diff --git a/docs/index.html b/docs/index.html
index 4c180d02..32d2f070 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="2024-02-28T17:22:37+00:00" />
+		<meta property="og:updated_time" content="2024-06-19T17:18:55+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -4977,7 +4977,8 @@ mapped  = (x) = │                                1  2                       
 						Now, if you look more closely at that right graphic, you'll notice something interesting: if we treat the red line as "the x axis", then
 						the point where the function crosses our line is really just a root for the cubic function x(t) through a shifted "x-axis"... and
 						<a href="#extremities">we've already seen</a> how to calculate roots, so let's just run cubic root finding - and not even the complicated
-						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is only root, simplifying the code we need!
+						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is at most a single root in the interval
+						[0,1], simplifying the code we need!
 					</p>
 					<p>First, let's look at the function for x(t):</p>
 					<!--
@@ -5026,7 +5027,7 @@ foreach p in xcoord: p.x -= x
 t = getRoots(p[0], p[1], p[2], p[3])[0]
 
 // find our answer:
-y = curve.get(t).y</textarea
+if t in [0,1] y = curve.get(t).y</textarea
 								>
 							</td>
 						</tr>
diff --git a/docs/ja-JP/index.html b/docs/ja-JP/index.html
index 70e2d3e1..9852cdf0 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="2024-02-28T17:22:37+00:00" />
+		<meta property="og:updated_time" content="2024-06-19T17:18:55+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -5022,7 +5022,8 @@ mapped  = (x) = │                                1  2                       
 						Now, if you look more closely at that right graphic, you'll notice something interesting: if we treat the red line as "the x axis", then
 						the point where the function crosses our line is really just a root for the cubic function x(t) through a shifted "x-axis"... and
 						<a href="#extremities">we've already seen</a> how to calculate roots, so let's just run cubic root finding - and not even the complicated
-						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is only root, simplifying the code we need!
+						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is at most a single root in the interval
+						[0,1], simplifying the code we need!
 					</p>
 					<p>First, let's look at the function for x(t):</p>
 					<!--
@@ -5071,7 +5072,7 @@ foreach p in xcoord: p.x -= x
 t = getRoots(p[0], p[1], p[2], p[3])[0]
 
 // find our answer:
-y = curve.get(t).y</textarea
+if t in [0,1] y = curve.get(t).y</textarea
 								>
 							</td>
 						</tr>
diff --git a/docs/ko-KR/index.html b/docs/ko-KR/index.html
index aa6ba701..ec55a0f9 100644
--- a/docs/ko-KR/index.html
+++ b/docs/ko-KR/index.html
@@ -43,7 +43,7 @@
 		<meta property="og:locale" content="ko-KR" />
 		<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="2024-02-28T17:22:37+00:00" />
+		<meta property="og:updated_time" content="2024-06-19T17:18:55+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -5163,7 +5163,8 @@ mapped  = (x) = │                                1  2                       
 						Now, if you look more closely at that right graphic, you'll notice something interesting: if we treat the red line as "the x axis", then
 						the point where the function crosses our line is really just a root for the cubic function x(t) through a shifted "x-axis"... and
 						<a href="#extremities">we've already seen</a> how to calculate roots, so let's just run cubic root finding - and not even the complicated
-						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is only root, simplifying the code we need!
+						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is at most a single root in the interval
+						[0,1], simplifying the code we need!
 					</p>
 					<p>First, let's look at the function for x(t):</p>
 					<!--
@@ -5212,7 +5213,7 @@ foreach p in xcoord: p.x -= x
 t = getRoots(p[0], p[1], p[2], p[3])[0]
 
