diff --git a/docs/index.html b/docs/index.html
index 90b287e8..d9b59a0f 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -38,7 +38,7 @@
 		<meta property="og:locale" content="en-GB" />
 		<meta property="og:type" content="article" />
 		<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
-		<meta property="og:updated_time" content="2021-08-31T22:19:11+00:00" />
+		<meta property="og:updated_time" content="2021-09-01T16:39:16+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -6243,8 +6243,8 @@ lli = function(line1, line2):
 						are again all kinds of approaches we can take, and a simple-but-effective one is to set the length of that segment to "one third the
 						length of the baseline". This forces <code>e1</code> and <code>e2</code> to always be the "linear curve" distance apart, which means if we
 						place our three points on a line, it will actually <em>look</em> like a line. Nice! The last thing we'll need to do is make sure to flip
-						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't up creating a funky curve
-						with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
+						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't end up creating a funky
+						curve with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
 					</p>
 					<!--
 \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
diff --git a/docs/ja-JP/index.html b/docs/ja-JP/index.html
index d6e10c4f..c305d54c 100644
--- a/docs/ja-JP/index.html
+++ b/docs/ja-JP/index.html
@@ -41,7 +41,7 @@
 		<meta property="og:locale" content="ja-JP" />
 		<meta property="og:type" content="article" />
 		<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
-		<meta property="og:updated_time" content="2021-08-31T22:19:11+00:00" />
+		<meta property="og:updated_time" content="2021-09-01T16:39:16+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -6372,8 +6372,8 @@ lli = function(line1, line2):
 						are again all kinds of approaches we can take, and a simple-but-effective one is to set the length of that segment to "one third the
 						length of the baseline". This forces <code>e1</code> and <code>e2</code> to always be the "linear curve" distance apart, which means if we
 						place our three points on a line, it will actually <em>look</em> like a line. Nice! The last thing we'll need to do is make sure to flip
-						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't up creating a funky curve
-						with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
+						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't end up creating a funky
+						curve with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
 					</p>
 					<!--
 \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
diff --git a/docs/news/2020-09-18.html b/docs/news/2020-09-18.html
index e17c0643..b291396e 100644
--- a/docs/news/2020-09-18.html
+++ b/docs/news/2020-09-18.html
@@ -34,7 +34,7 @@
 		<meta property="og:locale" content="en-GB" />
 		<meta property="og:type" content="article" />
 		<meta property="og:published_time" content="Fri Sep 18 2020 00:00:00 +00:00" />
-		<meta property="og:updated_time" content="Tue Aug 31 2021 22:19:11 +00:00" />
+		<meta property="og:updated_time" content="Wed Sep 01 2021 16:39:16 +00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
diff --git a/docs/news/2020-11-22.html b/docs/news/2020-11-22.html
index 222969b0..80735682 100644
--- a/docs/news/2020-11-22.html
+++ b/docs/news/2020-11-22.html
@@ -34,7 +34,7 @@
 		<meta property="og:locale" content="en-GB" />
 		<meta property="og:type" content="article" />
 		<meta property="og:published_time" content="Sun Nov 22 2020 00:00:00 +00:00" />
-		<meta property="og:updated_time" content="Tue Aug 31 2021 22:19:11 +00:00" />
+		<meta property="og:updated_time" content="Wed Sep 01 2021 16:39:16 +00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
diff --git a/docs/news/index.html b/docs/news/index.html
index 35a4e454..4152b87f 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -33,7 +33,7 @@
 		<meta property="og:description" content="" />
 		<meta property="og:locale" content="en-GB" />
 		<meta property="og:type" content="article" />
-		<meta property="og:published_time" content="Tue Aug 31 2021 22:19:11 GMT+0000 (Coordinated Universal Time)" />
+		<meta property="og:published_time" content="Wed Sep 01 2021 16:39:16 GMT+0000 (Coordinated Universal Time)" />
 		<meta property="og:updated_time" content="" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
diff --git a/docs/news/rss.xml b/docs/news/rss.xml
index 7ead1fb0..9f1821fc 100644
--- a/docs/news/rss.xml
+++ b/docs/news/rss.xml
@@ -6,7 +6,7 @@
   <atom:link href="https://pomax.github.io/bezierinfo" rel="self"></atom:link>
