/sci/ - Science & Math

Literally what

>>12713048
Engineers use the approximation sinx = x near 0 (which works very well). Autists seethe.

>>12713052
Those graphs do not show sin(x) near 0. Hence the confusion.

Pam cute

>>12713052
This board is full of the most petty and retarded shit I've ever seen. I want to die

>>12713058
>implying angles above 5 degrees have practical purpose.

>>12713020
Every function is just the first term of their Taylor approximation near zero.
>t. Engineer

>>12713081
lol cos(x)=1

Anyone else have any good engineering approximation stories?
>taking controls midterm
>calculator dies 5 minutes in
>thisisfine.jpg
>last question
>need to know whether e^{pi/4} is larger than some decimal given (question asked for the dominant pole)
>approximate e^{pi/4} = 3^{3/4} = 3^1/2 * 3^1/4
>3^1/2 = 1.7 = 1.3^2
>get full marks
I checked later, this approximation was accurate within 0.02, or about 1% of the actual value.

>>12713020
if that makes you angry, just imagine there's a " + o(x)" or " + o(x^2)" written at the end of every formula. problem solved, your engineering textbook is now rigorous.

>>12713122
Big-O and little-o expressions have very specific meanings, and totally rigorous mathematical statements can be proven about them.

>>12713076
>>implying angles below 5 degrees have practical purpose.

>>12713052
I love pure math and I take no issue with people using sin x ≈ x near 0 if it's good enough not to produce errors, but I just find it gross cause I like exact stuff.

>>12713576
sin x = x + o(x) is an exact result

>>12713585
I like drawing a picture instead.

>>12713585
[math] \sin(x) = x + \mathcal{O}(x^2) [/math]

>>12713066
Leave retard

>>12713105
The engineers I work with can't do that shit. Their life is entangled with calculators. They couldn't approximate their way out of a paper bag.
I'm a physicist and we learned that stuff early on. Super helpful imo, especially when you have to estimate things irl.

>>12713611
x^3 even, fuuuuuu

>>12713081
That's only true for analytical functions.

>>12713520
How do you get the equation for a pendulum's movement again?

>>12713621
Oh yeah, knowing how to ballpark and do back-of-envelope math is depressingly rare. It's part of a larger problem with a bunch of engineers who just plug & chug and don't actually know what they're really doing when they use that formula (or how to think in general).

Here's another fun one from a friend of mine:
>prof says to bring a calculator to the test, doesn't have to be fancy just able to do the basics
>friend decides to be cheeky and bring one of those kiddie ones with the giant buttons
>he encounters the square root of some gross, biggish number
>his calculator can't do roots
>he takes the logical course of action and uses a taylor approximation at the nearest perfect square to estimate the root
>"yeah, it asked for 3 sigfigs so I took a 3rd order approximation just to be careful"

>>12713585
o(x) = sin(x) - x

>>12713654
that is the logical course of action though

>>12713076
ever heard of a right angle

>>12713520
jesus christ the cope in the picture

>>12713576

>>12713597
I teach a college math class and I’m trying to show them small angle approximation next week. Mind if I show them your drawing?

>>12713631
>That's only true for analytical functions.
you mean continuous functions

>>12713520
Such cope

>>12713058
Come, brother

>>/pol/

>>12713952
No.

>>12713631
>That's only true for analytical functions.
you mean linear functions

>>12713576>>12713585

>but I just find it gross cause I like exact stuff.
then you dont' like the real numbers and even less dubious functions like sin, and any infinite series

>>12715481
No.

>>12715598
meds

>>12713948
Whatchu doing asking that nigga?
Just still it pussy.

>>12713105
>3^1/2 = 1.7 = 1.3^2
I'm a retard, explain how you got this?

>>12713948
Go right ahead, buddy!

>>12715811
Not him, but think about that 13^2 = 169.

>>12713597
>>12715824
I'd like to use it in a teaching book that I'm writing currently. Would that be okay? How shall I cite you?

>>12715843
Put my name in as "Anonymous".

>>12713061
oh yeah

>>12715843
illustration provided by Dr.(of Mathematics) I.P. Freeleigh

>>12713052
im an ee and i used this because angle < 3° and 8bit mcu.

>measuring angles in degrees

>>12715837
Specifically, I was wondering how he got 1.7 from the 3^1/2 and why he has to turn it into another exponent

>>12716475
3^0.5 ~ 1.7 is just one of those approximations that I've got memorized since its handy, like 2^0.5 ~ 1.4 or ln(2) ~ 0.7. Since I needed to multiply 3^1/2 by 3^1/4, I computed 3^1/4, which is the square root of 1.7. As the other anon says, this is about 1.3 since 1.3^2 = 1.69 ~ 1.7

Engineer? More like GAY

>>12713597
"heh"

>>12715824
Thanks very much! If you’d be interested in delivering a guest lecture, I’d really appreciate it. I can leave you my info if so.

>>12715746
That would be theft of intellectual property! Although I am protected under fair use, I’d rather not chance it.

>>12713105
3^1/2 = 1.7

3^(1/4) = sqrt(3^(1/2)) = sqrt(1.7) = 1.3

So the answer was:
3^(1/2)*3^(1/4) = 1.7*1.3 = 2.21?

This row
>3^1/2 = 1.7 = 1.3^2
Was abit unclear.

>>12716941
Yup. Sorry for the lack of clarity, wasn't sure about the best way to succinctly link 3^1/2 = 1.7 & 3^1/4 = 1.3.

How Can I Argue Agains Trash That I Dont Learn?
But Still Half-Respect 2 Mathematics.

>>12716536
>3^0.5 ~ 1.7 is just one of those approximations that I've got memorized
I just get these from square numbers. Look for the square closest to 300, which is 289 = 17^2 and divide by sqrt(100) = 10.

>>12713935
>>12713989
It's a fairly common sentiment these days, unfortunately. Posting that picture on /pol/ is the (You) fishing equivalent of catching trout by tossing grenades in a pond.

I'm in EE and math sux, I just memorize all the little bullshit that I need to know.

>>12717003
Is this some kind of japanese light novel title?

>>12713020
>normie tv show meme
looks like you lost your way, here's where you belong:
>>>/reddit/

>>12718694

>>12718705
Who cares

Do engineers not learn taylor series? Whate the fuck do they learn in calc?

>>12719324
Physicist who ended up in aerospace engineering here.
No, they don't. Or they forget about it. They instead learn crude formulae for "linearization" without ever understanding the background. At least they're completely baffled when I show them an image of what Taylor series do and that using the terms up to linear order IS linearization.

>>12719324
>>12719420
Wtf are you talking about? Everyone learns Taylor series in Calc 2. If your coworkers are idiots that reflects poorly on you.

>>12719693
>Everyone learns Taylor series in Calc 2
What's so difficult to understand about
>Or they forget about it.
?
>your students = your coworkers
No.

>>12713576
>Irrational numbers
>Exact stuff
>>>/pol/