diff --git a/src/arc.scad b/src/arc.scad
index 171d9baa..19e21478 100644
--- a/src/arc.scad
+++ b/src/arc.scad
@@ -47,9 +47,9 @@ module arc(radius, angle, width, width_mode = "LINE_CROSS") {
         // outer arc path
         [__ra_to_xy(edge_r_begin(r_outer, angles[0]), angles[0])],
         m >= n ? [] : [for(i = [m:n]) __ra_to_xy(r_outer, a_step * i)],
-        [__ra_to_xy(edge_r_end(r_outer, angles[1]), angles[1])],
+        angles[1] == a_step * n ? [] : [__ra_to_xy(edge_r_end(r_outer, angles[1]), angles[1])],
         // inner arc path
-        [__ra_to_xy(edge_r_end(r_inner, angles[1]), angles[1])],
+        angles[1] == a_step * n ? [] : [__ra_to_xy(edge_r_end(r_inner, angles[1]), angles[1])],
         m >= n ? [] : [
             for(i = [m:n]) 
                 let(idx = (n + (m - i)))
diff --git a/src/pie.scad b/src/pie.scad
index 27d3ae64..5477a60c 100644
--- a/src/pie.scad
+++ b/src/pie.scad
@@ -35,7 +35,7 @@ module pie(radius, angle) {
     points = concat(
         [[0, 0], __ra_to_xy(edge_r_begin(angles[0]), angles[0])],
         m >= n ? [] : [for(i = [m:n]) __ra_to_xy(radius, a_step * i)],
-        [__ra_to_xy(edge_r_end(angles[1]), angles[1])]
+        angles[1] == a_step * n ? [] : [__ra_to_xy(edge_r_end(angles[1]), angles[1])]
     );
 
     polygon(points);