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'

---
 .../concept/cylindrical-polar-coordinates/index.md | 26 +++++++++++-----------
 1 file changed, 13 insertions(+), 13 deletions(-)

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

diff --git a/source/know/concept/cylindrical-polar-coordinates/index.md b/source/know/concept/cylindrical-polar-coordinates/index.md
index 8673c0b..686a4ed 100644
--- a/source/know/concept/cylindrical-polar-coordinates/index.md
+++ b/source/know/concept/cylindrical-polar-coordinates/index.md
@@ -10,12 +10,12 @@ layout: "concept"
 
 **Cylindrical polar coordinates** are an extension of polar coordinates to 3D,
 which describes the location of a point in space
-using the coordinates $(r, \varphi, z)$.
-The $z$-axis is unchanged from Cartesian coordinates,
+using the coordinates $$(r, \varphi, z)$$.
+The $$z$$-axis is unchanged from Cartesian coordinates,
 hence it is called a *cylindrical* system.
 
-Cartesian coordinates $(x, y, z)$
-and the cylindrical system $(r, \varphi, z)$ are related by:
+Cartesian coordinates $$(x, y, z)$$
+and the cylindrical system $$(r, \varphi, z)$$ are related by:
 
 $$\begin{aligned}
     \boxed{
@@ -27,8 +27,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Conversely, a point given in $(x, y, z)$
-can be converted to $(r, \varphi, z)$
+Conversely, a point given in $$(x, y, z)$$
+can be converted to $$(r, \varphi, z)$$
 using these formulae:
 
 $$\begin{aligned}
@@ -43,7 +43,7 @@ $$\begin{aligned}
 
 The cylindrical polar coordinates form an orthogonal
 [curvilinear system](/know/concept/curvilinear-coordinates/),
-whose scale factors $h_r$, $h_\varphi$ and $h_z$ we want to find.
+whose scale factors $$h_r$$, $$h_\varphi$$ and $$h_z$$ we want to find.
 To do so, we calculate the differentials of the Cartesian coordinates:
 
 $$\begin{aligned}
@@ -54,7 +54,7 @@ $$\begin{aligned}
     \dd{z} = \dd{z}
 \end{aligned}$$
 
-And then we calculate the line element $\dd{\ell}^2$,
+And then we calculate the line element $$\dd{\ell}^2$$,
 skipping many terms thanks to orthogonality,
 
 $$\begin{aligned}
@@ -68,7 +68,7 @@ $$\begin{aligned}
 
 Finally, we can simply read off
 the squares of the desired scale factors
-$h_r^2$, $h_\varphi^2$ and $h_z^2$:
+$$h_r^2$$, $$h_\varphi^2$$ and $$h_z^2$$:
 
 $$\begin{aligned}
     \boxed{
@@ -141,7 +141,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-The differential element of volume $\dd{V}$
+The differential element of volume $$\dd{V}$$
 takes the following form:
 
 $$\begin{aligned}
@@ -158,7 +158,7 @@ $$\begin{aligned}
     = \int_{-\infty}^{\infty} \int_0^{2\pi} \int_0^\infty f(r, \varphi, z) \: r \dd{r} \dd{\varphi} \dd{z}
 \end{aligned}$$
 
-The isosurface elements are as follows, where $S_r$ is a surface at constant $r$, etc.:
+The isosurface elements are as follows, where $$S_r$$ is a surface at constant $$r$$, etc.:
 
 $$\begin{aligned}
     \boxed{
@@ -172,7 +172,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Similarly, the normal vector element $\dd{\vu{S}}$ for an arbitrary surface is given by:
+Similarly, the normal vector element $$\dd{\vu{S}}$$ for an arbitrary surface is given by:
 
 $$\begin{aligned}
     \boxed{
@@ -183,7 +183,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-And finally, the tangent vector element $\dd{\vu{\ell}}$ of a given curve is as follows:
+And finally, the tangent vector element $$\dd{\vu{\ell}}$$ of a given curve is as follows:
 
 $$\begin{aligned}
     \boxed{
-- 
cgit v1.2.3