diff --git a/doc/api/axis_api.rst b/doc/api/axis_api.rst
index afea7afff682..56a2ea6d4ce9 100644
--- a/doc/api/axis_api.rst
+++ b/doc/api/axis_api.rst
@@ -109,8 +109,8 @@ Ticks, tick labels and Offset text
    Axis.axis_date
 
 
-Data and view internvals
-------------------------
+Data and view intervals
+-----------------------
 
 .. autosummary::
    :toctree: _as_gen
diff --git a/examples/animation/unchained.py b/examples/animation/unchained.py
index d4f164b2263f..faa2cf0a29c1 100644
--- a/examples/animation/unchained.py
+++ b/examples/animation/unchained.py
@@ -25,7 +25,7 @@
 # Generate random data
 data = np.random.uniform(0, 1, (64, 75))
 X = np.linspace(-1, 1, data.shape[-1])
-G = 1.5 * np.exp(-4 * X * X)
+G = 1.5 * np.exp(-4 * X ** 2)
 
 # Generate line plots
 lines = []
diff --git a/examples/api/custom_projection_example.py b/examples/api/custom_projection_example.py
index 1747027146ba..588b572441af 100644
--- a/examples/api/custom_projection_example.py
+++ b/examples/api/custom_projection_example.py
@@ -434,15 +434,11 @@ def __init__(self, resolution):
             self._resolution = resolution
 
         def transform_non_affine(self, xy):
-            x = xy[:, 0:1]
-            y = xy[:, 1:2]
-
-            quarter_x = 0.25 * x
-            half_y = 0.5 * y
-            z = np.sqrt(1.0 - quarter_x*quarter_x - half_y*half_y)
-            longitude = 2 * np.arctan((z*x) / (2.0 * (2.0*z*z - 1.0)))
+            x, y = xy.T
+            z = np.sqrt(1 - (x / 4) ** 2 - (y / 2) ** 2)
+            longitude = 2 * np.arctan((z * x) / (2 * (2 * z ** 2 - 1)))
             latitude = np.arcsin(y*z)
-            return np.concatenate((longitude, latitude), 1)
+            return np.column_stack([longitude, latitude])
         transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
 
         def inverted(self):
diff --git a/examples/api/scatter_piecharts.py b/examples/api/scatter_piecharts.py
index 8d401ec497c3..6e03994e6de8 100644
--- a/examples/api/scatter_piecharts.py
+++ b/examples/api/scatter_piecharts.py
@@ -7,7 +7,7 @@
 
 Thanks to Manuel Metz for the example
 """
-import math
+
 import numpy as np
 import matplotlib.pyplot as plt
 
@@ -16,35 +16,33 @@
 r2 = r1 + 0.4  # 40%
 
 # define some sizes of the scatter marker
-sizes = [60, 80, 120]
+sizes = np.array([60, 80, 120])
 
 # calculate the points of the first pie marker
 #
 # these are just the origin (0,0) +
 # some points on a circle cos,sin
-x = [0] + np.cos(np.linspace(0, 2*math.pi*r1, 10)).tolist()
-y = [0] + np.sin(np.linspace(0, 2*math.pi*r1, 10)).tolist()
-
+x = [0] + np.cos(np.linspace(0, 2 * np.pi * r1, 10)).tolist()
+y = [0] + np.sin(np.linspace(0, 2 * np.pi * r1, 10)).tolist()
 xy1 = list(zip(x, y))
-s1 = max(max(x), max(y))
+s1 = np.max(xy1)
 
-# ...
-x = [0] + np.cos(np.linspace(2*math.pi*r1, 2*math.pi*r2, 10)).tolist()
-y = [0] + np.sin(np.linspace(2*math.pi*r1, 2*math.pi*r2, 10)).tolist()
+x = [0] + np.cos(np.linspace(2 * np.pi * r1, 2 * np.pi * r2, 10)).tolist()
+y = [0] + np.sin(np.linspace(2 * np.pi * r1, 2 * np.pi * r2, 10)).tolist()
 xy2 = list(zip(x, y))
-s2 = max(max(x), max(y))
+s2 = np.max(xy2)
 
-x = [0] + np.cos(np.linspace(2*math.pi*r2, 2*math.pi, 10)).tolist()
-y = [0] + np.sin(np.linspace(2*math.pi*r2, 2*math.pi, 10)).tolist()
+x = [0] + np.cos(np.linspace(2 * np.pi * r2, 2 * np.pi, 10)).tolist()
+y = [0] + np.sin(np.linspace(2 * np.pi * r2, 2 * np.pi, 10)).tolist()
 xy3 = list(zip(x, y))
-s3 = max(max(x), max(y))
+s3 = np.max(xy3)
 
 fig, ax = plt.subplots()
-ax.scatter(np.arange(3), np.arange(3), marker=(xy1, 0),
-           s=[s1*s1*_ for _ in sizes], facecolor='blue')
-ax.scatter(np.arange(3), np.arange(3), marker=(xy2, 0),
-           s=[s2*s2*_ for _ in sizes], facecolor='green')
-ax.scatter(np.arange(3), np.arange(3), marker=(xy3, 0),
-           s=[s3*s3*_ for _ in sizes], facecolor='red')
+ax.scatter(range(3), range(3), marker=(xy1, 0),
+           s=s1 ** 2 * sizes, facecolor='blue')
+ax.scatter(range(3), range(3), marker=(xy2, 0),
+           s=s2 ** 2 * sizes, facecolor='green')
+ax.scatter(range(3), range(3), marker=(xy3, 0),
+           s=s3 ** 2 * sizes, facecolor='red')
 
 plt.show()
diff --git a/examples/event_handling/timers.py b/examples/event_handling/timers.py
index b9b82ee8c179..aba9393699dd 100644
--- a/examples/event_handling/timers.py
+++ b/examples/event_handling/timers.py
@@ -18,7 +18,7 @@ def update_title(axes):
 fig, ax = plt.subplots()
 
 x = np.linspace(-3, 3)
-ax.plot(x, x*x)
+ax.plot(x, x ** 2)
 
 # Create a new timer object. Set the interval to 100 milliseconds
 # (1000 is default) and tell the timer what function should be called.
diff --git a/examples/event_handling/trifinder_event_demo.py b/examples/event_handling/trifinder_event_demo.py
index 4232e96a5e73..7d21e8da43cc 100644
--- a/examples/event_handling/trifinder_event_demo.py
+++ b/examples/event_handling/trifinder_event_demo.py
@@ -11,16 +11,15 @@
 from matplotlib.tri import Triangulation
 from matplotlib.patches import Polygon
 import numpy as np
-import math
 
 
 def update_polygon(tri):
     if tri == -1:
         points = [0, 0, 0]
     else:
-        points = triangulation.triangles[tri]
-    xs = triangulation.x[points]
-    ys = triangulation.y[points]
+        points = triang.triangles[tri]
+    xs = triang.x[points]
+    ys = triang.y[points]
     polygon.set_xy(list(zip(xs, ys)))
 
 
@@ -39,23 +38,22 @@ def motion_notify(event):
 n_radii = 5
 min_radius = 0.25
 radii = np.linspace(min_radius, 0.95, n_radii)
-angles = np.linspace(0, 2*math.pi, n_angles, endpoint=False)
+angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
 angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
-angles[:, 1::2] += math.pi / n_angles
+angles[:, 1::2] += np.pi / n_angles
 x = (radii*np.cos(angles)).flatten()
 y = (radii*np.sin(angles)).flatten()
-triangulation = Triangulation(x, y)
-xmid = x[triangulation.triangles].mean(axis=1)
-ymid = y[triangulation.triangles].mean(axis=1)
-mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)
-triangulation.set_mask(mask)
+triang = Triangulation(x, y)
+triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+                         y[triang.triangles].mean(axis=1))
+                < min_radius)
 
 # Use the triangulation's default TriFinder object.
-trifinder = triangulation.get_trifinder()
+trifinder = triang.get_trifinder()
 
 # Setup plot and callbacks.
 plt.subplot(111, aspect='equal')
-plt.triplot(triangulation, 'bo-')
+plt.triplot(triang, 'bo-')
 polygon = Polygon([[0, 0], [0, 0]], facecolor='y')  # dummy data for xs,ys
 update_polygon(-1)
 plt.gca().add_patch(polygon)
diff --git a/examples/images_contours_and_fields/tricontour_demo.py b/examples/images_contours_and_fields/tricontour_demo.py
index bcd6d9b9abf2..47f8f74411ed 100644
--- a/examples/images_contours_and_fields/tricontour_demo.py
+++ b/examples/images_contours_and_fields/tricontour_demo.py
@@ -8,7 +8,6 @@
 import matplotlib.pyplot as plt
 import matplotlib.tri as tri
 import numpy as np
-import math
 
 ###############################################################################
 # Creating a Triangulation without specifying the triangles results in the
@@ -20,22 +19,21 @@
 min_radius = 0.25
 radii = np.linspace(min_radius, 0.95, n_radii)
 
-angles = np.linspace(0, 2 * math.pi, n_angles, endpoint=False)
+angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
 angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
-angles[:, 1::2] += math.pi / n_angles
+angles[:, 1::2] += np.pi / n_angles
 
 x = (radii * np.cos(angles)).flatten()
 y = (radii * np.sin(angles)).flatten()
-z = (np.cos(radii) * np.cos(angles * 3.0)).flatten()
+z = (np.cos(radii) * np.cos(3 * angles)).flatten()
 
 # Create the Triangulation; no triangles so Delaunay triangulation created.
 triang = tri.Triangulation(x, y)
 
 # Mask off unwanted triangles.
-xmid = x[triang.triangles].mean(axis=1)
-ymid = y[triang.triangles].mean(axis=1)
-mask = np.where(xmid * xmid + ymid * ymid < min_radius * min_radius, 1, 0)
-triang.set_mask(mask)
+triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+                         y[triang.triangles].mean(axis=1))
+                < min_radius)
 
