rolling.html: Eliminate pointless `h2' and promote subheadings.

[dep-ui] / rolling-eqn.html
diff --git a/rolling-eqn.html b/rolling-eqn.html

index 4077c8ccadfbb3799b810506b29f43b70b00ea68..c2383c40e0379c30c976a17b38f6e271d8ad7fb5 100644 (file)
--- a/rolling-eqn.html
+++ b/rolling-eqn.html
@@ -3,6 +3,8 @@
  <html>
  <head>
    <title>Rolling wire-strip calculator: equations</title>
+  <meta name=viewport content="width=device-width initial-scale=1.0">
+  <link rel=stylesheet type="text/css" href="rolling.css">
    <script type="text/x-mathjax-config">
      MathJax.Hub.Config({
        tex2jax: { inlineMath: [['$', '$'], ['\\(', '\\)']] }
@@ -11,8 +13,6 @@
    <script type="text/javascript"
           src="https://www.distorted.org.uk/javascript/mathjax/MathJax.js?config=TeX-AMS_HTML">
    </script>
-  <meta name=viewport content="width=device-width initial-scale=1.0">
-  <link rel=stylesheet type="text/css" href="rolling.css">
  <head>
  <body>
  
@@ -26,26 +26,26 @@ here&rsquo;s how it currently works.
  <p>Let&rsquo;s suppose we start with square wire, with side&nbsp;$S$,
  and we roll it to thickness&nbsp;$t$.  Then we find that the
  wire&rsquo;s width is
-\[ w = \sqrt{\frac{S^3}{t}} \]
+\[ w = \sqrt{\frac{S^3}{t}} \,\text{.} \]
  Rearranging, we find that
-\[ S = \sqrt[3]{w^2 t} \]
+\[ S = \sqrt[3]{w^2 t} \,\text{.} \]
  For round wire, we assume that the cross-section area is the important
  bit, so a round wire with diameter&nbsp;$D$ ought to work as well as
  square wire with side $S$ if $S^2 = \pi D^2/4$, i.e.,
-\[ D = \sqrt{\frac{4 S^2}{\pi}} = \frac{2 S}{\sqrt\pi} \]
+\[ D = \sqrt{\frac{4 S^2}{\pi}} = \frac{2 S}{\sqrt\pi} \,\text{.} \]
  Volume is conserved, so if the original and final wire lengths
-are&nbsp;$L$ and&nbsp;$l$ respectively, then
-\[ L S^2 = l w t \]
+are&nbsp;$L$ and&nbsp;$\ell$ respectively, then
+\[ L S^2 = \ell w t \,\text{,} \]
  and hence
-\[ L = \frac{l w t}{S^2} \]
+\[ L = \frac{\ell w t}{S^2} \,\text{.} \]
  Finally, determining the required initial stock length&nbsp;$L_0$ given
  its side&nbsp;$S_0$ (for square stock) or diameter&nbsp;$D_0$ (for
  round) again makes use of conservation of volume:
-\[ L_0 = \frac{S^2 L}{S_0^2} = \frac{4 S^2 L}{\pi D_0^2} \]
+\[ L_0 = \frac{S^2 L}{S_0^2} = \frac{4 S^2 L}{\pi D_0^2} \,\text{.} \]
  
-<p>[This page uses <a href="http://www.mathjax.org/">MathJax</a> for
-rendering equations.  It probably doesn't work if you don't enable
-JavaScript.]
+<p>[This page uses <a href="https://www.mathjax.org/">MathJax</a> for
+rendering equations.  It probably doesn&rsquo;t work if you don&rsquo;t
+enable Javascript.]
  
  </body>
  </html>