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Comment by the_other | Hacker News Reader

I'm interested in this from the perspective of learning maths, rather than writing code (for now).

I've wondered for a few years now whether teaching angles and trig using turns, rather than degrees or radians, would be better from the very beginning. Degrees are arbitrary and based on the numeric preferences of a dead culture, rather than on what's happening on the page or in 3d space. Radians seem better because the units are related to a property of the circle, but they're hard to visualise and reason about because they don't fit a circle in whole numbers. Surely turns are the most clear.

I'm rusty and don't practice maths much. If I did I'd probably have the skills of 14y/o me, for anything outside set theory. I'd definitely do a trigonometry course based on turns if I could find one.

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Radians makes the most sense just because (as others have pointed out) pi appears all over in math, and in all those places if you are working with a unit of raidans the math becomes a lot easier. In a few cases turns are easier to work with, but teaching them is a dead end to the vast majority of students who will never work in those domains, and even the few students who work in a domain where turns make sense they will still spend time in other areas of math that works much better in radians.

If mathematicians believed things can’t change or improve, and we have to stick with the status quo only because it’s common and popular, we’d never have had radians in the first place, we’d be stuck with degrees, no? Why assume that people can’t convert between turns and radians as needed, when we all already convert between degrees and radians all the time? Why not imagine a pedagogy that teaches turns and radians and degrees, giving students more flexibility than the current set rather than less?

> but they're hard to visualise and reason about because they don't fit a circle in whole numbers.

I think, unfortunately, that you can't avoid encountering irrational numbers in trig. You would need to constrain yourself to working only with right angles, but in those cases sin and cos are trivial[0] so there would be no need to use trig in the first place.

[0]: 1 or 0, you're either on the right axis or you're not. No circles involved.

> Radians seem better because the units are related to a property of the circle, but they're hard to visualise and reason about because they don't fit a circle in whole numbers.

When I was learning this in school, radians were always expressed as (fraction * pi), not the final number.

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