 ###############################################################################
 # pcolor plot.
diff --git a/examples/images_contours_and_fields/tricontour_smooth_user.py b/examples/images_contours_and_fields/tricontour_smooth_user.py
index 2523fc18d7e7..b51bcb0596cd 100644
--- a/examples/images_contours_and_fields/tricontour_smooth_user.py
+++ b/examples/images_contours_and_fields/tricontour_smooth_user.py
@@ -10,7 +10,6 @@
 import matplotlib.pyplot as plt
 import matplotlib.cm as cm
 import numpy as np
-import math
 
 
 #-----------------------------------------------------------------------------
@@ -36,9 +35,9 @@ def function_z(x, y):
 min_radius = 0.15
 radii = np.linspace(min_radius, 0.95, n_radii)
 
-angles = np.linspace(0, 2 * math.pi, n_angles, endpoint=False)
+angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
 angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
-angles[:, 1::2] += math.pi / n_angles
+angles[:, 1::2] += np.pi / n_angles
 
 x = (radii * np.cos(angles)).flatten()
 y = (radii * np.sin(angles)).flatten()
@@ -50,10 +49,9 @@ def function_z(x, y):
 triang = tri.Triangulation(x, y)
 
 # Mask off unwanted triangles.
-xmid = x[triang.triangles].mean(axis=1)
-ymid = y[triang.triangles].mean(axis=1)
-mask = np.where(xmid * xmid + ymid * ymid < min_radius * min_radius, 1, 0)
-triang.set_mask(mask)
+triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+                         y[triang.triangles].mean(axis=1))
+                < min_radius)
 
 #-----------------------------------------------------------------------------
 # Refine data
diff --git a/examples/images_contours_and_fields/trigradient_demo.py b/examples/images_contours_and_fields/trigradient_demo.py
index 9470c51126d7..911b49402762 100644
--- a/examples/images_contours_and_fields/trigradient_demo.py
+++ b/examples/images_contours_and_fields/trigradient_demo.py
@@ -5,12 +5,11 @@
 
 Demonstrates computation of gradient with matplotlib.tri.CubicTriInterpolator.
 """
-from matplotlib.tri import Triangulation, UniformTriRefiner,\
-    CubicTriInterpolator
+from matplotlib.tri import (
+    Triangulation, UniformTriRefiner, CubicTriInterpolator)
 import matplotlib.pyplot as plt
 import matplotlib.cm as cm
 import numpy as np
-import math
 
 
 #-----------------------------------------------------------------------------
@@ -33,9 +32,9 @@ def dipole_potential(x, y):
 min_radius = 0.2
 radii = np.linspace(min_radius, 0.95, n_radii)
 
-angles = np.linspace(0, 2*math.pi, n_angles, endpoint=False)
+angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
 angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
-angles[:, 1::2] += math.pi/n_angles
+angles[:, 1::2] += np.pi / n_angles
 
 x = (radii*np.cos(angles)).flatten()
 y = (radii*np.sin(angles)).flatten()
@@ -46,10 +45,9 @@ def dipole_potential(x, y):
 triang = Triangulation(x, y)
 
 # Mask off unwanted triangles.
-xmid = x[triang.triangles].mean(axis=1)
-ymid = y[triang.triangles].mean(axis=1)
-mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)
-triang.set_mask(mask)
+triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+                         y[triang.triangles].mean(axis=1))
+                < min_radius)
 
 #-----------------------------------------------------------------------------
 # Refine data - interpolates the electrical potential V
diff --git a/examples/images_contours_and_fields/tripcolor_demo.py b/examples/images_contours_and_fields/tripcolor_demo.py
index d2f95a99f2fe..8c885744895d 100644
--- a/examples/images_contours_and_fields/tripcolor_demo.py
+++ b/examples/images_contours_and_fields/tripcolor_demo.py
@@ -8,7 +8,6 @@
 import matplotlib.pyplot as plt
 import matplotlib.tri as tri
 import numpy as np
-import math
 
 ###############################################################################
 # Creating a Triangulation without specifying the triangles results in the
@@ -20,22 +19,21 @@
 min_radius = 0.25
 radii = np.linspace(min_radius, 0.95, n_radii)
 
-angles = np.linspace(0, 2 * math.pi, n_angles, endpoint=False)
+angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
 angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
-angles[:, 1::2] += math.pi / n_angles
+angles[:, 1::2] += np.pi / n_angles
 
 x = (radii * np.cos(angles)).flatten()
 y = (radii * np.sin(angles)).flatten()
-z = (np.cos(radii) * np.cos(angles * 3.0)).flatten()
+z = (np.cos(radii) * np.cos(3 * angles)).flatten()
 
 # Create the Triangulation; no triangles so Delaunay triangulation created.
 triang = tri.Triangulation(x, y)
 
 # Mask off unwanted triangles.
-xmid = x[triang.triangles].mean(axis=1)
-ymid = y[triang.triangles].mean(axis=1)
-mask = np.where(xmid * xmid + ymid * ymid < min_radius * min_radius, 1, 0)
-triang.set_mask(mask)
+triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+                         y[triang.triangles].mean(axis=1))
+                < min_radius)
 
 ###############################################################################
 # tripcolor plot.
diff --git a/examples/images_contours_and_fields/triplot_demo.py b/examples/images_contours_and_fields/triplot_demo.py
index b160026e899d..d3a65762d021 100644
--- a/examples/images_contours_and_fields/triplot_demo.py
+++ b/examples/images_contours_and_fields/triplot_demo.py
@@ -8,7 +8,6 @@
 import matplotlib.pyplot as plt
 import matplotlib.tri as tri
 import numpy as np
-import math
 
 ###############################################################################
 # Creating a Triangulation without specifying the triangles results in the
@@ -20,9 +19,9 @@
 min_radius = 0.25
 radii = np.linspace(min_radius, 0.95, n_radii)
 
-angles = np.linspace(0, 2 * math.pi, n_angles, endpoint=False)
+angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
 angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
-angles[:, 1::2] += math.pi / n_angles
+angles[:, 1::2] += np.pi / n_angles
 
 x = (radii * np.cos(angles)).flatten()
 y = (radii * np.sin(angles)).flatten()
@@ -31,10 +30,9 @@
 triang = tri.Triangulation(x, y)
 
 # Mask off unwanted triangles.
-xmid = x[triang.triangles].mean(axis=1)
-ymid = y[triang.triangles].mean(axis=1)
-mask = np.where(xmid * xmid + ymid * ymid < min_radius * min_radius, 1, 0)
-triang.set_mask(mask)
+triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+                         y[triang.triangles].mean(axis=1))
+                < min_radius)
 
 ###############################################################################
 # Plot the triangulation.
diff --git a/examples/lines_bars_and_markers/nan_test.py b/examples/lines_bars_and_markers/nan_test.py
index ad7cd6b5698c..4216f6960ae0 100644
--- a/examples/lines_bars_and_markers/nan_test.py
+++ b/examples/lines_bars_and_markers/nan_test.py
@@ -9,7 +9,7 @@
 import matplotlib.pyplot as plt
 
 t = np.arange(0.0, 1.0 + 0.01, 0.01)
-s = np.cos(2 * 2 * np.pi * t)
+s = np.cos(2 * 2*np.pi * t)
 t[41:60] = np.nan
 
 plt.subplot(2, 1, 1)
diff --git a/examples/misc/multipage_pdf.py b/examples/misc/multipage_pdf.py
index fd97409087f8..532d771849cb 100644
--- a/examples/misc/multipage_pdf.py
+++ b/examples/misc/multipage_pdf.py
@@ -35,7 +35,7 @@
 
     plt.rc('text', usetex=False)
     fig = plt.figure(figsize=(4, 5))
-    plt.plot(x, x*x, 'ko')
+    plt.plot(x, x ** 2, 'ko')
     plt.title('Page Three')
     pdf.savefig(fig)  # or you can pass a Figure object to pdf.savefig
     plt.close()
diff --git a/examples/misc/pythonic_matplotlib.py b/examples/misc/pythonic_matplotlib.py
index 41de00ca259b..07c6fa915a92 100644
--- a/examples/misc/pythonic_matplotlib.py
+++ b/examples/misc/pythonic_matplotlib.py
@@ -64,7 +64,7 @@
 fig = figure(1)
 
 ax1 = fig.add_subplot(211)
-ax1.plot(t, sin(2*pi*t))
+ax1.plot(t, sin(2*pi * t))
 ax1.grid(True)
 ax1.set_ylim((-2, 2))
 ax1.set_ylabel('1 Hz')
@@ -74,7 +74,7 @@
 
 
 ax2 = fig.add_subplot(212)
-ax2.plot(t, sin(2*2*pi*t))
+ax2.plot(t, sin(2 * 2*pi * t))
 ax2.grid(True)
 ax2.set_ylim((-2, 2))
 l = ax2.set_xlabel('Hi mom')
diff --git a/examples/misc/table_demo.py b/examples/misc/table_demo.py
index 6b29df44b755..cc23492d5536 100644
--- a/examples/misc/table_demo.py
+++ b/examples/misc/table_demo.py
@@ -29,7 +29,7 @@
 bar_width = 0.4
 
 # Initialize the vertical-offset for the stacked bar chart.
-y_offset = np.array([0.0] * len(columns))
+y_offset = np.zeros(len(columns))
 
 # Plot bars and create text labels for the table
 cell_text = []
diff --git a/examples/mplot3d/tricontour3d.py b/examples/mplot3d/tricontour3d.py
index f78ff63c8532..7e9e6971bb62 100644
--- a/examples/mplot3d/tricontour3d.py
+++ b/examples/mplot3d/tricontour3d.py
@@ -26,16 +26,15 @@
 
 x = (radii*np.cos(angles)).flatten()
 y = (radii*np.sin(angles)).flatten()
-z = (np.cos(radii)*np.cos(angles*3.0)).flatten()
+z = (np.cos(radii)*np.cos(3*angles)).flatten()
 
