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rolling-eqn.html: Use `\ell' for `l' in mathematics.
author
Mark Wooding
<mdw@distorted.org.uk>
Sat, 9 Jan 2021 02:17:00 +0000
(
02:17
+0000)
committer
Mark Wooding
<mdw@distorted.org.uk>
Sat, 9 Jan 2021 02:17:00 +0000
(
02:17
+0000)
It's rather clearer.
rolling-eqn.html
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diff --git
a/rolling-eqn.html
b/rolling-eqn.html
index 4b5a9739db90545a37a7b783926fb677ac970482..c2383c40e0379c30c976a17b38f6e271d8ad7fb5 100644
(file)
--- a/
rolling-eqn.html
+++ b/
rolling-eqn.html
@@
-34,10
+34,10
@@
bit, so a round wire with diameter $D$ ought to work as well as
square wire with side $S$ if $S^2 = \pi D^2/4$, i.e.,
\[ D = \sqrt{\frac{4 S^2}{\pi}} = \frac{2 S}{\sqrt\pi} \,\text{.} \]
Volume is conserved, so if the original and final wire lengths
square wire with side $S$ if $S^2 = \pi D^2/4$, i.e.,
\[ D = \sqrt{\frac{4 S^2}{\pi}} = \frac{2 S}{\sqrt\pi} \,\text{.} \]
Volume is conserved, so if the original and final wire lengths
-are $L$ and $l$ respectively, then
-\[ L S^2 = l w t \,\text{,} \]
+are $L$ and $
\el
l$ respectively, then
+\[ L S^2 =
\el
l w t \,\text{,} \]
and hence
and hence
-\[ L = \frac{l w t}{S^2} \,\text{.} \]
+\[ L = \frac{
\el
l w t}{S^2} \,\text{.} \]
Finally, determining the required initial stock length $L_0$ given
its side $S_0$ (for square stock) or diameter $D_0$ (for
round) again makes use of conservation of volume:
Finally, determining the required initial stock length $L_0$ given
its side $S_0$ (for square stock) or diameter $D_0$ (for
round) again makes use of conservation of volume: