User:ShadowWolf/Math example - Revision history

ShadowWolf: Reformat, add information and some other bits

2007-11-06T03:15:31Z

Reformat, add information and some other bits

← Older revision		Revision as of 22:15, 5 November 2007
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	<math>\mathrm{F} = \frac{1}{2} \rho \mathrm{v}^2 C_d A</math>		Equations I have recently solved:
			:Drag Equation: <math>\mathrm{F} = \frac{1}{2} \rho \mathrm{v}^2 C_d A</math>

	<math>\rho = \rho_p \cdot \left[ \frac{T_b} { T_b + L_b \cdot ( h - h_b ) } \right]^{\left( \frac{g_0 \cdot M}{ R^* \cdot L_b } \right) +1}</math>		:Barometric Formula for Air Density: <math>\rho = \rho_p \cdot \left[ \frac{T_b} { T_b + L_b \cdot ( h - h_b ) } \right]^{\left( \frac{g_0 \cdot M}{ R^* \cdot L_b } \right) +1}</math>

	<math>E_{rest} = ~~m c~~^2</math> ~~because~~ <math>~~E = \gamma~~ m ~~c^2</math> where <math>\gamma</math> is <math>\gamma~~ = \frac{1}{~~\sqrt{1-\beta~~^2}}</math> ~~and <math>\beta</math> is the velocity expressed as a ratio of the speed of light.~~		:Einsteins Formula for Mass Equivalence: <math>E_{rest} = mc^2</math> (in the form of <math> m = \frac{E_{rest}}{c^2} </math>)

	<math>E \~~approx m c~~^~~2 +~~ \begin{matrix} \frac{1}{2} \end{matrix} ~~m v^2~~</math>		:Fireball Radius of a Nuclear Weapon: <math> R = \left( { \frac{E t^2}{\rho} } \right)^{\begin{matrix}\frac{1}{5}\end{matrix}} </math>

	<math>~~L_1~~ = \~~frac{L_0}~~{~~\gamma~~}</math>		:Pythagoras: <math>x^2 + y^2 = z^2</math> hence <math>z = \sqrt{x^2 + y^2}</math>

	<math>\gamma \ ~~\stackrel{\mathrm{def}}{~~=} \frac{1}{\sqrt{1 - \~~frac{u~~^2~~}{c^2}~~}}</math>		Other Equations:
			:Einsteins formula for Mass Equivalence (complete and with all definitions): <math>E = \gamma m c^2</math> where γ is <math>\gamma = \frac{1}{\sqrt{1-\beta^2}}</math> and β is the velocity expressed as a ratio of the speed of light.

	<math>\~~Delta t~~^~~' =~~ \~~gamma (~~ {~~\Delta t -~~ \frac{~~v \Delta x~~}{c^2} } )</math>		:Approximation of Mass-Equivalence: <math>E \approx m c^2 + \begin{matrix} \frac{1}{2} \end{matrix} m v^2</math>

	<math>x^2 ~~+ y~~^2 = z^2</math> ~~hence~~ <math>z = \sqrt{x^2 ~~+ y~~^2}</math>		:Lorentz Transformation: <math>L_1 = \frac{L_0}{\gamma}</math> where γ is <math>\gamma \ \stackrel{\mathrm{def}}{=} \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}</math>

			:Time Dilation Equation: <math>\Delta t^' = \gamma \left( {\Delta t - \frac{v \Delta x}{c^2} } \right)</math> where γ is <math>\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}</math>

ShadowWolf: fix some typographical problems in the TeX and the examples

2007-11-05T09:17:51Z

fix some typographical problems in the TeX and the examples

← Older revision		Revision as of 04:17, 5 November 2007
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	<math>\mathrm{F} = { 1 ~~\over~~ 2 } \rho v^2 C_d A</math>		<math>\mathrm{F} = \frac{1}{2} \rho \mathrm{v}^2 C_d A</math>

	<math>\rho = \rho_p \cdot {[ \frac{T_b}{T_b + L_b \cdot ( h - h_b )} ]}^{( { {g_0 \cdot M} ~~\over~~ {R^* \cdot L_b} } )+1}</math>		<math>\rho = \rho_p \cdot \left[ \frac{T_b} { T_b + L_b \cdot ( h - h_b ) } \right]^{\left( \frac{g_0 \cdot M}{ R^* \cdot L_b } \right) +1}</math>

	<math>\~~mathrm~~{~~E_0~~} ~~= m_0~~ c^2</math>		<math>E_{rest} = m c^2</math> because <math>E = \gamma m c^2</math> where <math>\gamma</math> is <math>\gamma = \frac{1}{\sqrt{1-\beta^2}}</math> and <math>\beta</math> is the velocity expressed as a ratio of the speed of light.

			<math>E \approx m c^2 + \begin{matrix} \frac{1}{2} \end{matrix} m v^2</math>

	<math>L_1 = \frac{L_0}{\gamma}</math>		<math>L_1 = \frac{L_0}{\gamma}</math>

ShadowWolf: simple page demonstrating the $tag$

2007-11-05T08:52:10Z

simple page demonstrating the <math> tag

New page

<math>\mathrm{F} = { 1 \over 2 } \rho v^2 C_d A</math>

<math>\rho = \rho_p \cdot {[ \frac{T_b}{T_b + L_b \cdot ( h - h_b )} ]}^{( { {g_0 \cdot M} \over {R^* \cdot L_b} } )+1}</math>

<math>\mathrm{E_0} = m_0 c^2</math>

<math>L_1 = \frac{L_0}{\gamma}</math>

<math>\gamma \ \stackrel{\mathrm{def}}{=} \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}}</math>

<math>\Delta t^' = \gamma ( {\Delta t - \frac{v \Delta x}{c^2} } )</math>

<math>x^2 + y^2 = z^2</math> hence <math>z = \sqrt{x^2 + y^2}</math>

User:ShadowWolf/Math example - Revision history

ShadowWolf: Reformat, add information and some other bits

ShadowWolf: fix some typographical problems in the TeX and the examples

ShadowWolf: simple page demonstrating the tag

ShadowWolf: simple page demonstrating the $tag$