 # Create a custom triangulation.
 triang = tri.Triangulation(x, y)
 
 # Mask off unwanted triangles.
-xmid = x[triang.triangles].mean(axis=1)
-ymid = y[triang.triangles].mean(axis=1)
-mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)
-triang.set_mask(mask)
+triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+                         y[triang.triangles].mean(axis=1))
+                < min_radius)
 
 fig = plt.figure()
 ax = fig.gca(projection='3d')
diff --git a/examples/mplot3d/tricontourf3d.py b/examples/mplot3d/tricontourf3d.py
index 27513f2bd5cd..eebb3ef62e6a 100644
--- a/examples/mplot3d/tricontourf3d.py
+++ b/examples/mplot3d/tricontourf3d.py
@@ -27,16 +27,15 @@
 
 x = (radii*np.cos(angles)).flatten()
 y = (radii*np.sin(angles)).flatten()
-z = (np.cos(radii)*np.cos(angles*3.0)).flatten()
+z = (np.cos(radii)*np.cos(3*angles)).flatten()
 
 # Create a custom triangulation.
 triang = tri.Triangulation(x, y)
 
 # Mask off unwanted triangles.
-xmid = x[triang.triangles].mean(axis=1)
-ymid = y[triang.triangles].mean(axis=1)
-mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)
-triang.set_mask(mask)
+triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+                         y[triang.triangles].mean(axis=1))
+                < min_radius)
 
 fig = plt.figure()
 ax = fig.gca(projection='3d')
diff --git a/examples/mplot3d/trisurf3d_2.py b/examples/mplot3d/trisurf3d_2.py
index 3a6677c76c01..24d19e60b498 100644
--- a/examples/mplot3d/trisurf3d_2.py
+++ b/examples/mplot3d/trisurf3d_2.py
@@ -61,7 +61,7 @@
 # Map radius, angle pairs to x, y, z points.
 x = (radii*np.cos(angles)).flatten()
 y = (radii*np.sin(angles)).flatten()
-z = (np.cos(radii)*np.cos(angles*3.0)).flatten()
+z = (np.cos(radii)*np.cos(3*angles)).flatten()
 
 # Create the Triangulation; no triangles so Delaunay triangulation created.
 triang = mtri.Triangulation(x, y)
diff --git a/examples/pyplots/annotation_polar.py b/examples/pyplots/annotation_polar.py
index f3b032b7377a..129291aae167 100644
--- a/examples/pyplots/annotation_polar.py
+++ b/examples/pyplots/annotation_polar.py
@@ -10,7 +10,7 @@
 fig = plt.figure()
 ax = fig.add_subplot(111, polar=True)
 r = np.arange(0,1,0.001)
-theta = 2*2*np.pi*r
+theta = 2 * 2*np.pi * r
 line, = ax.plot(theta, r, color='#ee8d18', lw=3)
 
 ind = 800
diff --git a/examples/ticks_and_spines/date_demo_convert.py b/examples/ticks_and_spines/date_demo_convert.py
index 43621d00e1b8..e1f266cbe09b 100644
--- a/examples/ticks_and_spines/date_demo_convert.py
+++ b/examples/ticks_and_spines/date_demo_convert.py
@@ -7,17 +7,17 @@
 import datetime
 import matplotlib.pyplot as plt
 from matplotlib.dates import DayLocator, HourLocator, DateFormatter, drange
-from numpy import arange
+import numpy as np
 
 date1 = datetime.datetime(2000, 3, 2)
 date2 = datetime.datetime(2000, 3, 6)
 delta = datetime.timedelta(hours=6)
 dates = drange(date1, date2, delta)
 
-y = arange(len(dates) * 1.0)
+y = np.arange(len(dates))
 
 fig, ax = plt.subplots()
-ax.plot_date(dates, y * y)
+ax.plot_date(dates, y ** 2)
 
 # this is superfluous, since the autoscaler should get it right, but
 # use date2num and num2date to convert between dates and floats if
@@ -28,7 +28,7 @@
 # tick, not the base multiple
 
 ax.xaxis.set_major_locator(DayLocator())
-ax.xaxis.set_minor_locator(HourLocator(arange(0, 25, 6)))
+ax.xaxis.set_minor_locator(HourLocator(range(0, 25, 6)))
 ax.xaxis.set_major_formatter(DateFormatter('%Y-%m-%d'))
 
 ax.fmt_xdata = DateFormatter('%Y-%m-%d %H:%M:%S')
diff --git a/examples/units/basic_units.py b/examples/units/basic_units.py
index 6526e394a7c1..be07f0c9fce5 100644
--- a/examples/units/basic_units.py
+++ b/examples/units/basic_units.py
@@ -4,6 +4,8 @@
 ===========
 
 """
+import six
+
 import math
 
 import numpy as np
@@ -108,7 +110,7 @@ def __call__(self, *args):
         return TaggedValue(ret, ret_unit)
 
 
-class _TaggedValue(object):
+class TaggedValue(six.with_metaclass(TaggedValueMeta)):
 
     _proxies = {'__add__': ConvertAllProxy,
                 '__sub__': ConvertAllProxy,
@@ -140,18 +142,15 @@ def __init__(self, value, unit):
         self.proxy_target = self.value
 
     def __getattribute__(self, name):
-        if (name.startswith('__')):
+        if name.startswith('__'):
             return object.__getattribute__(self, name)
         variable = object.__getattribute__(self, 'value')
-        if (hasattr(variable, name) and name not in self.__class__.__dict__):
+        if hasattr(variable, name) and name not in self.__class__.__dict__:
             return getattr(variable, name)
         return object.__getattribute__(self, name)
 
-    def __array__(self, t=None, context=None):
-        if t is not None:
-            return np.asarray(self.value).astype(t)
-        else:
-            return np.asarray(self.value, 'O')
+    def __array__(self, dtype=object):
+        return np.asarray(self.value).astype(dtype)
 
     def __array_wrap__(self, array, context):
         return TaggedValue(array, self.unit)
@@ -166,23 +165,17 @@ def __len__(self):
         return len(self.value)
 
     def __iter__(self):
-        class IteratorProxy(object):
-            def __init__(self, iter, unit):
-                self.iter = iter
-                self.unit = unit
-
-            def __next__(self):
-                value = next(self.iter)
-                return TaggedValue(value, self.unit)
-            next = __next__  # for Python 2
-        return IteratorProxy(iter(self.value), self.unit)
+        # Return a generator expression rather than use `yield`, so that
+        # TypeError is raised by iter(self) if appropriate when checking for
+        # iterability.
+        return (TaggedValue(inner, self.unit) for inner in self.value)
 
     def get_compressed_copy(self, mask):
         new_value = np.ma.masked_array(self.value, mask=mask).compressed()
         return TaggedValue(new_value, self.unit)
 
     def convert_to(self, unit):
-        if (unit == self.unit or not unit):
+        if unit == self.unit or not unit:
             return self
         new_value = self.unit.convert_value_to(self.value, unit)
         return TaggedValue(new_value, unit)
@@ -194,9 +187,6 @@ def get_unit(self):
         return self.unit
 
 
-TaggedValue = TaggedValueMeta('TaggedValue', (_TaggedValue, ), {})
-
-
 class BasicUnit(object):
     def __init__(self, name, fullname=None):
         self.name = name
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index e2610703489d..15ba96030a89 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -2,9 +2,10 @@
                         unicode_literals)
 
 import six
-from six.moves import reduce, xrange, zip, zip_longest
+from six.moves import xrange, zip, zip_longest
 
 from collections import Sized
+import functools
 import itertools
 import math
 import warnings
@@ -16,14 +17,12 @@
 from matplotlib import _preprocess_data
 
 import matplotlib.cbook as cbook
-from matplotlib.cbook import (
-    mplDeprecation, STEP_LOOKUP_MAP, iterable, safe_first_element)
 import matplotlib.collections as mcoll
 import matplotlib.colors as mcolors
 import matplotlib.contour as mcontour
 import matplotlib.category as _  # <-registers a category unit converter
 import matplotlib.dates as _  # <-registers a date unit converter
-from matplotlib import docstring
+import matplotlib.docstring as docstring
 import matplotlib.image as mimage
 import matplotlib.legend as mlegend
 import matplotlib.lines as mlines
@@ -39,9 +38,10 @@
 import matplotlib.ticker as mticker
 import matplotlib.transforms as mtransforms
 import matplotlib.tri as mtri
+from matplotlib.cbook import (
+    _backports, mplDeprecation, STEP_LOOKUP_MAP, iterable, safe_first_element)
 from matplotlib.container import BarContainer, ErrorbarContainer, StemContainer
-from matplotlib.axes._base import _AxesBase
-from matplotlib.axes._base import _process_plot_format
+from matplotlib.axes._base import _AxesBase, _process_plot_format
 
 
 rcParams = matplotlib.rcParams
@@ -2002,20 +2002,11 @@ def bar(self, left, height, width=0.8, bottom=None, **kwargs):
         label = kwargs.pop('label', '')
         tick_labels = kwargs.pop('tick_label', None)
 
