From 16555851b6514a736c5c9d8e73de7da7fc9b6288 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 20 Oct 2022 18:25:31 +0200
Subject: Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'

---
 .../cylindrical-parabolic-coordinates/index.md     | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

(limited to 'source/know/concept/cylindrical-parabolic-coordinates')

diff --git a/source/know/concept/cylindrical-parabolic-coordinates/index.md b/source/know/concept/cylindrical-parabolic-coordinates/index.md
index 76ff756..c8e16da 100644
--- a/source/know/concept/cylindrical-parabolic-coordinates/index.md
+++ b/source/know/concept/cylindrical-parabolic-coordinates/index.md
@@ -9,11 +9,11 @@ layout: "concept"
 ---
 
 **Cylindrical parabolic coordinates** are a coordinate system
-that describes a point in space using three coordinates $(\sigma, \tau, z)$.
-The $z$-axis is unchanged from the Cartesian system,
+that describes a point in space using three coordinates $$(\sigma, \tau, z)$$.
+The $$z$$-axis is unchanged from the Cartesian system,
 hence it is called a *cylindrical* system.
-In the $z$-isoplane, however, confocal parabolas are used.
-These coordinates can be converted to the Cartesian $(x, y, z)$ as follows:
+In the $$z$$-isoplane, however, confocal parabolas are used.
+These coordinates can be converted to the Cartesian $$(x, y, z)$$ as follows:
 
 $$\begin{aligned}
     \boxed{
@@ -39,7 +39,7 @@ $$\begin{aligned}
 
 Cylindrical parabolic coordinates form an orthogonal
 [curvilinear system](/know/concept/curvilinear-coordinates/),
-so we would like to find its scale factors $h_\sigma$, $h_\tau$ and $h_z$.
+so we would like to find its scale factors $$h_\sigma$$, $$h_\tau$$ and $$h_z$$.
 The differentials of the Cartesian coordinates are as follows:
 
 $$\begin{aligned}
@@ -50,7 +50,7 @@ $$\begin{aligned}
     \dd{z} = \dd{z}
 \end{aligned}$$
 
-We calculate the line segment $\dd{\ell}^2$,
+We calculate the line segment $$\dd{\ell}^2$$,
 skipping many terms thanks to orthogonality:
 
 $$\begin{aligned}
@@ -58,7 +58,7 @@ $$\begin{aligned}
     &= (\sigma^2 + \tau^2) \:\dd{\sigma}^2 + (\tau^2 + \sigma^2) \:\dd{\tau}^2 + \dd{z}^2
 \end{aligned}$$
 
-From this, we can directly read off the scale factors $h_\sigma^2$, $h_\tau^2$ and $h_z^2$,
+From this, we can directly read off the scale factors $$h_\sigma^2$$, $$h_\tau^2$$ and $$h_z^2$$,
 which turn out to be:
 
 $$\begin{aligned}
@@ -131,7 +131,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-The differential element of volume $\dd{V}$
+The differential element of volume $$\dd{V}$$
 in cylindrical parabolic coordinates is given by:
 
 $$\begin{aligned}
@@ -141,7 +141,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 The differential elements of the isosurfaces are as follows,
-where $\dd{S_\sigma}$ is the $\sigma$-isosurface, etc.:
+where $$\dd{S_\sigma}$$ is the $$\sigma$$-isosurface, etc.:
 
 $$\begin{aligned}
     \boxed{
@@ -155,8 +155,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-The normal element $\dd{\vu{S}}$ of a surface and
-the tangent element $\dd{\vu{\ell}}$ of a curve are respectively:
+The normal element $$\dd{\vu{S}}$$ of a surface and
+the tangent element $$\dd{\vu{\ell}}$$ of a curve are respectively:
 
 $$\begin{aligned}
     \boxed{
-- 
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