The last step of subtracting from numbers with lots of zeros is done mentally.

You can easily justify it using the "Same Distance, Same Difference" strategy in @howiehua.bsky.social's video.

Although I first encountered it as a "Vedic Math" sutra — "All from nine and last from ten"!

That means there are more questions like this? 👀

All great points! Full disclosure, this all came about because I wanted a quote for a calculus book I’m working on that isn’t just Ye Olde White Dude Newton or Leibniz again. Madhava and the Kerala school are some of my favorite examples of how much broader the history of calculus is. 🙂

Much appreciated! Are there any places where I could look at verified quotes from the work of the Kerala school in general that express a similar sentiment?

I'm a fan of James Tanton's treatment! He motivates the sine and cosine from the question of "how high up is the sun?" and builds everything very intuitively based on that.

www.youtube.com/playlist?lis...

Honestly the best thing has been including the phonetic pronunciation wherever I can. 😂 Have not tried the anti-burrito method!

What do you do?

That part was never the problem with the honorific and last name approach. You need to pronounce names correctly either way.

(And I remember that lit teacher ALWAYS got my last name right. Which has always been pretty uncommon, even sometimes from people who've known me for years.)

My 9th grade literature teacher did this! At the time it made us feel very "grown up" and professional. That's why I also did so myself when I taught high school.

I don't follow this practice anymore nowadays, though — I'm not a fan of the constant gender reinforcement.

xkcd.com/552/

"Logarithmic form" never made sense to me — I could never remember how it goes. If a^b = c, is it log_a b = c? Or log_b c = a? Which of the six permutations is the right one?

And I always found the phrase "a logarithm is an exponent" utterly unhelpful.

Inverses tell us WHY it's the order it is!

Here's how I always think of it:

e^(ln x) = x for the same reason that (x + 5) - 5 = x.

The whole point of logarithms is that they undo exponentiation, and vice versa.

If you do a thing, and then you undo that thing, you get back to where you started.

Inverses are the very heart of algebra!

Will order it today! Thank you!

Funnily enough I hadn’t considered linear combinations yet. I agree they’re really useful, but how would somebody have thought to apply that definition to little arrows in space and noticing that they measure alignment?

Put another way, if I want to teach my Calc III class about these products, how could I have them “naturally” come out of some exploration, where they could make the “oh yeah” leap themselves?