I definitely agree but there's no way this is "English/American style". It's because people have grand plans of making their article/book accessible to everyone, and they start off explaining e.g. what a vector is, but pretty soon realise the don't want to write an entire vector algebra textbook so they seamlessly give up and jump straight into Stoke's theorem or whatever.

I read a Synopsys simulator manual that explained what double clicking was.

English/American style of explanation fascinates me.

First, they show some algebra formulas and mention dot product and cross product. But then they start introducing a definition of a vector! With images!

Why, oh why do you need to waste yours and reader's time to introduce basic definitions, if any reader of the article definitely knows that? If they haven't, they wouldn't be able to read the first paragraph at all.

PS: Russian style of explanation is more like: "Here's the essence of my idea, maybe with some leading pre-definitions, but definitely without basics. If you are here, you probably is as curious as I am to already know/heard of all the basics." In total, there's more material, because it's easier to write and read it, as author didn't need to explain 101s to PhDs.

love your writing, can anyone recommend blogs like these

Wow the interactive 3D illustrations are awesome. Works perfectly on touchscreen, feels very natural.

I stopped reading at this paragraph near the top :

“In this post we will re-invent a form of math that is far superior to the one you learned in school. The ideas herein are nothing short of revolutionary.”

Yes, this. Though Zero to Geo is one of the links at the bottom of the article.

It is really a shame that article does not clarify that, btw, what we've just derived is a re-derivation of a thing that has already been expressed and named, by Clifford, and well-characterized: https://en.wikipedia.org/wiki/Geometric_algebra

Such a bummer to see very slick but very ahistorical articles.

You're right about that being wrong, and the author makes the same mistake consistently, but otherwise it looks correct. Some steps have details elided where it maybe should have been noted that things were being skipped, but with correct results. I think it's wonderfully written and a great exposition.

The writing is cute and the animations are nice, but none of it makes any sense. I stopped reading at

> It is important to remember that bivectors have a certain redundancy built into them in the sense that s a ⃗ ∧ b ⃗ = a ⃗ ∧ s b ⃗ s a ∧ b = a ∧s b . We can write them using 6 numbers or 3 numbers, but they actually convey 5 degrees of freedom.

Three (real) numbers have three degrees of freedom, by definition. (And nothing about complex numbers was mentioned.) Is this a parody I don’t get? I feel like I have wasted ten minutes on nonsense.