diff --git a/docs/src/geometry/api/g/Polyline/prototype/simplify.html b/docs/src/geometry/api/g/Polyline/prototype/simplify.html
index 3232a4958..30d2af322 100644
--- a/docs/src/geometry/api/g/Polyline/prototype/simplify.html
+++ b/docs/src/geometry/api/g/Polyline/prototype/simplify.html
@@ -3,4 +3,4 @@
 
 <p>This function modifies the original polyline and returns self. If the polyline has fewer than 3 points, the polyline is not modified.</p>
 
-<p>By default, a point is considered non-essential only if it lies directly on the connection line between the previous and the following point. You can specify a tolerance range by providing a <code>threshold</code> value within the <code>opt</code> object. Polyline points that are closer to the connection line than this value (inclusive) are removed; points that are farther from the connection line (exclusive) are kept.</p>
+<p>By default, a point is considered non-essential only if it lies directly on the connection line between the previous and the following point. You can specify a tolerance range by providing a <code>threshold</code> value within the <code>opt</code> object (the default is <code>1e-10</code>). Polyline points that are closer to the connection line than this value (inclusive) are removed; points that are farther from the connection line (exclusive) are kept.</p>
diff --git a/src/g/polyline.mjs b/src/g/polyline.mjs
index 4dbdc17b3..430690935 100644
--- a/src/g/polyline.mjs
+++ b/src/g/polyline.mjs
@@ -351,7 +351,10 @@ Polyline.prototype = {
         if (points.length < 3) return this; // we need at least 3 points
 
         // TODO: we may also accept startIndex and endIndex to specify where to start and end simplification
-        const threshold = opt.threshold || 0; // = max distance of middle point from chord to be simplified
+
+        // Due to the nature of the algorithm, we do not use 0 as the default value for `threshold`
+        // because of the rounding errors that can occur when comparing distances.
+        const threshold = opt.threshold || 1e-10; // = max distance of middle point from chord to be simplified
 
         // start at the beginning of the polyline and go forward
         let currentIndex = 0;
diff --git a/test/geometry/polyline.js b/test/geometry/polyline.js
index 9202827fe..ffc6b60cc 100644
--- a/test/geometry/polyline.js
+++ b/test/geometry/polyline.js
@@ -1041,6 +1041,8 @@ QUnit.module('polyline', function() {
                 assert.equal((new g.Polyline(['10 0'])).simplify().serialize(), '10,0');
                 assert.equal((new g.Polyline('10,0')).simplify().serialize(), '10,0');
 
+                assert.equal((new g.Polyline(['210 740', '250 740', '570 740'])).simplify().serialize(), '210,740 570,740');
+
                 assert.equal((new g.Polyline()).simplify().serialize(), '');
             });