Essays

Some answers are better written down

One concept per page, with the answer in the first paragraph.

A video is a bad place to answer a specific question. You can't skim it, you can't quote it, and you certainly can't check one number in it while standing next to a treadmill. So the ideas from the series also live here as writing: each page takes one concept, gives the short answer straight away, and then spends the rest of its time on why that answer is true.

These aren't transcripts. A chapter that covers three ideas becomes three pages, each one finishing its own thought.

Ratio

A ratio isn't a slice of a whole

Why a percentage is allowed to pass 100%, what separates a ratio from a proportion, and why a comparison never needs the absolute sizes.

Derivative

"Marginal" is just the economist's word for a derivative

Marginal cost is dTC/dQ. Why MR = MC is the first-derivative test in a business suit, and why the textbook's one-unit version differs slightly.

Trigonometry

Slope and angle aren't the same number

Why a 15% treadmill incline is about 8.5°, not 15° — what percent grade actually measures, and why grade and degrees drift apart as the hill steepens.

Linear algebra

Coordinates are counts of building blocks

What a basis vector is, what makes a transformation linear, and why the columns of a matrix are simply where the basis vectors landed.

More on the way

One page per chapter so far, each taking the corner of that chapter people actually search for. Next in line are the ideas the chapter in production keeps leaning on: nudging a point on a surface, and what a directional derivative is once you have vectors.

In the meantime, the four published chapters are on the series page.