Comments on: LaTeX Sandbox http://asymptotia.com Mon, 13 Oct 2008 11:42:54 +0000 http://wordpress.org/?v=2.5.1 By: bobo http://asymptotia.com/latex-sandbox/#comment-126296 bobo Sun, 05 Oct 2008 21:01:28 +0000 http://asymptotia.com/latex-sandbox/#comment-126296 N = q_1, q_2, q_3, ..., q_s \Rightarrow p_i \neq q_j \forall i,j \in {1,2,3,...} N = q_1, q_2, q_3, …, q_s \Rightarrow p_i \neq q_j \forall i,j \in {1,2,3,…}

]]> By: Yosef http://asymptotia.com/latex-sandbox/#comment-126140 Yosef Mon, 29 Sep 2008 13:52:41 +0000 http://asymptotia.com/latex-sandbox/#comment-126140 [tex] \bigtriangle \hspace{-5pt} \bigtriangledown [/tex] \bigtriangle \hspace{-5pt} \bigtriangledown

]]> By: Yosef http://asymptotia.com/latex-sandbox/#comment-126139 Yosef Mon, 29 Sep 2008 13:50:59 +0000 http://asymptotia.com/latex-sandbox/#comment-126139 [tex] \bigtriangle \hspace{-10pt} \bigtriangledown [/tex] \bigtriangle \hspace{-10pt} \bigtriangledown

]]> By: Yosef http://asymptotia.com/latex-sandbox/#comment-126138 Yosef Mon, 29 Sep 2008 13:47:26 +0000 http://asymptotia.com/latex-sandbox/#comment-126138 \buildrel{\bigtriangle}{\bigtriangledown} [tex] \ buildrel{\bigtriangle}{\bigtriangledown} [/tex] \buildrel{\bigtriangle}{\bigtriangledown}
\ buildrel{\bigtriangle}{\bigtriangledown}

]]> By: Yosef http://asymptotia.com/latex-sandbox/#comment-126137 Yosef Mon, 29 Sep 2008 13:44:40 +0000 http://asymptotia.com/latex-sandbox/#comment-126137 \stackrel{\bigtriangle}{\bigtriangledown} [tex] \stackrel{\bigtriangle}{\bigtriangledown} [/tex] \stackrel{\bigtriangle}{\bigtriangledown}
\stackrel{\bigtriangle}{\bigtriangledown}

]]> By: Yosef http://asymptotia.com/latex-sandbox/#comment-126136 Yosef Mon, 29 Sep 2008 13:41:00 +0000 http://asymptotia.com/latex-sandbox/#comment-126136 \stackrel{\bigtriangle}{bigtriangledown} [tex] \stackrel{\bigtriangle}{bigtriangledown} [/tex] \stackrel{\bigtriangle}{bigtriangledown}

\stackrel{\bigtriangle}{bigtriangledown}

]]> By: Yosef http://asymptotia.com/latex-sandbox/#comment-126135 Yosef Mon, 29 Sep 2008 13:35:06 +0000 http://asymptotia.com/latex-sandbox/#comment-126135 [tex] \star \star \star [/tex] [tex] \bigtriangledown [/tex] [tex] \bigtriangle [/tex] \star \star \star

\bigtriangledown

\bigtriangle

]]> By: Yosef http://asymptotia.com/latex-sandbox/#comment-126134 Yosef Mon, 29 Sep 2008 13:31:19 +0000 http://asymptotia.com/latex-sandbox/#comment-126134 [tex] \star \bigstar [/tex] \star \bigstar

]]> By: yosef http://asymptotia.com/latex-sandbox/#comment-126132 yosef Mon, 29 Sep 2008 13:27:12 +0000 http://asymptotia.com/latex-sandbox/#comment-126132 \star \bigstar \star

\bigstar

]]> By: Frank http://asymptotia.com/latex-sandbox/#comment-125880 Frank Thu, 18 Sep 2008 20:38:18 +0000 http://asymptotia.com/latex-sandbox/#comment-125880 <blockquote> Quote </blockquote>

Quote

]]> By: Frank http://asymptotia.com/latex-sandbox/#comment-125879 Frank Thu, 18 Sep 2008 20:36:37 +0000 http://asymptotia.com/latex-sandbox/#comment-125879 <q>Hallo!!</q> Trying to quote Hallo!!
Trying to quote

]]> By: Payman http://asymptotia.com/latex-sandbox/#comment-125754 Payman Thu, 11 Sep 2008 17:21:39 +0000 http://asymptotia.com/latex-sandbox/#comment-125754 a test [tex]\frac{x}{y}[/tex] a test \frac{x}{y}

]]> By: test http://asymptotia.com/latex-sandbox/#comment-125425 test Thu, 28 Aug 2008 05:48:01 +0000 http://asymptotia.com/latex-sandbox/#comment-125425 [tex]\displaystyle \sum_{k=1}^{n} k! [/tex] \displaystyle \sum_{k=1}^{n} k!

