Explanations for everyone.
I want to share hard-won “a ha!” moments in clear and simple language. Even math shortcuts can be fun, I promise.
Math & Numbers
- Intro: Mental math shortcuts, adding 1-100, how to learn math, understanding averages
- Numbers: number systems, visual arithmetic, different bases, Prime numbers
- Statistics: Combinations & permutations, Birthday Paradox, Bayes’ Theorem,
- Geometry: Pythagorean uses, Pythagorean distance, degrees vs radians
- Exponents & Logs: Intuitive exponents, natural log
- Complex numbers: visual introduction, intuitive arithmetic
- Calculus: a gentle introduction, discovering pi
- Vector Calculus: Gradient, Flux, Divergence, Curl & Circulation
Programming & Web Development
- Site tweaks: Faster Javascript load time (examples), HTTP caching, gzip compression
- Ruby on Rails: Starting Ruby on Rails, Understanding MVC
- Tools: version control, distributed VCS
- Web Development: Debugging with Firefox, Javascript Reference, load XML/JSON data, gmail XSRF attack, GUIDs, making bookmarklets
- Low-level Programming: binary files, byte order, unicode, XOR variable swap, Fast 1/sqrt, gdb debugging, symbol tables
Business, Writing & Communication
- Writing: wordpress tips, how to blog
- Business: Rule of 72, pareto principle, marketing lessons, stock market, accounting 101, interest rates
- Thoughts: know thyself, simplicity vs. complexity, japanese innovation, notes on happiness
Recent Articles (See all)
Intuitive Understanding Of Euler’s Formula
Euler's identity seems baffling:
It emerges from a more general formula:
Yowza -- we're relating an imaginary exponent to sine and cosine! And somehow plugging in pi gives -1? Could this ever be intuitive?
Not according to 1800s mathematician Benjamin Peirce:
It is absolutely paradoxical; we cannot understand it, and we don't know what it means, ...
