[kortilla]

> Am I wrong?

Yes. Trigonometry is extensively taught in the US. People forget this stuff if they don’t use it.

Ask some 30 year old chef in whatever country you fantasize teaches properly to compare and contrast turns vs radians and you’ll get similar responses.

[js2]

I'm a 50 yo programmer. I have a CS degree. I don't even remember my college calculus much less my high school trig. I just haven't had cause to use it in my career, not as a sysadmin, not as a programmer. My son is taking calc 3 and I knew I happened to have my calc 3 notes from the mid-90s, so I pulled them out of the filing cabinet and my very carefully taken notes, my proofs, my hand drawn graphs, it was all gibberish to me. That was stuff I knew like the back of my hand when I graduated but it quickly faded away.

[jerf]

By far the most annoying myth I face when trying to discuss the pros and cons of various education techniques is the pervasive idea that everybody is a magical knowledge sponge and will go to their grave still remembering how to integrate by parts and every detail about some particular battle they covered in seventh grade, and therefore, if we slightly tweak a curriculum plan to drop something that was included on theirs we'll be stealing that knowledge from all the 70 year olds who will eventually have been on that plan.

Where this idea comes from I have no idea. Personally looking around in school itself it was plainly obvious this was all going in one ear and out the other for the majority of students even at the time. The better students retained it long enough to spew it out on the test but that was already above average performance. That doesn't mean there isn't still a certain amount of value in that in terms of what that knowledge may do to their brain during the brief period of time it is lodged in there. (I think there's a lot of value in just learning the "shape" of all this stuff, and perhaps having some index of what might be valuable to know.) But the idea that we can spend 15 minutes and a one-page homework assignment on something and expect that to last 60+ years is just nonsensical.

I mean, honestly, anyone over the age of 22 or so ought to be able to notice a distinctly sub-100% retention rate simply by looking inside themselves.

Yes, to a first approximation everyone with a normal education in the US has been present while some sort of trig was discussed. Not all of them, but still quite a lot of them, were present for the Taylor expansion discussion. The vast bulk of them have had it decay by 25, and there simply isn't anything to be done about that if you're talking about humans and not some homo educationous who mythically retain all knowledge they were exposed to even for 30 seconds just as the mythical as homo economicus perfectly rationally conducts all their economic business at all times. Perhaps they're actually the same species.

[simiones]

I remember being amused by this same observation when my own country decided to reduce mandatory education from k+12 to k+10 (cutting two years of high-school). They immediately began re-arranging the curriculum in high-school, for example to move organic chemistry from 11th grade to 10th grade, on the basis that it's important for students who only finish the mandatory 10th grade to know some organic chemistry as well, instead of the old curriculum which would have only taught them inorganic chemistry after 10th grade (this has the bonus of making the chemistry curriculum inorganic I -> organic I -> inorganic II -> organic II, for maximum confusion).

To me, even though I was barely out of high-school at the time, this was obviously absurd - expecting especially someone who wants to drop out of high-school early to retain any notion of organic chemistry taught in a school year, that they couldn't learn on the job if it was really required, seems so obviously nonsense that I couldn't help but laugh. Especially since the same thing was done to basically every other subject as well, with the same intentions.

One note: in my country, the curriculum is completely centralized; there is some small amount of choice, but it amounts to, at most, 1-2 classes per semester; everything else is fixed.

[PKop]

Think it's part of the equality/blank-slate myth that everyone is the same and has the same potential and natural abilities.

[nightpool]

Actually, it's almost entirely the opposite—the idea that students are a "sponge" that can soak up knowledge perfectly is then taken directly to mean that some students are better at soaking up / retaining knowledge then others, and that the "smart" kids who do the best on the tests are the ones who are going to retain the knowledge the best. And then the ones that were the best knowledge-sponges will eventually go on to become the next generation of teachers, since they know the most information. Whereas for most kids it's completely the opposite—they memorize the information in their short-term memory without understanding the fundamentals, they do great on the tests, and then they forget all of it immediately. But they stand out from their peers as better students, because they're able to play the "game" of school better and optimize for being a knowledge-sponge that will absorb the most information as possible and forget it as quickly as possible.

