From aca28a1d25ea50c837b2699964ef3c53f449f0c1 Mon Sep 17 00:00:00 2001 From: Mark Wooding Date: Sat, 9 Jan 2021 02:17:00 +0000 Subject: [PATCH] rolling-eqn.html: Use `\ell' for `l' in mathematics. It's rather clearer. --- rolling-eqn.html | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/rolling-eqn.html b/rolling-eqn.html index 4b5a973..c2383c4 100644 --- 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 -are $L$ and $l$ respectively, then -\[ L S^2 = l w t \,\text{,} \] +are $L$ and $\ell$ respectively, then +\[ L S^2 = \ell w t \,\text{,} \] and hence -\[ L = \frac{l w t}{S^2} \,\text{.} \] +\[ L = \frac{\ell w t}{S^2} \,\text{.} \] 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: -- 2.11.0