Site updates for

After a few years, I thought it was time for a new layout. The goals:

  • Be warm & friendly
  • Be clean & readable (more whitespace & larger fonts)
  • Be easy to skim & search (search results and posts have image previews)

BetterExplained isn’t an authority lecturing you on facts: it’s an excited friend sharing what actually helped when learning.

Understanding Why Similarity Works

Similarity has bothered me for a long time. Why do all circles have the same formula for area — how do we know nothing sneaky happens when we make them larger? In physics, don’t weird things happen when you scale things (particles, insects, small children) to gargantuan sizes?

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, but we have proved it, and therefore we know it must be the truth.