[ngc248]

>>> simply isn't anything to be done about that if you're talking about humans and not some homo educationous who mythically retain all knowledge they were exposed to even for 30 seconds just as the mythical as homo economicus perfectly rationally conducts all their economic business at all times. Perhaps they're actually the same species.

Yeah they belong to the genus homo mythicus

[airstrike]

I just wanted to say I deeply appreciate the eloquence of this comment. Thank you

[fisherjeff]

On a related note, it bothers me that there’s so much urgency to teach younger kids more and more advanced math. I use more and higher math on a day-to-day basis than practically anyone I know, but it’s very rarely even calculus, and even then it’s typically just discrete integrals or derivatives.

There’s just an absolute ton of math being taught that’s going completely to waste, and it’s at the expense of the humanities.

[Swizec]

My biggest “Screw everything” moment about math was the first lecture of my numerical methods class in college when the professor said: “All that calculus you’ve been learning your whole lives? It’s useless. Carefully curated set of a few dozen problems that are doable by hand. Here’s how it’s really done for anything remotely practical”

And then we learned a bunch of algorithms that spit out approximate answers to almost anything. And a bunch of ways to verify that the algorithm doesn’t have a bug and spat out an approximately correct answer. It was amazing.

But the most long-term useful math class (beyond arithmetic and percentages) has been the semester on probabilities and the semester on stats. I don’t remember the formulae anymore, but it gave me a great “feel” for thinking about the real world. We should be teaching that earlier.

[JackFr]

When I took 400 level Real Analysis: “All that calculus you’ve been learning your whole life? It’s a lie. Those epsilon delta proofs? They were fake - none of you were smart enough to challenge us on ‘limits’. And now we’re gonna do it all again only this time it’s really gonna be rigorous.”

[tsimionescu]

Is there any somewhat simple explanation of what are the limitations of the epsilon-delta definition of limits that make it non-rigorous? I've been trying to find some information about your comment, but have so far come up empty.

[JackFr]

I'm shaky on this - it's been thirty years - but I believe the Calc I epsilon delta proofs relied on the notion of an open and closed intervals on the real line, which we all intuitively understood.

The upper level Real Analysis made us bring some rigor as to what an interval on the real line actually meant going from raw points and sets to topological spaces to metric spaces, then compactness, continuity, etc. all with fun and crazy counterexamples.

[BeFlatXIII]

100% agreement on teaching stats as the "pinnacle" of high school mathematics. Those are what directly rule the lives of the average non-engineer.

[MichaelCollins]

I think much of math 'education' is constructed as a filter to identify a small handful of math prodigies. The general population suffering anxiety and youth lost in the filter is seen as an acceptable sacrifice for the greater good of finding the math prodigies so those can be given a real math education.

[fisherjeff]

Yes, this is a very good point. In my experience from, uh, several decades ago, it also felt like a lot of math educators watched (and showed in class...) Stand and Deliver way too many times and the only message they took away was "we should teach everyone calculus!"

[BeFlatXIII]

I doubt the students would actually learn humanities in the extra time allotted if it's not used for math. I remember a distinct refusal to internalize, especially in my male peers, during "English" classes.

[MichaelCollins]

Forget humanities. The hours a week after school that highschool students spend on calculus homework would probably be better spent socializing with their friends. They'll never be young again, wasting the time of a teenager with unproductive busywork is a horrible thing to do.

[cjbgkagh]

I’m the opposite, Im 15 years into my career of applied research which for me is like an extension of university. I tend to lean on Mathematica to do my calculus though. I think high school curriculum was optimized to expose a lot of people to things they won’t need on the off chance that a few will end up as researchers of some sort. It would be more efficient to identify such people earlier and split them off. I think historically that was the idea but there has been an egalitarian push to broaden the pool.

[schindlabua]

I think the point of high school is to make kids' brains do work, and what you are learning is secondary.