-        def make_iterable(x):
-            if not iterable(x):
-                return [x]
-            else:
-                return x
-
-        # make them safe to take len() of
         _left = left
-        left = make_iterable(left)
-        height = make_iterable(height)
-        width = make_iterable(width)
         _bottom = bottom
-        bottom = make_iterable(bottom)
-        linewidth = make_iterable(linewidth)
+        left, height, width, bottom = np.broadcast_arrays(
+            # Make args iterable too.
+            np.atleast_1d(left), height, width, bottom)
 
         adjust_ylim = False
         adjust_xlim = False
@@ -2027,11 +2018,7 @@ def make_iterable(x):
             if _bottom is None:
                 if self.get_yscale() == 'log':
                     adjust_ylim = True
-                bottom = [0]
-
-            nbars = len(left)
-            if len(bottom) == 1:
-                bottom *= nbars
+                bottom = np.zeros_like(bottom)
 
             tick_label_axis = self.xaxis
             tick_label_position = left
@@ -2043,54 +2030,23 @@ def make_iterable(x):
             if _left is None:
                 if self.get_xscale() == 'log':
                     adjust_xlim = True
-                left = [0]
-
-            nbars = len(bottom)
-            if len(left) == 1:
-                left *= nbars
+                left = np.zeros_like(left)
 
             tick_label_axis = self.yaxis
             tick_label_position = bottom
         else:
             raise ValueError('invalid orientation: %s' % orientation)
 
-        if len(height) == 1:
-            height *= nbars
-        if len(width) == 1:
-            width *= nbars
-        if len(linewidth) < nbars:
-            linewidth *= nbars
-
-        color = list(mcolors.to_rgba_array(color))
-        if len(color) == 0:  # until to_rgba_array is changed
-            color = [[0, 0, 0, 0]]
-        if len(color) < nbars:
-            color *= nbars
-
+        linewidth = itertools.cycle(np.atleast_1d(linewidth))
+        color = itertools.chain(itertools.cycle(mcolors.to_rgba_array(color)),
+                                # Fallback if color == "none".
+                                itertools.repeat([0, 0, 0, 0]))
         if edgecolor is None:
-            edgecolor = [None] * nbars
+            edgecolor = itertools.repeat(None)
         else:
-            edgecolor = list(mcolors.to_rgba_array(edgecolor))
-            if len(edgecolor) == 0:     # until to_rgba_array is changed
-                edgecolor = [[0, 0, 0, 0]]
-            if len(edgecolor) < nbars:
-                edgecolor *= nbars
-
-        # input validation
-        if len(left) != nbars:
-            raise ValueError("incompatible sizes: argument 'left' must "
-                             "be length %d or scalar" % nbars)
-        if len(height) != nbars:
-            raise ValueError("incompatible sizes: argument 'height' "
-                             "must be length %d or scalar" % nbars)
-        if len(width) != nbars:
-            raise ValueError("incompatible sizes: argument 'width' "
-                             "must be length %d or scalar" % nbars)
-        if len(bottom) != nbars:
-            raise ValueError("incompatible sizes: argument 'bottom' "
-                             "must be length %d or scalar" % nbars)
-
-        patches = []
+            edgecolor = itertools.chain(mcolors.to_rgba_array(edgecolor),
+                                        # Fallback if edgecolor == "none".
+                                        itertools.repeat([0, 0, 0, 0]))
 
         # lets do some conversions now since some types cannot be
         # subtracted uniformly
@@ -2108,13 +2064,14 @@ def make_iterable(x):
 
         if align == 'center':
             if orientation == 'vertical':
-                left = [l - w / 2. for l, w in zip(left, width)]
+                left = left - width / 2
             elif orientation == 'horizontal':
-                bottom = [b - h / 2. for b, h in zip(bottom, height)]
+                bottom = bottom - height / 2
 
         elif align != 'edge':
             raise ValueError('invalid alignment: %s' % align)
 
+        patches = []
         args = zip(left, bottom, width, height, color, edgecolor, linewidth)
         for l, b, w, h, c, e, lw in args:
             r = mpatches.Rectangle(
@@ -2179,15 +2136,7 @@ def make_iterable(x):
         self.add_container(bar_container)
 
         if tick_labels is not None:
-            tick_labels = make_iterable(tick_labels)
-            if isinstance(tick_labels, six.string_types):
-                tick_labels = [tick_labels]
-            if len(tick_labels) == 1:
-                tick_labels *= nbars
-            if len(tick_labels) != nbars:
-                raise ValueError("incompatible sizes: argument 'tick_label' "
-                                 "must be length %d or string" % nbars)
-
+            tick_labels = _backports.broadcast_to(tick_labels, len(patches))
             tick_label_axis.set_ticks(tick_label_position)
             tick_label_axis.set_ticklabels(tick_labels)
 
@@ -2613,7 +2562,7 @@ def get_next_color():
         for frac, label, expl in zip(x, labels, explode):
             x, y = center
             theta2 = (theta1 + frac) if counterclock else (theta1 - frac)
-            thetam = 2 * math.pi * 0.5 * (theta1 + theta2)
+            thetam = 2 * np.pi * 0.5 * (theta1 + theta2)
             x += expl * math.cos(thetam)
             y += expl * math.sin(thetam)
 
@@ -4782,22 +4731,12 @@ def fill_between(self, x, y1, y2=0, where=None, interpolate=False,
                 raise ValueError('Input passed into argument "%r"' % name +
                                  'is not 1-dimensional.')
 
-        if y1.ndim == 0:
-            y1 = np.ones_like(x) * y1
-        if y2.ndim == 0:
-            y2 = np.ones_like(x) * y2
-
         if where is None:
-            where = np.ones(len(x), bool)
-        else:
-            where = np.asarray(where, bool)
-
-        if not (x.shape == y1.shape == y2.shape == where.shape):
-            raise ValueError("Argument dimensions are incompatible")
+            where = True
+        where = where & ~functools.reduce(np.logical_or,
+                                          map(np.ma.getmask, [x, y1, y2]))
 
-        mask = reduce(ma.mask_or, [ma.getmask(a) for a in (x, y1, y2)])
-        if mask is not ma.nomask:
-            where &= ~mask
+        x, y1, y2 = np.broadcast_arrays(np.atleast_1d(x), y1, y2)
 
         polys = []
         for ind0, ind1 in mlab.contiguous_regions(where):
@@ -4943,22 +4882,12 @@ def fill_betweenx(self, y, x1, x2=0, where=None,
                 raise ValueError('Input passed into argument "%r"' % name +
                                  'is not 1-dimensional.')
 
-        if x1.ndim == 0:
-            x1 = np.ones_like(y) * x1
-        if x2.ndim == 0:
-            x2 = np.ones_like(y) * x2
-
         if where is None:
-            where = np.ones(len(y), bool)
-        else:
-            where = np.asarray(where, bool)
-
-        if not (y.shape == x1.shape == x2.shape == where.shape):
-            raise ValueError("Argument dimensions are incompatible")
+            where = True
+        where = where & ~functools.reduce(np.logical_or,
+                                          map(np.ma.getmask, [y, x1, x2]))
 
-        mask = reduce(ma.mask_or, [ma.getmask(a) for a in (y, x1, x2)])
-        if mask is not ma.nomask:
-            where &= ~mask
+        y, x1, x2 = np.broadcast_arrays(np.atleast_1d(y), x1, x2)
 
         polys = []
         for ind0, ind1 in mlab.contiguous_regions(where):
@@ -6584,7 +6513,6 @@ def psd(self, x, NFFT=None, Fs=None, Fc=None, detrend=None,
         if logi == 0:
             logi = .1
         step = 10 * logi
-        #print vmin, vmax, step, intv, math.floor(vmin), math.ceil(vmax)+1
         ticks = np.arange(math.floor(vmin), math.ceil(vmax) + 1, step)
         self.set_yticks(ticks)
 
diff --git a/lib/matplotlib/backends/backend_agg.py b/lib/matplotlib/backends/backend_agg.py
index b8b0eca92b0c..7e88d4064e5c 100644
--- a/lib/matplotlib/backends/backend_agg.py
+++ b/lib/matplotlib/backends/backend_agg.py
@@ -190,7 +190,8 @@ def draw_text(self, gc, x, y, s, prop, angle, ismath=False, mtext=None):
         flags = get_hinting_flag()
         font = self._get_agg_font(prop)
 
-        if font is None: return None
+        if font is None:
+            return None
         if len(s) == 1 and ord(s) > 127:
             font.load_char(ord(s), flags=flags)
         else:
diff --git a/lib/matplotlib/backends/backend_qt5.py b/lib/matplotlib/backends/backend_qt5.py
index 9b924ce8ecb1..aae0da3e501e 100644
--- a/lib/matplotlib/backends/backend_qt5.py
+++ b/lib/matplotlib/backends/backend_qt5.py
@@ -648,8 +648,8 @@ def edit_parameters(self):
             QtWidgets.QMessageBox.warning(
                 self.parent, "Error", "There are no axes to edit.")
             return
-        if len(allaxes) == 1:
-            axes = allaxes[0]
+        elif len(allaxes) == 1:
+            axes, = allaxes
         else:
             titles = []
             for axes in allaxes:
diff --git a/lib/matplotlib/backends/backend_wx.py b/lib/matplotlib/backends/backend_wx.py
index f7df0707e637..2ad0106ce64c 100644
--- a/lib/matplotlib/backends/backend_wx.py
+++ b/lib/matplotlib/backends/backend_wx.py
@@ -316,7 +316,7 @@ def draw_text(self, gc, x, y, s, prop, angle, ismath=False, mtext=None):
         if angle == 0.0:
             gfx_ctx.DrawText(s, x, y)
         else:
-            rads = angle / 180.0 * math.pi
+            rads = math.radians(angle)
             xo = h * math.sin(rads)
             yo = h * math.cos(rads)
             gfx_ctx.DrawRotatedText(s, x - xo, y - yo, rads)
diff --git a/lib/matplotlib/cbook/__init__.py b/lib/matplotlib/cbook/__init__.py
index 838081e33f66..f93f07beca97 100644
--- a/lib/matplotlib/cbook/__init__.py
+++ b/lib/matplotlib/cbook/__init__.py
@@ -11,7 +11,6 @@
 
