User:ShadowWolf/Math example

<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>

<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>\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>