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| -rw-r--r-- | examples/math.html | 25 |
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diff --git a/examples/math.html b/examples/math.html index 413d169..49d4952 100644 --- a/examples/math.html +++ b/examples/math.html @@ -36,6 +36,7 @@ </section> <section> + <h2>The Lorenz Equations</h2> \[\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ @@ -43,6 +44,30 @@ \end{aligned} \] </section> + <section> + <h2>The Cauchy-Schwarz Inequality</h2> + + \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \] + </section> + + <section> + <h2>A Cross Product Formula</h2> + + \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} + \mathbf{i} & \mathbf{j} & \mathbf{k} \\ + \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ + \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 + \end{vmatrix} \] + </section> + + <section> + <h2>An Identity of Ramanujan</h2> + + \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = + 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} + {1+\frac{e^{-8\pi}} {1+\ldots} } } } \] + </section> + </div> </div> |