 import six
 from six.moves import xrange, zip
-from itertools import repeat
 import collections
 import datetime
 import errno
@@ -19,6 +18,7 @@
 import glob
 import gzip
 import io
+from itertools import repeat
 import locale
 import numbers
 import os
@@ -1628,7 +1628,7 @@ def delete_masked_points(*args):
             except:  # Fixme: put in tuple of possible exceptions?
                 pass
     if len(masks):
-        mask = functools.reduce(np.logical_and, masks)
+        mask = np.logical_and.reduce(masks)
         igood = mask.nonzero()[0]
         if len(igood) < nrecs:
             for i, x in enumerate(margs):
@@ -1993,7 +1993,7 @@ def _reshape_2D(X, name):
     *name* is used to generate the error message for invalid inputs.
     """
     # Iterate over columns for ndarrays, over rows otherwise.
-    X = X.T if isinstance(X, np.ndarray) else np.asarray(X)
+    X = np.atleast_1d(X.T if isinstance(X, np.ndarray) else np.asarray(X))
     if X.ndim == 1 and X.dtype.type != np.object_:
         # 1D array of scalars: directly return it.
         return [X]
diff --git a/lib/matplotlib/colors.py b/lib/matplotlib/colors.py
index 4cef8be06b69..8a35c6617bef 100644
--- a/lib/matplotlib/colors.py
+++ b/lib/matplotlib/colors.py
@@ -58,10 +58,12 @@
 
 from __future__ import (absolute_import, division, print_function,
                         unicode_literals)
+
 import six
 from six.moves import zip
 
 from collections import Sized
+import itertools
 import re
 import warnings
 
@@ -793,25 +795,23 @@ def __init__(self, colors, name='from_list', N=None):
 
             the list will be extended by repetition.
         """
-        self.colors = colors
         self.monochrome = False  # True only if all colors in map are
                                  # identical; needed for contouring.
         if N is None:
-            N = len(self.colors)
+            self.colors = colors
+            N = len(colors)
         else:
-            if isinstance(self.colors, six.string_types):
-                self.colors = [self.colors] * N
+            if isinstance(colors, six.string_types):
+                self.colors = [colors] * N
                 self.monochrome = True
-            elif cbook.iterable(self.colors):
-                self.colors = list(self.colors)  # in case it was a tuple
-                if len(self.colors) == 1:
+            elif cbook.iterable(colors):
+                if len(colors) == 1:
                     self.monochrome = True
-                if len(self.colors) < N:
-                    self.colors = list(self.colors) * N
-                del(self.colors[N:])
+                self.colors = list(
+                    itertools.islice(itertools.cycle(colors), N))
             else:
                 try:
-                    gray = float(self.colors)
+                    gray = float(colors)
                 except TypeError:
                     pass
                 else:
diff --git a/lib/matplotlib/gridspec.py b/lib/matplotlib/gridspec.py
index c9779cf23dd1..999dbd8c2029 100644
--- a/lib/matplotlib/gridspec.py
+++ b/lib/matplotlib/gridspec.py
@@ -98,28 +98,24 @@ def get_grid_positions(self, fig):
         # calculate accumulated heights of columns
         cellH = totHeight / (nrows + hspace*(nrows-1))
         sepH = hspace * cellH
-
         if self._row_height_ratios is not None:
             netHeight = cellH * nrows
             tr = float(sum(self._row_height_ratios))
             cellHeights = [netHeight * r / tr for r in self._row_height_ratios]
         else:
             cellHeights = [cellH] * nrows
-
         sepHeights = [0] + ([sepH] * (nrows-1))
         cellHs = np.cumsum(np.column_stack([sepHeights, cellHeights]).flat)
 
         # calculate accumulated widths of rows
         cellW = totWidth/(ncols + wspace*(ncols-1))
         sepW = wspace*cellW
-
         if self._col_width_ratios is not None:
             netWidth = cellW * ncols
             tr = float(sum(self._col_width_ratios))
             cellWidths = [netWidth*r/tr for r in self._col_width_ratios]
         else:
             cellWidths = [cellW] * ncols
-
         sepWidths = [0] + ([sepW] * (ncols-1))
         cellWs = np.cumsum(np.column_stack([sepWidths, cellWidths]).flat)
 
diff --git a/lib/matplotlib/legend.py b/lib/matplotlib/legend.py
index 9d3a9ab46775..b9afbb6f3e7a 100644
--- a/lib/matplotlib/legend.py
+++ b/lib/matplotlib/legend.py
@@ -294,7 +294,7 @@ def __init__(self, parent, handles, labels,
             self._scatteryoffsets = np.array([3. / 8., 4. / 8., 2.5 / 8.])
         else:
             self._scatteryoffsets = np.asarray(scatteryoffsets)
-        reps = int(self.scatterpoints / len(self._scatteryoffsets)) + 1
+        reps = self.scatterpoints // len(self._scatteryoffsets) + 1
         self._scatteryoffsets = np.tile(self._scatteryoffsets,
                                         reps)[:self.scatterpoints]
 
diff --git a/lib/matplotlib/lines.py b/lib/matplotlib/lines.py
index 256e59c2eb2e..929082206049 100644
--- a/lib/matplotlib/lines.py
+++ b/lib/matplotlib/lines.py
@@ -665,20 +665,8 @@ def recache(self, always=False):
         else:
             y = self._y
 
-        if len(x) == 1 and len(y) > 1:
-            x = x * np.ones(y.shape, float)
-        if len(y) == 1 and len(x) > 1:
-            y = y * np.ones(x.shape, float)
-
-        if len(x) != len(y):
-            raise RuntimeError('xdata and ydata must be the same length')
-
-        self._xy = np.empty((len(x), 2), dtype=float)
-        self._xy[:, 0] = x
-        self._xy[:, 1] = y
-
-        self._x = self._xy[:, 0]  # just a view
-        self._y = self._xy[:, 1]  # just a view
+        self._xy = np.column_stack(np.broadcast_arrays(x, y)).astype(float)
+        self._x, self._y = self._xy.T  # views
 
         self._subslice = False
         if (self.axes and len(x) > 1000 and self._is_sorted(x) and
diff --git a/lib/matplotlib/offsetbox.py b/lib/matplotlib/offsetbox.py
index e15fcad221b7..d62a509eb3dc 100644
--- a/lib/matplotlib/offsetbox.py
+++ b/lib/matplotlib/offsetbox.py
@@ -71,22 +71,19 @@ def _get_packed_offsets(wd_list, total, sep, mode="fixed"):
     # d_list is currently not used.
 
     if mode == "fixed":
-        offsets_ = np.add.accumulate([0] + [w + sep for w in w_list])
+        offsets_ = np.cumsum([0] + [w + sep for w in w_list])
         offsets = offsets_[:-1]
-
         if total is None:
             total = offsets_[-1] - sep
-
         return total, offsets
 
     elif mode == "expand":
         if len(w_list) > 1:
             sep = (total - sum(w_list)) / (len(w_list) - 1.)
         else:
-            sep = 0.
-        offsets_ = np.add.accumulate([0] + [w + sep for w in w_list])
+            sep = 0
+        offsets_ = np.cumsum([0] + [w + sep for w in w_list])
         offsets = offsets_[:-1]
-
         return total, offsets
 
     elif mode == "equal":
@@ -94,10 +91,8 @@ def _get_packed_offsets(wd_list, total, sep, mode="fixed"):
         if total is None:
             total = (maxh + sep) * len(w_list)
         else:
-            sep = float(total) / (len(w_list)) - maxh
-
-        offsets = np.array([(maxh + sep) * i for i in range(len(w_list))])
-
+            sep = total / len(w_list) - maxh
+        offsets = (maxh + sep) * np.arange(len(w_list))
         return total, offsets
 
     else:
diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
index 29f11519d70d..37c92f119359 100644
--- a/lib/matplotlib/patches.py
+++ b/lib/matplotlib/patches.py
@@ -1389,10 +1389,10 @@ def getpoints(self, x1, y1, x2, y2, k):
         b = -2 * y2
         c = y2 ** 2. - k ** 2. * pm ** 2. / (1. + pm ** 2.)
 
-        y3a = (-b + math.sqrt(b ** 2. - 4 * a * c)) / (2. * a)
+        y3a = (-b + math.sqrt(b ** 2 - 4 * a * c)) / (2 * a)
         x3a = (y3a - y2) / pm + x2
 
-        y3b = (-b - math.sqrt(b ** 2. - 4 * a * c)) / (2. * a)
+        y3b = (-b - math.sqrt(b ** 2 - 4 * a * c)) / (2 * a)
         x3b = (y3b - y2) / pm + x2
         return x3a, y3a, x3b, y3b
 
@@ -1651,8 +1651,7 @@ def theta_stretch(theta, scale):
         theta2 = theta_stretch(self.theta2, width / height)
 
         # Get width and height in pixels
-        width, height = self.get_transform().transform_point(
-            (width, height))
+        width, height = self.get_transform().transform_point((width, height))
         inv_error = (1.0 / 1.89818e-6) * 0.5
         if width < inv_error and height < inv_error:
             self._path = Path.arc(theta1, theta2)
@@ -2883,10 +2882,10 @@ def connect(self, posA, posB):
             x1, y1 = posA
             x2, y2 = posB
 
-            cosA, sinA = (math.cos(self.angleA / 180. * math.pi),
-                          math.sin(self.angleA / 180. * math.pi))
-            cosB, sinB = (math.cos(self.angleB / 180. * math.pi),
-                          math.sin(self.angleB / 180. * math.pi))
+            cosA = math.cos(math.radians(self.angleA))
+            sinA = math.sin(math.radians(self.angleA))
+            cosB = math.cos(math.radians(self.angleB))
+            sinB = math.sin(math.radians(self.angleB))
 
             cx, cy = get_intersection(x1, y1, cosA, sinA,
                                       x2, y2, cosB, sinB)
@@ -2928,10 +2927,10 @@ def connect(self, posA, posB):
             x1, y1 = posA
             x2, y2 = posB
 
