math.html 2.7 KB

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  22. <section>
  23. <h1>Reveal.js Math Plugin</h1>
  24. </section>
  25. <section>
  26. <h2>The Lorenz Equations</h2>
  27. \[\begin{aligned}
  28. \dot{x} &amp; = \sigma(y-x) \\
  29. \dot{y} &amp; = \rho x - y - xz \\
  30. \dot{z} &amp; = -\beta z + xy
  31. \end{aligned} \]
  32. </section>
  33. <section>
  34. <h2>The Cauchy-Schwarz Inequality</h2>
  35. \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
  36. </section>
  37. <section>
  38. <h2>A Cross Product Formula</h2>
  39. \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
  40. \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
  41. \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
  42. \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
  43. \end{vmatrix} \]
  44. </section>
  45. <section>
  46. <h2>An Identity of Ramanujan</h2>
  47. \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
  48. 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
  49. {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
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