People love to hate on their school curriculum and all the useless knowledge they had to acquire but I'm positive it makes you a smarter person overall, and the body of high school knowledge makes learning more specialized knowledge easier (even if that's baking bread or whatever)

(People also love to talk about how little they remember from school, yes the brain is a muscle and you stopped working out, congratulations.)

[mathieuh]

I'm 27, educated in the UK, all I remember about trigonometry is SOHCAHTOA.

[_0nsg]

USA here, same acro. I still start off solving by writing it off and drawing slashes through O/H A/H O/A for reference.

Came to use trig functions quite frequently while playing video games, and that was a big surprise to me. Not to assume you've played it, but I've recently discovered that Stormworks is a programmer's game - you can write microcontroller code in LUA for your vehicle designs. And, wow, does it ever use my trig knowledge everywhere.

Realized the transponder beeps can be triangulated, tick being 1/60th of a sec and that's a distance estimate resolution of up to 5-10 km. And that's when cos and sin came back to be useful because you can do intersection of circles and figure out where to do a sea rescue more precisely. So video games, trig. Who would've thought?

[mcv]

The Dutch version was SOSCASTOA, with a picture of a ship called the Castoa sending out an SOS because it was sinking. That picture really helped.

And I even remember what it means:

SOS: sine = opposing side divided by diagonal (schuine) side

CAS: cosine = adjacent divided by diagonal

TOA: tan = opposing divided by adjacent.

I don't think I've ever used it for anything practical, but I can still reproduce it after all this time (I'm 47 now).

[js2]

> I don't think I've ever used it for anything practical.

Just the other day I wanted to compute viewing angle and did it by hand even though there are plenty of calculators like this out there:

http://www.hometheaterengineering.com/viewingdistancecalcula...

I’d say I use it for something practical/random like that a few times a year?

Another example was placing some ceiling speakers whose tweeters had a 15° angle so that they were pointed directly at a seating position below. How far did I need to place them in front of the seating position from directly overhead.

I would guess any sort of construction you’re using it fairly often.

[dylan604]

The one that I still use is the 3-4-5 rule to ensure a right angle. Still use that one to chalk off sporting fields of play.

[mcv]

I use that one all the time, but that's Pythagoras, not sin and cos.

[dylan604]

Yeah, I know it's not the same type of math, but it's one of the few things that I still use today. To be honest, I can't think of one time in my professional career that I have needed to calculate the area under a curve to solve a life problem. Geometry has been the most used branch of math past basic arithmetic, oh, and algebra. It amazes me the number of people that don't realize how many times in a day they have solved for X.

[dllthomas]

It was by no means uncommon when I was taught in the US but I somehow missed it, instead just internalizing the various relationships directly, and was briefly confused when classmates started talking about SOHCAHTOA working together in college math courses.

What I remember from trig is to draw a unit circle. Most of the rest falls out of that.

[js2]

I’m handy outside of work and use sohcahtoa often enough to remember it. Triangles are everywhere and sometimes you need to compute angles and lengths of sides.

Statistics is also useful and applicable to everyday life, but I didn’t learn that till college as best I can recall.

I don’t regret having spent time learning calc, or physics or chemistry or biology for that matter. If you asked me to come up with a curriculum I’d have a really hard time prioritizing. Maybe the one thing I’d like to see kids learn better is how to be self-directed learners. I’m still fairly surprised at the number of colleagues I have who seem unable to problem solve and figure something the fuck out. Even knowing when and how to ask for help.

[mech422]

I'm a 50+ year old American, of british decent... I never managed to remember the 'american' mnemomic, but my dad taught me one the used to use in England around WWII: Percy has a bald head, poor boy

Perpendicular/hypotanuse = Sin

Base / Hypotanuse: CoSin

Perpendicular / Base: Tan

edit: try to fix the HN god awful formatting

[duncan-donuts]

Ha I also remember the mnemonic but I don’t have a clue how to use it.

[krallja]

it's to remember the ratios for trigonometric functions on a right triangle:

Sine: Opposite over Hypotenuse

Cosine: Adjacent over Hypotenuse

Tangent: Opposite over Adjacent

[dev_tty01]

Otto had a heap of apples.