]]> By: test http://asymptotia.com/latex-sandbox/#comment-125424 test Thu, 28 Aug 2008 05:47:00 +0000 http://asymptotia.com/latex-sandbox/#comment-125424 [tex]\displaystyle \sum_{k=1}^{n} k! [\tex] [tex]\displaystyle \sum_{k=1}^{n} k! [\tex]

]]> By: test http://asymptotia.com/latex-sandbox/#comment-125423 test Thu, 28 Aug 2008 05:45:12 +0000 http://asymptotia.com/latex-sandbox/#comment-125423 [tex]sum_{k=1}^n k! [/tex] sum_{k=1}^n k!

]]> By: Cozmo http://asymptotia.com/latex-sandbox/#comment-124963 Cozmo Tue, 12 Aug 2008 03:57:54 +0000 http://asymptotia.com/latex-sandbox/#comment-124963 [tex]=f(\tau)[/tex] =f(\tau)

]]> By: Cozmo http://asymptotia.com/latex-sandbox/#comment-124962 Cozmo Tue, 12 Aug 2008 03:55:20 +0000 http://asymptotia.com/latex-sandbox/#comment-124962 =f(\tau) =f(\tau)

]]> By: Pepe http://asymptotia.com/latex-sandbox/#comment-124228 Pepe Thu, 31 Jul 2008 13:10:03 +0000 http://asymptotia.com/latex-sandbox/#comment-124228 [tex] \vec{a} [/tex] \vec{a}

]]> By: test http://asymptotia.com/latex-sandbox/#comment-123000 test Thu, 10 Jul 2008 22:55:17 +0000 http://asymptotia.com/latex-sandbox/#comment-123000 \begin{eqnarray} E &=& mc^2 \\ m &=& \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} \end{eqnarray} \begin{eqnarray}
E &=& mc^2 \\
m &=& \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}
\end{eqnarray}

]]> By: erik http://asymptotia.com/latex-sandbox/#comment-119443 erik Fri, 30 May 2008 16:47:08 +0000 http://asymptotia.com/latex-sandbox/#comment-119443 [tex](\f.(\x.f (x x)) (\x.f (x x))[/tex] (\f.(\x.f (x x)) (\x.f (x x))

]]> By: Plareplane http://asymptotia.com/latex-sandbox/#comment-117943 Plareplane Fri, 16 May 2008 04:32:23 +0000 http://asymptotia.com/latex-sandbox/#comment-117943 For Tom Petty [tex] \int_1^{15} xe^(ax) dx = xe^(ax)/a - e^(ax)/a^2 \rvert_1^{15} = (15e^(a15)/a - e^(a15)/a^2) - (e^a/a - e^a/a^2) [/tex] For Tom Petty
\int_1^{15} xe^(ax) dx = xe^(ax)/a - e^(ax)/a^2 \rvert_1^{15} = (15e^(a15)/a - e^(a15)/a^2) - (e^a/a - e^a/a^2)

]]> By: Zylinder http://asymptotia.com/latex-sandbox/#comment-117380 Zylinder Thu, 08 May 2008 22:10:11 +0000 http://asymptotia.com/latex-sandbox/#comment-117380 [tex]f(r, \phi, z)=\left(\array{rcos(\phi)\\rsin(\phi)\\z}\right)[/tex] [tex]f'(r,\phi, z)= \left(\matrix{cos(\phi)&-rsin(\phi)&0 \cr sin(\phi)&rcos(\phi)&0 \cr 0&0&1}\right)[/tex] f(r, \phi, z)=\left(\array{rcos(\phi)\\rsin(\phi)\\z}\right)

f&#8217;(r,\phi, z)= \left(\matrix{cos(\phi)&amp;-rsin(\phi)&amp;0 \cr sin(\phi)&amp;rcos(\phi)&amp;0 \cr 0&amp;0&amp;1}\right)