-            cosA, sinA = (math.cos(self.angleA / 180. * math.pi),
-                          math.sin(self.angleA / 180. * math.pi))
-            cosB, sinB = (math.cos(self.angleB / 180. * math.pi),
-                          math.sin(self.angleB / 180. * math.pi))
+            cosA = math.cos(math.radians(self.angleA))
+            sinA = math.sin(math.radians(self.angleA))
+            cosB = math.cos(math.radians(self.angleB))
+            sinB = math.sin(math.radians(self.angleB))
 
             cx, cy = get_intersection(x1, y1, cosA, sinA,
                                       x2, y2, cosB, sinB)
@@ -3004,8 +3003,8 @@ def connect(self, posA, posB):
             codes = [Path.MOVETO]
 
             if self.armA:
-                cosA = math.cos(self.angleA / 180. * math.pi)
-                sinA = math.sin(self.angleA / 180. * math.pi)
+                cosA = math.cos(math.radians(self.angleA))
+                sinA = math.sin(math.radians(self.angleA))
                 # x_armA, y_armB
                 d = self.armA - self.rad
                 rounded.append((x1 + d * cosA, y1 + d * sinA))
@@ -3013,8 +3012,8 @@ def connect(self, posA, posB):
                 rounded.append((x1 + d * cosA, y1 + d * sinA))
 
             if self.armB:
-                cosB = math.cos(self.angleB / 180. * math.pi)
-                sinB = math.sin(self.angleB / 180. * math.pi)
+                cosB = math.cos(math.radians(self.angleB))
+                sinB = math.sin(math.radians(self.angleB))
                 x_armB, y_armB = x2 + self.armB * cosB, y2 + self.armB * sinB
 
                 if rounded:
@@ -3099,14 +3098,11 @@ def connect(self, posA, posB):
             armA, armB = self.armA, self.armB
 
             if self.angle is not None:
-                theta0 = self.angle / 180. * math.pi
+                theta0 = np.deg2rad(self.angle)
                 dtheta = theta1 - theta0
-
                 dl = dd * math.sin(dtheta)
                 dL = dd * math.cos(dtheta)
-
                 x2, y2 = x1 + dL * math.cos(theta0), y1 + dL * math.sin(theta0)
-
                 armB = armB - dl
 
                 # update
@@ -3354,8 +3350,8 @@ def _get_arrow_wedge(self, x0, y0, x1, y1,
 
         def transmute(self, path, mutation_size, linewidth):
 
-            head_length, head_width = self.head_length * mutation_size, \
-                                      self.head_width * mutation_size
+            head_length = self.head_length * mutation_size
+            head_width = self.head_width * mutation_size
             head_dist = math.sqrt(head_length ** 2 + head_width ** 2)
             cos_t, sin_t = head_length / head_dist, head_width / head_dist
 
@@ -3364,8 +3360,7 @@ def transmute(self, path, mutation_size, linewidth):
             x1, y1 = path.vertices[1]
 
             # If there is no room for an arrow and a line, then skip the arrow
-            has_begin_arrow = (self.beginarrow and
-                               not ((x0 == x1) and (y0 == y1)))
+            has_begin_arrow = self.beginarrow and not (x0 == x1 and y0 == y1)
             if has_begin_arrow:
                 verticesA, codesA, ddxA, ddyA = \
                            self._get_arrow_wedge(x1, y1, x0, y0,
diff --git a/lib/matplotlib/path.py b/lib/matplotlib/path.py
index fcaf191dc04b..28612925de84 100644
--- a/lib/matplotlib/path.py
+++ b/lib/matplotlib/path.py
@@ -758,7 +758,7 @@ def circle(cls, center=(0., 0.), radius=1., readonly=False):
         """
         MAGIC = 0.2652031
         SQRTHALF = np.sqrt(0.5)
-        MAGIC45 = np.sqrt((MAGIC*MAGIC) / 2.0)
+        MAGIC45 = SQRTHALF * MAGIC
 
         vertices = np.array([[0.0, -1.0],
 
@@ -818,7 +818,7 @@ def unit_circle_righthalf(cls):
         if cls._unit_circle_righthalf is None:
             MAGIC = 0.2652031
             SQRTHALF = np.sqrt(0.5)
-            MAGIC45 = np.sqrt((MAGIC*MAGIC) / 2.0)
+            MAGIC45 = SQRTHALF * MAGIC
 
             vertices = np.array(
                 [[0.0, -1.0],
diff --git a/lib/matplotlib/projections/geo.py b/lib/matplotlib/projections/geo.py
index 00071e6d05dc..926a22fa5de5 100644
--- a/lib/matplotlib/projections/geo.py
+++ b/lib/matplotlib/projections/geo.py
@@ -382,15 +382,11 @@ def __init__(self, resolution):
             self._resolution = resolution
 
         def transform_non_affine(self, xy):
-            x = xy[:, 0:1]
-            y = xy[:, 1:2]
-
-            quarter_x = 0.25 * x
-            half_y = 0.5 * y
-            z = np.sqrt(1.0 - quarter_x*quarter_x - half_y*half_y)
-            longitude = 2 * np.arctan((z*x) / (2.0 * (2.0*z*z - 1.0)))
+            x, y = xy.T
+            z = np.sqrt(1 - (x / 4) ** 2 - (y / 2) ** 2)
+            longitude = 2 * np.arctan((z * x) / (2 * (2 * z ** 2 - 1)))
             latitude = np.arcsin(y*z)
-            return np.concatenate((longitude, latitude), 1)
+            return np.column_stack([longitude, latitude])
         transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
 
         def inverted(self):
diff --git a/lib/matplotlib/projections/polar.py b/lib/matplotlib/projections/polar.py
index e059c1ee375a..5955ffb5fb1e 100644
--- a/lib/matplotlib/projections/polar.py
+++ b/lib/matplotlib/projections/polar.py
@@ -1,7 +1,7 @@
 from __future__ import (absolute_import, division, print_function,
                         unicode_literals)
 
-import collections
+from collections import OrderedDict
 
 import numpy as np
 
@@ -646,7 +646,7 @@ def _gen_axes_patch(self):
         return mpatches.Wedge((0.5, 0.5), 0.5, 0.0, 360.0)
 
     def _gen_axes_spines(self):
-        spines = collections.OrderedDict([
+        spines = OrderedDict([
             ('polar', mspines.Spine.arc_spine(self, 'top',
                                               (0.5, 0.5), 0.5, 0.0, 360.0)),
             ('start', mspines.Spine.linear_spine(self, 'left')),
diff --git a/lib/matplotlib/stackplot.py b/lib/matplotlib/stackplot.py
index 8b34f7697711..2c0b7e6d1b82 100644
--- a/lib/matplotlib/stackplot.py
+++ b/lib/matplotlib/stackplot.py
@@ -55,10 +55,7 @@ def stackplot(axes, x, *args, **kwargs):
     element in the stacked area plot.
     """
 
-    if len(args) == 1:
-        y = np.atleast_2d(*args)
-    elif len(args) > 1:
-        y = np.row_stack(args)
+    y = np.row_stack(args)
 
     labels = iter(kwargs.pop('labels', []))
 
