additional math examples #531

diff --git a/examples/math.html b/examples/math.html
index 413d1690c8dca5bdf6d645ff437417268cfe38d3..49d49526ec891a145f6a5ef46af1cf68861f1ccf 100644 (file)
--- a/examples/math.html
+++ b/examples/math.html
@@ -36,6 +36,7 @@
                                </section>
 
                                <section>
+                                       <h2>The Lorenz Equations</h2>
                                        \[\begin{aligned}
                                        \dot{x} &amp; = \sigma(y-x) \\
                                        \dot{y} &amp; = \rho x - y - xz \\
@@ -43,6 +44,30 @@
                                        \end{aligned} \]
                                </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>
+
+                                       \[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
+                                       \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
+                                       \frac{\partial X}{\partial u} &amp;  \frac{\partial Y}{\partial u} &amp; 0 \\
+                                       \frac{\partial X}{\partial v} &amp;  \frac{\partial Y}{\partial v} &amp; 0
+                                       \end{vmatrix}  \]
+                               </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>