Neither in (German) high school nor in the many math courses of a physics B.Sc. have I ever used the secant function. I am surprised the article does not explain it in the beginning. I assume for other people it must be a common function?
100 Years to Solve an Integral (2020)
11–20 of 66 posts
Re: 100 Years to Solve an Integral (2020)
#12Oh! This was already discussed five years ago with 77 pts and 40 comments (https://news.ycombinator.com/item?id=24304311)
Re: 100 Years to Solve an Integral (2020)
#13Neither in (German) high school nor in the many math courses of a physics B.Sc. have I ever used the secant function. I am surprised the article does not explain it in the beginning. I assume for other people it must be a common function?
I'm sure you used inverse of a cosine multiple times. Didactic math today is just not bothering to give it a name. Probably because people think that sin, cos and tan is enough. Even ctg which is just inverse of tan is often skipped.
Re: 100 Years to Solve an Integral (2020)
#14Neither in (German) high school nor in the many math courses of a physics B.Sc. have I ever used the secant function. I am surprised the article does not explain it in the beginning. I assume for other people it must be a common function?
I'm sure you used inverse of a cosine multiple times. Didactic math today is just not bothering to give it a name. Probably because people think that sin, cos and tan is enough. Even ctg which is just inverse of tan is often skipped.
The secant is the reciprocal of a cosine – the hypotenuse over the adjacent
Re: 100 Years to Solve an Integral (2020)
#15Earlier quoted context omitted.
I'm sure you used inverse of a cosine multiple times. Didactic math today is just not bothering to give it a name. Probably because people think that sin, cos and tan is enough. Even ctg which is just inverse of tan is often skipped.
The secant is the reciprocal of a cosine – the hypotenuse over the adjacent
That’s right, it’s a distribution. And that fact has me, a non-mathematician, personally caused some huge headaches, because I thought I could treat it just like a function… Yeah, turns out really weird things happen if you try to do so without knowing what you’re doing. For example, taking its square does not make sense.
Re: 100 Years to Solve an Integral (2020)
#16Neither in (German) high school nor in the many math courses of a physics B.Sc. have I ever used the secant function. I am surprised the article does not explain it in the beginning. I assume for other people it must be a common function?
I'm sure you used inverse of a cosine multiple times. Didactic math today is just not bothering to give it a name. Probably because people think that sin, cos and tan is enough. Even ctg which is just inverse of tan is often skipped.
I know what you mean, but as a sibling pointed out for everyone else's benefit, parent is using the word inverse where they mean reciprocal.
The inverse of cosine is arccosine (sometimes written acos or cos^{-1}). Secant is the reciprocal of cos ie sec x = 1/cos(x)).
Likewise cotan is the reciprocal of tan (1/tan). The inverse of tan is atan/arctan/tan^{-1}.
This is confusing for a lot of people because if you write x^{-1} that means 1/x. If you write f^{-1} and f is a function, then _generally_ it means the inverse of f. In the case of trig functions this is doubly confusing because people write sin^2 theta meaning (sin theta)^2 but sin^-1 theta means arcsin theta.
That's why in my maths studies they started by teaching you to do the inverse with a -1 so when you see it you don't get confused but changed to preferring arcsin etc as this is unambiguous and if you learn to write this way you won't confuse others.
Re: 100 Years to Solve an Integral (2020)
#17Neither in (German) high school nor in the many math courses of a physics B.Sc. have I ever used the secant function. I am surprised the article does not explain it in the beginning. I assume for other people it must be a common function?
Trig is full of functions that fall into disuse and are forgotten.
For example "versine"
versin theta = 1-cos theta.
There is also "haversine" which is (1-cos theta)/2. Which is used in navigation apparently https://en.wikipedia.org/wiki/Versine
Re: 100 Years to Solve an Integral (2020)
#18It feels like LLMs could be good contenders for solving symbolically integrals. After spending some time, it really feels like translating between two languages.
Wolfram engine was taking integrals just fine way before LLMs were even a thing.
Re: 100 Years to Solve an Integral (2020)
#19Neither in (German) high school nor in the many math courses of a physics B.Sc. have I ever used the secant function. I am surprised the article does not explain it in the beginning. I assume for other people it must be a common function?
>Neither in (German) high school nor in the many math courses of a physics B.Sc. have I ever used the secant function
I think we used it in geometry in US high school, but only to complete an assignment or two to show we could use trig functions correctly. I had to relearn how all of them worked to help my kid with homework, it's mostly look at the angles and sides you have available and pick which trig function is necessary to figure out which one you're solving for. I'm sure there are real life uses for trig functions, and I hate to be one of those "when are we ever going to use this" types, but I've never used any of them outside of math classes.
Re: 100 Years to Solve an Integral (2020)
#20It feels like LLMs could be good contenders for solving symbolically integrals. After spending some time, it really feels like translating between two languages.
Wolfram engine was taking integrals just fine way before LLMs were even a thing.
And Lisps too, fitting a sector from a disk:
https://justine.lol/sectorlisp2/
And probably a small forth too, with a dictionary defining every math word, something not so different to Lisp.
LLM's? 4GB of RAM? Your grampa's 486 with 16MB of RAM can do calculus too.