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Comment by helterskelter | Hacker News Reader

I've been relearning trigonometry lately by myself for navigation and astronomy; not for work, just curiosity I guess. One book I've really enjoyed is Heavenly Mathematics by Van Bremmelen. It's a spherical trig textbook, but it's written by a math historian who describes how trigonometry was gradually developed over human history and he discusses its early proofs, methods and applications. I have to confess that the historical approach has really helped me develop a more complete mental picture and appreciation of the math itself. Understanding the "how" and "why" of its development, and seeing the early practical need and implementation for some of this stuff has made the topic a lot more engaging.

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It seems like you'd get a lot deeper understanding by doing it that way, and be much more able to adapt the knowledge to the real world, vs only knowing how to solve problems in the exact form they were presented to you. I had so many semesters of undergrad math, did fine, but feel like I took basically nothing from it.

This is the approach I take to learning just about everything: Ask the five W's: Who, what, when, where, why?

It compounds, as you learn more history, you're able to connect more and more dots, and learning new information becomes easier on average.

Yep, build up your interior knowledge graph, each connection reinforces the nodes it joins.

Is spherical trig still a thing? Calculation is so cheap now. If you want to find the spherical distance between cities from first principles, it's easiest to convert to 3D rectangular coordinates and find the angle ABC from the vector dot product, where A and C are the cities and B is the center of the earth. Same for other types of navigational calculations like headings. But, I've never looked into it really.

Yep, it's mostly used in for navigation, especially as a backup in case GPS fails (in the case of a lightning strike on a sailboat, for instance, probably all your electronics are toast). The military still uses it with slide rules/log tables, in case of jamming, etc. It kind of "disappeared" sometime after WWII, and there aren't many new books on it, but you'll see it come up in computer graphics and animation quite a bit, and I'm pretty sure it's used extensively in surveying still.

Sorry, author's name was Van Brummelen, not Van Bremmelen.

You know you can edit your comment right. You are still in that edit window.

Edit window is 10m now.

Oh! My bad.

This is a very entertaining hobby to have. Wishing you a lot of fun.

Next stop, making sundials and reading astrolabe.

I was so surprised to know that Chaucer had such interest in the workings of an Astrolabe. It's not much of a surprise if you think that Astrolabe were the pocket GPS, pocket watch, pocket star chart of those times.

Honestly I've been thinking about putting some standing stones in my yard to act as solar clock and calendar, maybe doing a lunar calendar as well...

I don't that's against code (yet).

All the best for your Stonehenge.

Just knowing that the Sun doesn't really rise on the East (barring exceptions) is a fun reward in itself.

Solarigraphy and Analemma tracking are great fun if you have the luxury of an undisturbed access to the skies.

https://en.wikipedia.org/wiki/Solarigraphy

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