[dekhn]

There's lots of stuff I knew well and then forgot, but can re-learn quickly. For example, nearly all of calculus (useful when dealing with machine learning). Other bits I've retained and never forgotten, such as everything I've seen involving matrices. There are even things which I had conveniently completely "forgotten" but later emerged as suppressed latent memories- for example, set theory. I was so unhappy with the lead-up to Russell's paradox that I actively suppressed thinking about sets, groups, rings, and fields for several decades.

There are even other bits that I was shown, never incorporated into my brain at all, but later recognized as truly important (Taylor series expansions, the central limit theorem, the prime number theorem, etc).

[bee_rider]

Informally, big-O and limits have a similar smell to them, calc might have helped get some wheels turning in your head for that.

I do recall taking a "probability in CS" as an electrical engineering student -- it was pretty mind-blowing to me the extent to which the CS students did not like to talk about any continuous math. It makes sense, though, these are different specialties after all.

[HideousKojima]

Honestly the typical developer needs a solid understanding of algebra, but not much beyond that. Though any time I get into game dev stuff I start ripping my yair out over quaternions

[sbf501]

Thankfully you didn't publish a blog post claiming you discovered a new way to represent coordinates, and then assert that programmers should switch.

[LeifCarrotson]

I'd argue it's not so much taught in the US as it is tested. The common core standards say [0] that students should:

> Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

> Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

and so on. However, in practice, this means that students need to be able to answer "C" when presented with the question:

> One radian is:

> A) Another word for degree.

> B) Half the diameter.

> C) The angle subtended on a unit circle by an arc of length 1.

> D) Equal to the square root of 2.

A surprising number of students can get through without ever really comprehending what a radian is. They might just choose the longest answer (which works way too often), identify trick answers and obviously wrong answers, and eventually guess the teacher's password from a lineup by association of the word salad of "radians" and "subtended."

They might not even have a clue what the word "subtended" means, but they know it's got something to do with "radian" and that's enough. It is more important for the school that the students answer (C) than that they understand what a radian is.

[0] https://web.archive.org/web/20220112000314/http://www.corest...

[kortilla]

No, you’re missing the point. I went to school in the 80s and learned this stuff without multiple choice and fully understood it all of the way through undergrad where I took up through calc 3 and differential equations. Then I spent nearly 30 years as a SWE not using it and forgot nearly all of the details within maybe 15 years.

This happens with very basic things like human languages. Bilingual people can forget an entire secondary language if they don’t use it for a decade+.

[mlyle]

It's taught extensively in the US, but what's never done is showing how terrible many of those identities or integrals are in degrees.

Derivative of sin(x) is cos(x). Many people probably think this works for degrees, but it's actually some abomination like pi cos(pi x/180)/180.

Of course, turns are very reasonable units sometimes for sure.

[tzs]

> Derivative of sin(x) is cos(x). Many people probably think this works for degrees, but it's actually some abomination like pi cos(pi x/180)/180.

That's what it would be if you are using sin in degrees and cos in radians. But if you are using degrees for both then the derivative of sin(x) is pi/180 cos(x).

[mlyle]

Yup, I knew I'd mess it up. :D

[zugi]

Like most here, I've learned and forgotton lots of trig and calculus.

However, I still remember that "eureka!" moment of realizing that radians were special, that the small angle approximation of sin(x) = x, and many related math rules, work only when x is expressed in radians. I guess that's a credit to my math teacher, who basically led the class in deriving mathematical formulas rather than just presenting them to us.

I think the article is still valid and interesting, as "turns" in some use cases might improve performance and accuracy. But radians aren't at all "arbitrary" - if we ever encounter technologically advanced aliens, they certainly won't use degrees, but they will understand radians.

[jeltz]

Sure, but are people here chefs? I would expect most programmers in mu country to remember this, but most chefs to have forgot it.

[bathtub365]

I would only really expect programmers who work with angles regularly (those working in 3D) to remember it. Even then, you’re likely just smashing quaternions together anyway.

[kortilla]

Effectively yes. A tiny subset of programmers need trig.