L=1/γ=1−v2−−−−−√

dL/dt=−γva=vn+1−vn

∂v/∂n=(vn+1−vn)/1=−γva

 

 

 

 

H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}

 

 

[math] H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}} [/math]

 

av

Edited December 14, 20223 yr by Lorentz Jr

Looks good so far.

use \frac { xxxx }{ yyyy } to get division..

 

e.g.

[math]f(x)=\frac{1}{x^2}[/math]

 

If you see that some other member has used LaTeX, RMB on his equation, pick up Show Math As > TeX commands, copy'n'paste and learn from it.

 

Thanks. This system is really finicky.

 

1 minute ago, Lorentz Jr said:

This system is really finicky.

Some (lazy) users use LaTeX online editors

https://www.google.com/search?q=latex+online+editor

(not me)

(I can even write code in x86/x64 assembler)

 

1 minute ago, Sensei said:

(I can even write code in x86/x64 assembler)

That's a little too hard-core for me. 😶

I don't mind writing straight (La)TeX, but the equation stays displayed when I edit the post, so I can't edit the equation.

And that square root keeps getting mangled for some reason.

55 minutes ago, Lorentz Jr said:

That's a little too hard-core for me. 😶

A few years ago, I sent a MySQL programmer (i.e. Oracle dev team) a source code that contained only ~ 1000 lines of x64 machine code and told him "analyze it, find the error, this is what I will do this evening/night" (he had previously told me that he had spent a whole month writing 30 lines of C/C++ code at his previous company)..

My only concern about this code was the amount of beer on the table that I had.

Some people took it too literally and began to offer me to write programs for beer....

Edited December 14, 20223 yr by Sensei

1 hour ago, Sensei said:

My only concern about this code was the amount of beer on the table that I had.

What does that mean? It's over my head.

Spilling beverage on hardcopy?

By the way, I seem to be the forum pariah now. I wouldn't want you to get in trouble chatting with me.

text

L=1/γ=1−v2−−−−−√

 

OMG, the system is working PERFECTLY now, and I have ZERO idea why. 😖

Oops! Spoke too soon. It's F-ed up again.

Oops! It's working again. Still don't know why.

[math] L = 1/\gamma = \sqrt{1-v^2} [/math]

[math] \gamma = 1 + O(v^2) [/math]

[math] v(n,t) \equiv w(n)z(t) [/math]

[math] \frac{\partial v}{\partial n} = -v \frac{\partial v}{\partial t} [/math]

[math] w'z = -(wz)(z'w) = -w^2 z'z [/math]

Edited December 14, 20223 yr by Lorentz Jr

2 minutes ago, Lorentz Jr said:

What does that mean? It's over my head.

Mortals can't handle it..

3 minutes ago, Lorentz Jr said:

By the way, I seem to be the forum pariah now.

Not really. People are suspended for days, weeks and months. For breaking the rules. Usually for being rude.

 

Don't be rude, and you can get up to 100 negative reputation points if you want

 

This system is a nightmare. Equations get mangled; they change when I click edit, do NOTHING, and redisplay; now they don't seem to be working at all. 😱

Edited December 14, 20223 yr by Lorentz Jr

If you want to reply something that is controversial, turn off the PC/mobile and wait until you sober up or so..

 

5 minutes ago, Lorentz Jr said:

This system is a nightmare. Equations get mangled, they change when I click edit, do NOTHING, and redisplay, now they don't seem to be working at all. 😱

This is not dependent on the members here. Older forum software allowed you to preview math equations before posting. A newer forum update screwed that up.

 

 

 

Edited December 14, 20223 yr by Sensei

text

[math] - \frac{w'}{w^2} = z' = k_1 [/math]

[math] z = k_1 t + k_2 [/math]

[math] z(0) = 0 [/math], so [math] k_2 = 0 [/math].

[math] -dw/dn = k_1 w^2 [/math]

[math] - \frac{dw}{w^2} = k_1 dn [/math]

[math] 1/w = k_1(n + k_3) [/math]

[math] v = wz = [k_1 (n+k_3)]^{-1} k_1 t = \frac{t}{n+k_3} [/math]

[math] v_0 \equiv a_0 t  = \frac{t}{0+k_3} [/math], so [math] k_3 = 1/a_0 [/math]

[math] v = \frac{a_0 t}{1 + a_0 n} [/math]

[math] v = \frac{a_0 t}{1 + (a_0 L n / c^2)} [/math]

[math] a = \frac{a_0}{1 + (a_0 L n / c^2)} [/math]

text

Edited December 14, 20223 yr by Lorentz Jr

4 hours ago, Lorentz Jr said:

This system is a nightmare.  😱

I guess I was pasting the code as rich text. The fixed-width font is from the "Show Math As" window, and the curvy font is from copying the equation directly. 🙄

Maybe this thread should be moved to the sandbox.

@Lorentz Jr You can do it better - use nested frac commands..

 

1 hour ago, Sensei said:

nested frac commands

[math]v = \frac{a_0 t}{1 + \frac{a_0 L n}{c^2}}[/math]

Letters too small, eqn too tall. I have at least 15 lines of math, plus explanatory text.

Don't want to make too long of a post or make people squint too much.