diff --git a/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.pdf b/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.pdf
index 952ed88f4d8d..eeb8969fa702 100644
Binary files a/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.pdf and b/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.pdf differ
diff --git a/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.png b/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.png
index 7d705b038b43..59c32a9084d7 100644
Binary files a/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.png and b/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.png differ
diff --git a/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.svg b/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.svg
index cb7a2e09ee12..35a003c97c21 100644
--- a/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.svg
+++ b/lib/matplotlib/tests/baseline_images/test_axes/fill_between_interpolate.svg
@@ -27,7 +27,7 @@ z
 " style="fill:#ffffff;"/>
    </g>
    <g id="PolyCollection_1">
-    <path clip-path="url(#p602a1e79e0)" d="M 72 121.745455 
+    <path clip-path="url(#p2a28627d87)" d="M 72 121.745455 
 L 72 121.745455 
 L 76.464 115.182551 
 L 80.928 108.723148 
@@ -50,8 +50,8 @@ L 80.928 91.473805
 L 76.464 106.118686 
 L 72 121.745455 
 z
-" style="fill:url(#hddfc7df858);stroke:#000000;"/>
-    <path clip-path="url(#p602a1e79e0)" d="M 183.6 121.745455 
+" style="fill:url(#hd3108e6b65);stroke:#000000;"/>
+    <path clip-path="url(#p2a28627d87)" d="M 183.6 121.745455 
 L 188.064 128.308358 
 L 192.528 134.767761 
 L 196.992 141.021795 
@@ -84,8 +84,8 @@ L 196.992 78.731004
 L 192.528 91.473805 
 L 188.064 106.118686 
 z
-" style="fill:url(#hddfc7df858);stroke:#000000;"/>
-    <path clip-path="url(#p602a1e79e0)" d="M 295.2 121.745455 
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+    <path clip-path="url(#p2a28627d87)" d="M 295.2 121.745455 
 L 299.664 115.182551 
 L 304.128 108.723148 
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@@ -106,8 +106,8 @@ L 308.592 78.731004
 L 304.128 91.473805 
 L 299.664 106.118686 
 z
-" style="fill:url(#hddfc7df858);stroke:#000000;"/>
-    <path clip-path="url(#p602a1e79e0)" d="M 406.8 121.745455 
+" style="fill:url(#hd3108e6b65);stroke:#000000;"/>
+    <path clip-path="url(#p2a28627d87)" d="M 406.8 121.745455 
 L 411.264 128.308358 
 L 415.728 134.767761 
 L 420.192 141.021795 
@@ -140,16 +140,16 @@ L 420.192 78.731004
 L 415.728 91.473805 
 L 411.264 106.118686 
 z
-" style="fill:url(#hddfc7df858);stroke:#000000;"/>
+" style="fill:url(#hd3108e6b65);stroke:#000000;"/>
    </g>
    <g id="PolyCollection_2">
-    <path clip-path="url(#p602a1e79e0)" d="M 72 121.745455 
+    <path clip-path="url(#p2a28627d87)" d="M 72 121.745455 
 L 72 121.745455 
 L 72 121.745455 
 L 72 121.745455 
 z
 " style="fill:#ff0000;stroke:#000000;"/>
-    <path clip-path="url(#p602a1e79e0)" d="M 112.508717 74.184994 
+    <path clip-path="url(#p2a28627d87)" d="M 112.508717 74.184994 
 L 116.64 71.944677 
 L 121.104 70.309322 
 L 125.568 69.485146 
@@ -185,7 +185,7 @@ L 121.104 98.613846
 L 116.64 84.811167 
 z
 " style="fill:#ff0000;stroke:#000000;"/>
-    <path clip-path="url(#p602a1e79e0)" d="M 254.691283 169.305915 
+    <path clip-path="url(#p2a28627d87)" d="M 254.691283 169.305915 
 L 255.024 169.125489 
 L 259.488 165.957535 
 L 263.952 162.09233 
@@ -209,7 +209,7 @@ L 259.488 178.601496
 L 255.024 170.161705 
 z
 " style="fill:#ff0000;stroke:#000000;"/>
-    <path clip-path="url(#p602a1e79e0)" d="M 335.708717 74.184994 
+    <path clip-path="url(#p2a28627d87)" d="M 335.708717 74.184994 
 L 339.84 71.944677 
 L 344.304 70.309322 
 L 348.768 69.485146 
@@ -245,7 +245,7 @@ L 344.304 98.613846
 L 339.84 84.811167 
 z
 " style="fill:#ff0000;stroke:#000000;"/>
-    <path clip-path="url(#p602a1e79e0)" d="M 477.891283 169.305915 
+    <path clip-path="url(#p2a28627d87)" d="M 477.891283 169.305915 
 L 478.224 169.125489 
 L 482.688 165.957535 
 L 487.152 162.09233 
@@ -269,7 +269,7 @@ z
 " style="fill:#ff0000;stroke:#000000;"/>
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    <g id="line2d_1">
-    <path clip-path="url(#p602a1e79e0)" d="M 72 121.745455 
+    <path clip-path="url(#p2a28627d87)" d="M 72 121.745455 
 L 76.464 115.182551 
 L 80.928 108.723148 
 L 85.392 102.469114 
@@ -372,7 +372,7 @@ L 513.936 128.308358
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    </g>
    <g id="line2d_2">
-    <path clip-path="url(#p602a1e79e0)" d="M 72 121.745455 
+    <path clip-path="url(#p2a28627d87)" d="M 72 121.745455 
 L 76.464 106.118686 
 L 80.928 91.473805 
 L 85.392 78.731004 
@@ -500,68 +500,68 @@ L 518.4 43.2
       <defs>
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       <g>
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+       <use style="stroke:#000000;stroke-width:0.5;" x="72" xlink:href="#me5bf4c00e3" y="200.290909"/>
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       <g>
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       <g>
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       <g>
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     <g id="xtick_5">
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       <g>
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@@ -572,92 +572,92 @@ L 0 4
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       <g>
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@@ -799,7 +799,7 @@ L 121.104 266.787525
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-    <path clip-path="url(#p460367ad90)" d="M 254.691283 351.618008 
+    <path clip-path="url(#pb48d8066ea)" d="M 254.691283 351.618008 
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@@ -823,7 +823,7 @@ L 259.488 362.772705
 L 255.024 352.644955 
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-    <path clip-path="url(#p460367ad90)" d="M 335.708717 237.472901 
+    <path clip-path="url(#pb48d8066ea)" d="M 335.708717 237.472901 
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@@ -859,7 +859,7 @@ L 344.304 266.787525
 L 339.84 250.224309 
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-    <path clip-path="url(#p460367ad90)" d="M 477.891283 351.618008 
+    <path clip-path="url(#pb48d8066ea)" d="M 477.891283 351.618008 
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@@ -883,7 +883,7 @@ z
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-    <path clip-path="url(#p460367ad90)" d="M 72 294.545455 
+    <path clip-path="url(#pb48d8066ea)" d="M 72 294.545455 
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 L 80.928 278.918686 
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@@ -986,7 +986,7 @@ L 513.936 302.420939
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-    <path clip-path="url(#p460367ad90)" d="M 76.464 275.793333 
+    <path clip-path="url(#pb48d8066ea)" d="M 76.464 275.793333 
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@@ -1091,60 +1091,60 @@ L 518.4 231.709091
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+  <clipPath id="pb48d8066ea">
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-  <pattern height="72" id="hddfc7df858" patternUnits="userSpaceOnUse" width="72" x="0" y="0">
+  <pattern height="72" id="hd3108e6b65" patternUnits="userSpaceOnUse" width="72" x="0" y="0">
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diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index f7e5ffe87cb2..7a0e8f326fc2 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -1718,9 +1718,7 @@ def bump(a):
             x = 1 / (.1 + np.random.random())
             y = 2 * np.random.random() - .5
             z = 10 / (.1 + np.random.random())
-            for i in range(m):
-                w = (i / float(m) - y) * z
-                a[i] += x * np.exp(-w * w)
+            a += x * np.exp(-((np.arange(m) / m - y) * z) ** 2)
         a = np.zeros((m, n))
         for i in range(n):
             for j in range(5):
diff --git a/lib/matplotlib/tests/test_backend_bases.py b/lib/matplotlib/tests/test_backend_bases.py
index c0831669339a..4f84a78bc578 100644
--- a/lib/matplotlib/tests/test_backend_bases.py
+++ b/lib/matplotlib/tests/test_backend_bases.py
@@ -34,11 +34,9 @@ def check(master_transform, paths, all_transforms,
                                    [], 'data')]
         uses = rb._iter_collection_uses_per_path(
             paths, all_transforms, offsets, facecolors, edgecolors)
-        seen = [0] * len(raw_paths)
-        for i in ids:
-            seen[i] += 1
-        for n in seen:
-            assert n in (uses-1, uses)
+        if raw_paths:
+            seen = np.bincount(ids, minlength=len(raw_paths))
+            assert set(seen).issubset([uses - 1, uses])
 
     check(id, paths, tforms, offsets, facecolors, edgecolors)
     check(id, paths[0:1], tforms, offsets, facecolors, edgecolors)
diff --git a/lib/matplotlib/tests/test_bbox_tight.py b/lib/matplotlib/tests/test_bbox_tight.py
index 183d8bc39107..b4f9bdf30f1f 100644
--- a/lib/matplotlib/tests/test_bbox_tight.py
+++ b/lib/matplotlib/tests/test_bbox_tight.py
@@ -26,7 +26,7 @@ def test_bbox_inches_tight():
     ind = np.arange(len(colLabels)) + 0.3  # the x locations for the groups
     cellText = []
     width = 0.4     # the width of the bars
-    yoff = np.array([0.0] * len(colLabels))
+    yoff = np.zeros(len(colLabels))
     # the bottom values for stacked bar chart
     fig, ax = plt.subplots(1, 1)
     for row in range(rows):
diff --git a/lib/matplotlib/tests/test_image.py b/lib/matplotlib/tests/test_image.py
index 8e3f173186ce..7bcc9d65d661 100644
--- a/lib/matplotlib/tests/test_image.py
+++ b/lib/matplotlib/tests/test_image.py
@@ -313,10 +313,8 @@ def test_image_edges():
 
     data = np.tile(np.arange(12), 15).reshape(20, 9)
 
-    im = ax.imshow(data, origin='upper',
-                   extent=[-10, 10, -10, 10], interpolation='none',
-                   cmap='gray'
-                   )
+    im = ax.imshow(data, origin='upper', extent=[-10, 10, -10, 10],
+                   interpolation='none', cmap='gray')
 
     x = y = 2
     ax.set_xlim([-x, x])
diff --git a/lib/matplotlib/tests/test_table.py b/lib/matplotlib/tests/test_table.py
index fc21ecb01eb4..071c3f1cb1d5 100644
--- a/lib/matplotlib/tests/test_table.py
+++ b/lib/matplotlib/tests/test_table.py
@@ -28,7 +28,7 @@ def test_zorder():
     rowLabels = ['%d year' % x for x in (100, 50)]
 
     cellText = []
-    yoff = np.array([0.0] * len(colLabels))
+    yoff = np.zeros(len(colLabels))
     for row in reversed(data):
         yoff += row
         cellText.append(['%1.1f' % (x/1000.0) for x in yoff])
diff --git a/lib/matplotlib/tests/test_triangulation.py b/lib/matplotlib/tests/test_triangulation.py
index a98ed260ab7a..28b314023a46 100644
--- a/lib/matplotlib/tests/test_triangulation.py
+++ b/lib/matplotlib/tests/test_triangulation.py
@@ -772,10 +772,9 @@ def z(x, y):
     y0 = (radii*np.sin(angles)).flatten()
     triang0 = mtri.Triangulation(x0, y0)  # Delaunay triangulation
     z0 = z(x0, y0)
-    xmid = x0[triang0.triangles].mean(axis=1)
-    ymid = y0[triang0.triangles].mean(axis=1)
-    mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)
-    triang0.set_mask(mask)
+    triang0.set_mask(np.hypot(x0[triang0.triangles].mean(axis=1),
+                              y0[triang0.triangles].mean(axis=1))
+                     < min_radius)
 
     # Then the plot
     refiner = mtri.UniformTriRefiner(triang0)
@@ -810,10 +809,9 @@ def dipole_potential(x, y):
     y = (radii*np.sin(angles)).flatten()
     V = dipole_potential(x, y)
     triang = mtri.Triangulation(x, y)
-    xmid = x[triang.triangles].mean(axis=1)
-    ymid = y[triang.triangles].mean(axis=1)
-    mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)
-    triang.set_mask(mask)
+    triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+                             y[triang.triangles].mean(axis=1))
+                    < min_radius)
 
     # Refine data - interpolates the electrical potential V
     refiner = mtri.UniformTriRefiner(triang)
diff --git a/lib/mpl_toolkits/mplot3d/art3d.py b/lib/mpl_toolkits/mplot3d/art3d.py
index 8c885a32ed06..3e9785813210 100644
--- a/lib/mpl_toolkits/mplot3d/art3d.py
+++ b/lib/mpl_toolkits/mplot3d/art3d.py
@@ -149,13 +149,9 @@ def line_2d_to_3d(line, zs=0, zdir='z'):
 def path_to_3d_segment(path, zs=0, zdir='z'):
     '''Convert a path to a 3D segment.'''
 
