(Trig)gered by mats in physics

>pi=e=3

Looking for physics formula proof.
Spend literally one hour, everything I find starts with sin(x)=x. Did the proof myself, got an accurate formula in 15 mins.

Why can't physicist just do maths properly?

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wolframalpha.com/input/?i=plot sinx and x
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There are conventional approximations in physics that to the uninducted may seem very arbitrary. Part of your issue is that with present-day computing power, these approximations are often unnecessary. This kind of approach comes from centuries of working things out by hand with numerical tables as a guide.

Because you don't prove things in physics. You get an expression and verify it experimentally.

But fuck optics. I'm with you there.

>when the derivation randomly contains a linearization/taylor-expansion-up-to-whatever-order

>you don't prove things in physics
I get that.
But don't mathematical model's that you've constructed have to be mathematically consistent? I mean physics is just an attempt to construct a mathematical model that would predict reality with most precision, so how can we even expect for it to work if the underlying maths doesn't?

Also you're right, fuck optics.

Curious what your proof is. Could you share it with us?

Physics is a one-trick pony. The goal is to ultimately apply perturbation theory to everything that isn't free particles. So what do physicists usually look at? Systems with correlation effects that are extreme in some sense compared to an analytical model that you can expand in low orders around it.

This is why I'm glad I majored in engineering. Why don't autistic math students realize that NOTHING would be solvable if we didn't make assumptions? On any engineering problem I make a list of assumptions and things turn out fine (generally

as a matter of fact, there are mathematical studies of approximate solutions. Things such as "approximate solutions to differential equations" , "the existence of approximate solutions"... It's just highly non-trivial.

Sin (x) ~ x is always true to some accuracy. Usually, you use significant figures, and usually an analytic solution will be irrational. So why go through the extra work if you're just going to round it off anyways?

This shit is why I'm not a physics major

>Why can't physicist just do maths properly?
So you're saying that truncating a Taylor series to the first term isn't doing maths properly? The reason is mostly simplicity and solubility, you can't solve [math] \ddot { \theta } -k \sin ( \theta ) = 0 [/math], but you can solve it where [math] \sin ( \theta ) \approx \theta [/math]. Furthermore, if you get this triggered over the small angle approximation, I suggest you stop now before you give yourself an aneurysm.

sin(x) =/= x, sin(x) = x + O(x^2).

There, happy?

e = pi = 3 is just a very loose shorthand for mental math, especially when you only care about order of magnitude. Obviously you'd use the more precise values if you had a computer/calculator on hand.

even better, its O(x^3). quite accurate for small x

Derp, this.

Furthermore OP, you're free to use a more accurate approximation like x - x^3 / 6, but now you have to solve a nonlinear ODE just for something as basic as simple harmonic motion. If you want to leave the sinusoid in, okay, but now the solution is a Bessel function, and the only way to evaluate the bessel function is numerically, i.e.: approximation. You can't escape it.

>Taking undergrad QFT
>excited to finally learn about one of the most accurate theories weve ever made
>Calculating some scattering amplitudes
>Get an expression that results in infinity - infinity
>obviously undefined, expect professor will use this to show that QFT can't predict everything
>'As you all know we can approximate this first divergent sum with -1/12 and this second one with -1/2 up to only infinity, thus we get a result of 5/12.'
>wtf
>Couple of people had a giggle at the sentence, but no one corrects him
>drop the class the next day
Im thinking of switching to a math major because I cant take these brainlights anymore

Taylor polynomial about w = 0. Known as small angle approx.

It's not that it actually equals w, just that w is pretty close up to a certain point.

sin(0) + cos(0)*w - (1/2)sin(0)*w^2 - (1/6)cos(0)*w^3.

The next non-zero term is on the order of x^3, so it's negligible for w

You could also just observe this visually as well.

sin(x) and x intersect at x = 0 and both have a slope of 1. Therefore it is intuitive that there is going to be some range over which sin(x) and x agree up to a reasonable degree of precision. This is going to depend on how different the higher order derivatives are.

wolframalpha.com/input/?i=plot sinx and x

the less math autists in my field the better

>"mathfags" need their hand held to make a simple Taylor expansion

This.

Fag. Enjoy your while your professor shoves up your ass crippled maths.

>you approximate sinx with x and get the result in a couple of minutes
>you punch in some irl numbers
>it's like you've measured
>Veeky Forums autist spends way more time/energy/computing power than you and solves the fucking nonlinear ode
>punches in the irl numbers
>his result varies from yours only from the fifth decimal onward
His time is wasted but at least his autism is satisfied and he's now a true matematician

>using numbers
Lmao gay as fuck.

1 ≈ 1.01 ≈ 1.02 ≈ ... ≈ ∞