additional math examples #531

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>