diff --git a/src/sage/plot/hyperbolic_arc.py b/src/sage/plot/hyperbolic_arc.py
index 1e658fc84d5..11ab9e85277 100644
--- a/src/sage/plot/hyperbolic_arc.py
+++ b/src/sage/plot/hyperbolic_arc.py
@@ -7,6 +7,7 @@
 """
 #*****************************************************************************
 #       Copyright (C) 2011 Hartmut Monien <monien@th.physik.uni-bonn.de>,
+#                     2015 Stefan Kraemer <skraemer@th.physik.uni-bonn.de>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #
@@ -70,7 +71,7 @@ def _hyperbolic_arc(self, z0, z3, first=False):
         the hyperbolic arc between the complex numbers z0 and z3 in the
         hyperbolic plane.
         """
-        if (z0-z3).real() == 0:
+        if abs((z0-z3).real()) < 10.**(-3):
             self.path.append([(z0.real(),z0.imag()), (z3.real(),z3.imag())])
             return
         z0, z3 = (CC(z0), CC(z3))
diff --git a/src/sage/plot/hyperbolic_polygon.py b/src/sage/plot/hyperbolic_polygon.py
index e6465183e04..7bc97f336ca 100644
--- a/src/sage/plot/hyperbolic_polygon.py
+++ b/src/sage/plot/hyperbolic_polygon.py
@@ -8,7 +8,8 @@
 """
 #*****************************************************************************
 #       Copyright (C) 2011 Hartmut Monien <monien@th.physik.uni-bonn.de>,
-#                     2014 Vincent Delecroix <20100.delecroix@gmail.com>
+#                     2014 Vincent Delecroix <20100.delecroix@gmail.com>,
+#                     2015 Stefan Kraemer <skraemer@th.physik.uni-bonn.de>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #
@@ -85,7 +86,7 @@ def _hyperbolic_arc(self, z0, z3, first=False):
         the hyperbolic arc between the complex numbers z0 and z3 in the
         hyperbolic plane.
         """
-        if (z0-z3).real() == 0:
+        if abs((z0-z3).real()) < 10.**(-3):
             self.path.append([(z0.real(), z0.imag()), (z3.real(), z3.imag())])
             return
         z0, z3 = (CC(z0), CC(z3))