From 5a4eb1d13110048b3714754817b3f38d7a55970b Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Wed, 14 Jun 2023 20:25:38 +0200
Subject: Improve knowledge base

---
 .../know/concept/orthogonal-curvilinear-coordinates/index.md | 12 +++++-------
 1 file changed, 5 insertions(+), 7 deletions(-)

(limited to 'source/know/concept/orthogonal-curvilinear-coordinates')

diff --git a/source/know/concept/orthogonal-curvilinear-coordinates/index.md b/source/know/concept/orthogonal-curvilinear-coordinates/index.md
index c7299ee..669358c 100644
--- a/source/know/concept/orthogonal-curvilinear-coordinates/index.md
+++ b/source/know/concept/orthogonal-curvilinear-coordinates/index.md
@@ -21,7 +21,8 @@ where the coordinate surfaces are always perpendicular.
 Examples of such orthogonal curvilinear systems include
 [spherical coordinates](/know/concept/spherical-coordinates/),
 [cylindrical polar coordinates](/know/concept/cylindrical-polar-coordinates/),
-and [cylindrical parabolic coordinates](/know/concept/cylindrical-parabolic-coordinates/).
+[cylindrical parabolic coordinates](/know/concept/cylindrical-parabolic-coordinates/),
+and (trivially) [Cartesian coordinates](/know/concept/cartesian-coordinates/).
 
 
 
@@ -690,12 +691,9 @@ When this index notation is written out in full, it becomes:
 
 $$\begin{aligned}
     \nabla^2 f
-    = \frac{1}{h_1 h_2 h_3}
-    \bigg(
-        \pdv{}{c_1}\Big(\! \frac{h_2 h_3}{h_1} \pdv{f}{c_1} \!\Big)
-        + \pdv{}{c_2}\Big(\! \frac{h_1 h_3}{h_2} \pdv{f}{c_2} \!\Big)
-        + \pdv{}{c_3}\Big(\! \frac{h_1 h_2}{h_3} \pdv{f}{c_3} \!\Big)
-    \bigg)
+    = \frac{1}{h_1 h_2 h_3} \bigg( \pdv{}{c_1} \Big( \frac{h_2 h_3}{h_1} \pdv{f}{c_1} \Big)
+    + \pdv{}{c_2} \Big( \frac{h_1 h_3}{h_2} \pdv{f}{c_2} \Big)
+    + \pdv{}{c_3} \Big( \frac{h_1 h_2}{h_3} \pdv{f}{c_3} \Big) \bigg)
 \end{aligned}$$
 
 This is trivial to prove: $$\nabla^2 f = \nabla \cdot (\nabla f)$$,
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