Edited December 16, 20223 yr by Lorentz Jr

Try wrapping both parts of the fraction in “\displaystyle{}”:

\[\displaystyle{v=\frac{a_{0} t}{1+\displaystyle{\frac{a_{0} L_{n}}{c^{2}}}}}\]

I’m not sure how to fix the equation being too tall, and not vertically centred on the equal sign.

Edited December 16, 20223 yr by Markus Hanke

[math]\displaystyle{v=\frac{a_0 t}{1+\frac{a_0 Ln}{c^2}}}[/math]

Hmm..... I thought I got an "unknown environment" error when I did that before.

Thanks, that's perfect.

Edited December 16, 20223 yr by Lorentz Jr

2 hours ago, Lorentz Jr said:

v=a0t1+a0Lnc2

Hmm..... I thought I got an "unknown environment" error when I did that before.

Thanks, that's perfect.

You’ll need to enclose both enumerator and denominator separately to make it look even better, like “\frac{\displaystyle{}}{\displaystyle{}}. It’s a bit of a pain, but it does make a difference to the way the output looks. As for proper vertical alignment and sizing, I haven’t figured this out myself yet (any ideas @studiot?).

24 minutes ago, Markus Hanke said:

\frac{\displaystyle{}}{\displaystyle{}}

I like the way it is. A little squinting is okay. 😊

@Lorentz Jr ...or you can press (also several times) ctrl+ on your keyboard to change the zoom level of your web browser (ctrl- to reverse, or click on the percentage in the title to reset it back to 100%)..

 

7 hours ago, Markus Hanke said:

Try wrapping both parts of the fraction in “\displaystyle{}”:

I like it.

7 hours ago, Markus Hanke said:

[math]\displaystyle{v=\frac{a_{0} t}{1+\displaystyle{\frac{a_{0} L_{n}}{c^{2}}}}}[/math]

I’m not sure how to fix the equation being too tall, and not vertically centred on the equal sign.

I reviewed your TeX commands - you don't need {} in some places i.e. a_{0} can be a_0, c^{2} can be c^2 etc. Basically {} tells that there is a bigger sequence.

Edited December 16, 20223 yr by Sensei

17 hours ago, Lorentz Jr said:

v=a0t1+a0Lnc2

Letters too small, eqn too tall. I have at least 15 lines of math, plus explanatory text.

Don't want to make too long of a post or make people squint too much.

 

16 hours ago, Markus Hanke said:

Try wrapping both parts of the fraction in “\displaystyle{}”:

 

v=a0t1+a0Lnc2

 

I’m not sure how to fix the equation being too tall, and not vertically centred on the equal sign.

 

I'm not sure what you mean about vertically aligned about the equals but I agree that I find the smae letter sizing problem when I paste in.

This never used to happen, but started here about one improving update ago.

My solution is to highlight the offending formula in TEX and change the font size in the site input editor box.

21 hours ago, Markus Hanke said:

Try wrapping both parts of the fraction in “\displaystyle{}”

21 hours ago, Lorentz Jr said:

Hmm..... I thought I got an "unknown environment" error when I did that before.

Ha! I was typing "\displaymath" instead of "\displaystyle". 🙄

Edited December 17, 20223 yr by Lorentz Jr

[math]\displaystyle{d\tau^2 = \left( 1 - \frac{1}{r}\right)dt^2 - r^2 d\theta^2}[/math]

[math]\displaystyle{c^2d\tau^{2}=c^2\left(1-\frac{r_{\textrm{s}}}{r}\right)dt^{2}-\left(1-\frac{r_{\textrm{s}}}{r}\right)^{-1}dr^{2}-r^{2}\sin^{2}\theta d\theta^{2}}[/math]

Edited December 26, 20222 yr by Lorentz Jr

[math]\displaystyle{d\tau^2 = \rho dt^2 - \frac{dr^2}{\rho} - rd\phi^2}[/math]

where c=1 and [math]\displaystyle{\rho \equiv \left(1-\frac{r_{\textrm{s}}}{r}\right)}[/math].

[math]\displaystyle{d\tau_A = \rho dt}[/math]

[math]\displaystyle{d\tau_D^2 = \rho dt^2 - rd\phi^2 = \frac{d\tau_A^2}{\rho} - rd\phi^2  }[/math]

[math]\displaystyle{\frac{d\tau_D^2}{d\tau_A^2} = \rho - \left(\frac{dr\phi}{d\tau_A}\right)^2}[/math]

[math]\displaystyle{\sqrt{ \rho - v_{DA}^2}}[/math]

 

Edited December 26, 20222 yr by Lorentz Jr

[math]2r_q = r_s[/math]
[math]4 r_q^2 = r_s^2[/math]
[math]Q^2 G / \pi \epsilon_0 = 4 G^2 M^2[/math]
[math]Q^2/M^2 = 4 G \pi \epsilon_0[/math]
[math]Q/M = 2 \sqrt{\pi G \epsilon_0} = 2 \sqrt{\pi (6.67*10^{-11} N m^2/kg^2) (8.85*10^{-12} C^2/N m^2)}[/math]
[math]Q/M = 8.6*10^{-11} C/kg[/math]

electron: [math]q/m = 1.6*10^{-19} C / 9.1*10^{-31} kg = 1.76*10^{-11} C/kg[/math]

 

Edited December 29, 20222 yr by Lorentz Jr