 // find our answer:
-y = curve.get(t).y</textarea
+if t in [0,1] y = curve.get(t).y</textarea
 								>
 							</td>
 						</tr>
diff --git a/docs/news/2020-09-18.html b/docs/news/2020-09-18.html
index e8612606..a1324b60 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="Wed Feb 28 2024 17:22:37 +00:00" />
+		<meta property="og:updated_time" content="Wed Jun 19 2024 17:18:55 +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 9a4a5fa1..75501ac6 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="Wed Feb 28 2024 17:22:37 +00:00" />
+		<meta property="og:updated_time" content="Wed Jun 19 2024 17:18:55 +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 42f42c3b..a05a664a 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="Wed Feb 28 2024 17:22:37 GMT+0000 (Coordinated Universal Time)" />
+		<meta property="og:published_time" content="Wed Jun 19 2024 17:18:55 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 9233e0c4..b4ab66d3 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>Wed Feb 28 2024 17:22:37 +00:00</lastBuildDate>
+  <lastBuildDate>Wed Jun 19 2024 17:18:55 +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 5c31124e..bcb78eed 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="2024-02-28T17:22:37+00:00" />
+		<meta property="og:updated_time" content="2024-06-19T17:18:55+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -5229,7 +5229,8 @@ mapped  = (x) = │                                1  2                       
 						Now, if you look more closely at that right graphic, you'll notice something interesting: if we treat the red line as "the x axis", then
 						the point where the function crosses our line is really just a root for the cubic function x(t) through a shifted "x-axis"... and
 						<a href="#extremities">we've already seen</a> how to calculate roots, so let's just run cubic root finding - and not even the complicated
-						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is only root, simplifying the code we need!
+						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is at most a single root in the interval
+						[0,1], simplifying the code we need!
 					</p>
 					<p>First, let's look at the function for x(t):</p>
 					<!--
@@ -5278,7 +5279,7 @@ foreach p in xcoord: p.x -= x
 t = getRoots(p[0], p[1], p[2], p[3])[0]
 
 // find our answer:
-y = curve.get(t).y</textarea
+if t in [0,1] y = curve.get(t).y</textarea
 								>
 							</td>
 						</tr>
diff --git a/docs/uk-UA/index.html b/docs/uk-UA/index.html
index 920b03d3..2f061d19 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="2024-02-28T17:22:37+00:00" />
+		<meta property="og:updated_time" content="2024-06-19T17:18:55+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -5193,7 +5193,8 @@ mapped  = (x) = │                                1  2                       
 						Now, if you look more closely at that right graphic, you'll notice something interesting: if we treat the red line as "the x axis", then
 						the point where the function crosses our line is really just a root for the cubic function x(t) through a shifted "x-axis"... and
 						<a href="#extremities">we've already seen</a> how to calculate roots, so let's just run cubic root finding - and not even the complicated
-						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is only root, simplifying the code we need!
+						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is at most a single root in the interval
+						[0,1], simplifying the code we need!
 					</p>
 					<p>First, let's look at the function for x(t):</p>
 					<!--
@@ -5242,7 +5243,7 @@ foreach p in xcoord: p.x -= x
 t = getRoots(p[0], p[1], p[2], p[3])[0]
 
 // find our answer:
-y = curve.get(t).y</textarea
+if t in [0,1] y = curve.get(t).y</textarea
 								>
 							</td>
 						</tr>
diff --git a/docs/zh-CN/index.html b/docs/zh-CN/index.html
index fd0e437c..ae6b0249 100644
--- a/docs/zh-CN/index.html
+++ b/docs/zh-CN/index.html
@@ -35,7 +35,7 @@
 		<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="2024-02-28T17:22:37+00:00" />
+		<meta property="og:updated_time" content="2024-06-19T17:18:55+00:00" />
 		<meta property="og:author" content="Mike 'Pomax' Kamermans" />
 		<meta property="og:section" content="Bézier Curves" />
 		<meta property="og:tag" content="Bézier Curves" />
@@ -4504,7 +4504,8 @@ mapped  = (x) = │                                1  2                       
 						Now, if you look more closely at that right graphic, you'll notice something interesting: if we treat the red line as "the x axis", then
 						the point where the function crosses our line is really just a root for the cubic function x(t) through a shifted "x-axis"... and
 						<a href="#extremities">we've already seen</a> how to calculate roots, so let's just run cubic root finding - and not even the complicated
-						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is only root, simplifying the code we need!
+						cubic case either: because of the kind of curve we're starting with, we <em>know</em> there is at most a single root in the interval
+						[0,1], simplifying the code we need!
 					</p>
 					<p>First, let's look at the function for x(t):</p>
 					<!--
@@ -4553,7 +4554,7 @@ foreach p in xcoord: p.x -= x
 t = getRoots(p[0], p[1], p[2], p[3])[0]
 
 // find our answer:
-y = curve.get(t).y</textarea
+if t in [0,1] y = curve.get(t).y</textarea
 								>
 							</td>
 						</tr>