   <description>News updates for the <a href="https://pomax.github.io/bezierinfo">primer on Bézier Curves</a> by Pomax</description>
   <language>en-GB</language>
-  <lastBuildDate>Tue Aug 31 2021 22:19:11 +00:00</lastBuildDate>
+  <lastBuildDate>Wed Sep 01 2021 16:39:16 +00:00</lastBuildDate>
   <image>
     <url>https://pomax.github.io/bezierinfo/images/og-image.png</url>
     <title>A Primer on Bézier Curves</title>
diff --git a/docs/ru-RU/index.html b/docs/ru-RU/index.html
index 296c2ac0..a8be9d84 100644
--- a/docs/ru-RU/index.html
+++ b/docs/ru-RU/index.html
@@ -34,7 +34,7 @@
 		<meta property="og:locale" content="ru-RU" />
 		<meta property="og:type" content="article" />
 		<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
-		<meta property="og:updated_time" content="2021-08-31T22:19:11+00:00" />
+		<meta property="og:updated_time" content="2021-09-01T16:39:16+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -6529,8 +6529,8 @@ lli = function(line1, line2):
 						are again all kinds of approaches we can take, and a simple-but-effective one is to set the length of that segment to "one third the
 						length of the baseline". This forces <code>e1</code> and <code>e2</code> to always be the "linear curve" distance apart, which means if we
 						place our three points on a line, it will actually <em>look</em> like a line. Nice! The last thing we'll need to do is make sure to flip
-						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't up creating a funky curve
-						with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
+						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't end up creating a funky
+						curve with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
 					</p>
 					<!--
 \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
diff --git a/docs/uk-UA/index.html b/docs/uk-UA/index.html
index 0f0159a9..9acbab0b 100644
--- a/docs/uk-UA/index.html
+++ b/docs/uk-UA/index.html
@@ -39,7 +39,7 @@
 		<meta property="og:locale" content="uk-UA" />
 		<meta property="og:type" content="article" />
 		<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
-		<meta property="og:updated_time" content="2021-08-31T22:19:11+00:00" />
+		<meta property="og:updated_time" content="2021-09-01T16:39:16+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -6505,8 +6505,8 @@ lli = function(line1, line2):
 						are again all kinds of approaches we can take, and a simple-but-effective one is to set the length of that segment to "one third the
 						length of the baseline". This forces <code>e1</code> and <code>e2</code> to always be the "linear curve" distance apart, which means if we
 						place our three points on a line, it will actually <em>look</em> like a line. Nice! The last thing we'll need to do is make sure to flip
-						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't up creating a funky curve
-						with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
+						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't end up creating a funky
+						curve with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
 					</p>
 					<!--
 \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
diff --git a/docs/zh-CN/index.html b/docs/zh-CN/index.html
index 3711a2f5..ba7620bf 100644
--- a/docs/zh-CN/index.html
+++ b/docs/zh-CN/index.html
@@ -41,7 +41,7 @@
 		<meta property="og:locale" content="zh-CN" />
 		<meta property="og:type" content="article" />
 		<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
-		<meta property="og:updated_time" content="2021-08-31T22:19:11+00:00" />
+		<meta property="og:updated_time" content="2021-09-01T16:39:16+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -6348,8 +6348,8 @@ lli = function(line1, line2):
 						are again all kinds of approaches we can take, and a simple-but-effective one is to set the length of that segment to "one third the
 						length of the baseline". This forces <code>e1</code> and <code>e2</code> to always be the "linear curve" distance apart, which means if we
 						place our three points on a line, it will actually <em>look</em> like a line. Nice! The last thing we'll need to do is make sure to flip
-						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't up creating a funky curve
-						with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
+						the sign of <code>d</code> depending on which side of the baseline our <code>B</code> is located, so we don't end up creating a funky
+						curve with a loop in it. To do this, we can use the <a href="https://en.wikipedia.org/wiki/Atan2">atan2</a> function:
 					</p>
 					<!--
 \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math