]]> By: dog http://asymptotia.com/latex-sandbox/#comment-116528 dog Sun, 27 Apr 2008 17:46:17 +0000 http://asymptotia.com/latex-sandbox/#comment-116528 \`{a} bient\^{o} = à bientô \`{a} bient\^{o} = à bientô

]]> By: Nathan http://asymptotia.com/latex-sandbox/#comment-113330 Nathan Sat, 29 Mar 2008 21:37:08 +0000 http://asymptotia.com/latex-sandbox/#comment-113330 [tex]\frac{\deltaI_{0}}{I_{0}}[/tex] \frac{\deltaI_{0}}{I_{0}}

]]> By: Plato http://asymptotia.com/latex-sandbox/#comment-111978 Plato Wed, 12 Mar 2008 06:41:34 +0000 http://asymptotia.com/latex-sandbox/#comment-111978 <b>Gravity and the Photon</b> The relativistic energy expression attributes a mass to any energetic particle, and for the photon [tex]E=mc^2=hv[/tex] The gravitational potential energy is then [tex]\LARGE U=\frac{-GMm}r=\frac{-GMh}{rc^2}{vo}[/tex] When the photon escapes the gravity field, it will have a different frequency [tex]\large hv=hv_o[{1-}\frac{GM}{rc^2}] \hspace9 v=v_o[{1-}\frac{GM}{rc^2}] \hspace9 \frac{\bigtriangledown v} {v_o}={-}\frac{GM}{rc^2}[/tex] Since it is reduced in frequency, this is called the gravitational red shift or the Einstein red shift. -------------------------------------------------- <b>Escape Energy for Photon</b> If the gravitational potential energy of the photon is exactly equal to the photon energy then [tex]\normal hv_o=\frac{GM}{rc^2}{v_o} \hspace9 \text or r=\frac {GM}{c^2}\\ \text so if Mass M collapses to radius r a photon will be redshifted to zero frequency[/tex] Note that this condition is independent of the frequency, and for a given mass M establishes a critical radius. Actually, Schwarzchilds's calculated gravitational radius differs from this result by a factor of 2 and is coincidently equal to the non-relativistic escape velocity expression [tex]v_e_s_c_a_p_e_ = \sqrt {\frac{2GM}{r}} \hspace9 \\ \text which if V is set equal\\to c gives a radius r=\frac {2GM}{c^2}\hspace9 \text Schwarzchild Radius[\tex] This equivalence is used as a mnenomic, but does not imply this is a valid way to derive the Schwarzchild Radius You can delete from your tipping light thread. Have a nice day. I acknowledge fully I am the student. While we see tipping light cones there is an actual qualitative understanding for the determination of the blackhole in this context? Gravity and the Photon

The relativistic energy expression attributes a mass to any energetic particle, and for the photon

E=mc^2=hv

The gravitational potential energy is then

\LARGE U=\frac{-GMm}r=\frac{-GMh}{rc^2}{vo}

When the photon escapes the gravity field, it will have a different frequency

\large hv=hv_o[{1-}\frac{GM}{rc^2}] \hspace9 v=v_o[{1-}\frac{GM}{rc^2}] \hspace9 \frac{\bigtriangledown v} {v_o}={-}\frac{GM}{rc^2}

Since it is reduced in frequency, this is called the gravitational red shift or the Einstein red shift.

————————————————–
Escape Energy for Photon

If the gravitational potential energy of the photon is exactly equal to the photon energy then

\normal hv_o=\frac{GM}{rc^2}{v_o} \hspace9 \text or r=\frac {GM}{c^2}\\ \text so if Mass M collapses to radius r a photon will be redshifted to zero frequency

Note that this condition is independent of the frequency, and for a given mass M establishes a critical radius. Actually, Schwarzchilds’s calculated gravitational radius differs from this result by a factor of 2 and is coincidently equal to the non-relativistic escape velocity expression

[tex]v_e_s_c_a_p_e_ = \sqrt {\frac{2GM}{r}} \hspace9 \\ \text which if V is set equal\\to c gives a radius r=\frac {2GM}{c^2}\hspace9 \text Schwarzchild Radius[\tex]

This equivalence is used as a mnenomic, but does not imply this is a valid way to derive the Schwarzchild Radius

You can delete from your tipping light thread. Have a nice day. I acknowledge fully I am the student. While we see tipping light cones there is an actual qualitative understanding for the determination of the blackhole in this context?

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