-    if not iterable(zs):
-        zs = np.ones(len(path)) * zs
-
-    seg = []
+    zs = _backports.broadcast_to(zs, len(path))
     pathsegs = path.iter_segments(simplify=False, curves=False)
-    for (((x, y), code), z) in zip(pathsegs, zs):
-        seg.append((x, y, z))
+    seg = [(x, y, z) for (((x, y), code), z) in zip(pathsegs, zs)]
     seg3d = [juggle_axes(x, y, z, zdir) for (x, y, z) in seg]
     return seg3d
 
@@ -165,21 +161,16 @@ def paths_to_3d_segments(paths, zs=0, zdir='z'):
     Convert paths from a collection object to 3D segments.
     '''
 
-    if not iterable(zs):
-        zs = np.ones(len(paths)) * zs
-
-    segments = []
-    for path, pathz in zip(paths, zs):
-        segments.append(path_to_3d_segment(path, pathz, zdir))
-    return segments
+    zs = _backports.broadcast_to(zs, len(paths))
+    segs = [path_to_3d_segment(path, pathz, zdir)
+            for path, pathz in zip(paths, zs)]
+    return segs
 
 
 def path_to_3d_segment_with_codes(path, zs=0, zdir='z'):
     '''Convert a path to a 3D segment with path codes.'''
 
-    if not iterable(zs):
-        zs = np.ones(len(path)) * zs
-
+    zs = _backports.broadcast_to(zs, len(path))
     seg = []
     codes = []
     pathsegs = path.iter_segments(simplify=False, curves=False)
@@ -195,9 +186,7 @@ def paths_to_3d_segments_with_codes(paths, zs=0, zdir='z'):
     Convert paths from a collection object to 3D segments with path codes.
     '''
 
-    if not iterable(zs):
-        zs = np.ones(len(paths)) * zs
-
+    zs = _backports.broadcast_to(zs, len(paths))
     segments = []
     codes_list = []
     for path, pathz in zip(paths, zs):
@@ -271,11 +260,9 @@ def __init__(self, *args, **kwargs):
         self.set_3d_properties(zs, zdir)
 
     def set_3d_properties(self, verts, zs=0, zdir='z'):
-        if not iterable(zs):
-            zs = np.ones(len(verts)) * zs
-
-        self._segment3d = [juggle_axes(x, y, z, zdir) \
-                for ((x, y), z) in zip(verts, zs)]
+        zs = _backports.broadcast_to(zs, len(verts))
+        self._segment3d = [juggle_axes(x, y, z, zdir)
+                           for ((x, y), z) in zip(verts, zs)]
         self._facecolor3d = Patch.get_facecolor(self)
 
     def get_path(self):
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index f387e5a5582e..cb5e7dbfede2 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -11,27 +11,28 @@
 """
 from __future__ import (absolute_import, division, print_function,
                         unicode_literals)
-import math
 
 import six
 from six.moves import map, xrange, zip, reduce
 
+import math
 import warnings
 from collections import defaultdict
 
 import numpy as np
+
 import matplotlib.axes as maxes
-from matplotlib.axes import Axes, rcParams
-from matplotlib import cbook
-import matplotlib.transforms as mtransforms
-from matplotlib.transforms import Bbox
+import matplotlib.cbook as cbook
 import matplotlib.collections as mcoll
-from matplotlib import docstring
+import matplotlib.colors as mcolors
+import matplotlib.docstring as docstring
 import matplotlib.scale as mscale
-from matplotlib.tri.triangulation import Triangulation
-from matplotlib import colors as mcolors
+import matplotlib.transforms as mtransforms
+from matplotlib.axes import Axes, rcParams
+from matplotlib.cbook import _backports
 from matplotlib.colors import Normalize, LightSource
-from matplotlib.cbook._backports import broadcast_to
+from matplotlib.transforms import Bbox
+from matplotlib.tri.triangulation import Triangulation
 
 from . import art3d
 from . import proj3d
@@ -1538,8 +1539,7 @@ def plot(self, xs, ys, *args, **kwargs):
         zdir = kwargs.pop('zdir', 'z')
 
         # Match length
-        if not cbook.iterable(zs):
-            zs = np.ones(len(xs)) * zs
+        zs = _backports.broadcast_to(zs, len(xs))
 
         lines = super(Axes3D, self).plot(xs, ys, *args, **kwargs)
         for line in lines:
@@ -2334,29 +2334,16 @@ def scatter(self, xs, ys, zs=0, zdir='z', s=20, c=None, depthshade=True,
 
         had_data = self.has_data()
 
-        xs = np.ma.ravel(xs)
-        ys = np.ma.ravel(ys)
-        zs = np.ma.ravel(zs)
-        if xs.size != ys.size:
-            raise ValueError("Arguments 'xs' and 'ys' must be of same size.")
-        if xs.size != zs.size:
-            if zs.size == 1:
-                zs = np.tile(zs[0], xs.size)
-            else:
-                raise ValueError(("Argument 'zs' must be of same size as 'xs' "
-                    "and 'ys' or of size 1."))
-
+        xs, ys, zs = np.broadcast_arrays(
+            *[np.ravel(np.ma.filled(t, np.nan)) for t in [xs, ys, zs]])
         s = np.ma.ravel(s)  # This doesn't have to match x, y in size.
 
         xs, ys, zs, s, c = cbook.delete_masked_points(xs, ys, zs, s, c)
 
-        patches = super(Axes3D, self).scatter(xs, ys, s=s, c=c, *args,
-                                              **kwargs)
-        if not cbook.iterable(zs):
-            is_2d = True
-            zs = np.ones(len(xs)) * zs
-        else:
-            is_2d = False
+        patches = super(Axes3D, self).scatter(
+            xs, ys, s=s, c=c, *args, **kwargs)
+        is_2d = not cbook.iterable(zs)
+        zs = _backports.broadcast_to(zs, len(xs))
         art3d.patch_collection_2d_to_3d(patches, zs=zs, zdir=zdir,
                                         depthshade=depthshade)
 
@@ -2395,8 +2382,7 @@ def bar(self, left, height, zs=0, zdir='z', *args, **kwargs):
 
         patches = super(Axes3D, self).bar(left, height, *args, **kwargs)
 
-        if not cbook.iterable(zs):
-            zs = np.ones(len(left)) * zs
+        zs = _backports.broadcast_to(zs, len(left))
 
         verts = []
         verts_zs = []
@@ -2478,43 +2464,17 @@ def bar3d(self, x, y, z, dx, dy, dz, color=None,
 
         had_data = self.has_data()
 
-        if not cbook.iterable(x):
-            x = [x]
-        if not cbook.iterable(y):
-            y = [y]
-        if not cbook.iterable(z):
-            z = [z]
-
-        if not cbook.iterable(dx):
-            dx = [dx]
-        if not cbook.iterable(dy):
-            dy = [dy]
-        if not cbook.iterable(dz):
-            dz = [dz]
-
-        if len(dx) == 1:
-            dx = dx * len(x)
-        if len(dy) == 1:
-            dy = dy * len(y)
-        if len(dz) == 1:
-            dz = dz * len(z)
-
-        if len(x) != len(y) or len(x) != len(z):
-            warnings.warn('x, y, and z must be the same length.')
-
-        # FIXME: This is archaic and could be done much better.
-        minx, miny, minz = 1e20, 1e20, 1e20
-        maxx, maxy, maxz = -1e20, -1e20, -1e20
+        x, y, z, dx, dy, dz = np.broadcast_arrays(
+            np.atleast_1d(x), y, z, dx, dy, dz)
+        minx = np.min(x)
+        maxx = np.max(x + dx)
+        miny = np.min(y)
+        maxy = np.max(y + dy)
+        minz = np.min(z)
+        maxz = np.max(z + dz)
 
         polys = []
         for xi, yi, zi, dxi, dyi, dzi in zip(x, y, z, dx, dy, dz):
-            minx = min(xi, minx)
-            maxx = max(xi + dxi, maxx)
-            miny = min(yi, miny)
-            maxy = max(yi + dyi, maxy)
-            minz = min(zi, minz)
-            maxz = max(zi + dzi, maxz)
-
             polys.extend([
                 ((xi, yi, zi), (xi + dxi, yi, zi),
                     (xi + dxi, yi + dyi, zi), (xi, yi + dyi, zi)),
@@ -2836,12 +2796,13 @@ def voxels(filled, **kwargs):
         if xyz is None:
             x, y, z = np.indices(coord_shape)
         else:
-            x, y, z = (broadcast_to(c, coord_shape) for c in xyz)
+            x, y, z = (_backports.broadcast_to(c, coord_shape) for c in xyz)
 
         def _broadcast_color_arg(color, name):
             if np.ndim(color) in (0, 1):
                 # single color, like "red" or [1, 0, 0]
-                return broadcast_to(color, filled.shape + np.shape(color))
+                return _backports.broadcast_to(
+                    color, filled.shape + np.shape(color))
             elif np.ndim(color) in (3, 4):
                 # 3D array of strings, or 4D array with last axis rgb
                 if np.shape(color)[:3] != filled.shape: