of practice almost every day, I was able to reach 43 words per minute on monkeytype o...
Ideas on New Keyboard Layouts (Colemak)
I unintentionally dove into the rabbit hole of alternative keyboard layouts, where I learned about the history of the QWERTY layount. I found this to be inte...
Ideas for a Blog LaTeX Parser
After writing a few blog posts using LaTeX, I have gotten used to writing math in Kramdown and MathJax. However, since I plan to post more regular reviews/su...
Andover
Freshman Winter English Project
Over the last two weeks, my English class accomplished a spectacular final project collectively. Inspired by the Annaresti spirit of collectivity from our cl...