Fix wrong angle ranges in Sphere documentation and add more examples (#3973)

* Made the document changes

* added additional example

* Apply some suggestions from code review

Co-authored-by: Francisco Manríquez Novoa <49853152+chopan050@users.noreply.github.com>

* Shorten sphere examples

* Fix line breaks and remove trailing whitespace

* Add example for showing portions of spheres

* Undo accidental overwrite of ExampleSphereOverlap

* Change name of manim code block

---------

Co-authored-by: Xiuyuan <u7678992@anu.edu.au>
Co-authored-by: TahitiX <136950383+TahitiX@users.noreply.github.com>
Co-authored-by: Francisco Manríquez Novoa <49853152+chopan050@users.noreply.github.com>
Co-authored-by: Francisco Manríquez Novoa <francisco.manriquezn@usm.cl>

Author: 4 people

manim/mobject/three_d/three_dimensions.py

@@ -379,13 +379,7 @@ class Sphere(Surface):
         class ExampleSphere(ThreeDScene):
             def construct(self):
                 self.set_camera_orientation(phi=PI / 6, theta=PI / 6)
-                sphere1 = Sphere(
-                    center=(3, 0, 0),
-                    radius=1,
-                    resolution=(20, 20),
-                    u_range=[0.001, PI - 0.001],
-                    v_range=[0, TAU]
-                )
+                sphere1 = Sphere(center=(3, 0, 0), radius=1, resolution=(20, 20))
                 sphere1.set_color(RED)
                 self.add(sphere1)
                 sphere2 = Sphere(center=(-1, -3, 0), radius=2, resolution=(18, 18))
@@ -394,6 +388,57 @@ def construct(self):
                 sphere3 = Sphere(center=(-1, 2, 0), radius=2, resolution=(16, 16))
                 sphere3.set_color(BLUE)
                 self.add(sphere3)
+
+    This example shows that overlapping spheres can intersect with rough transitions.
+
+    .. manim:: ExampleSphereOverlap
+        :save_last_frame:
+
+        class ExampleSphereOverlap(ThreeDScene):
+            def construct(self):
+                self.set_camera_orientation(phi=PI / 4, theta=PI / 4)
+                sphere1 = Sphere(center=(0, 0, 0), radius=1, resolution=(20, 20))
+                sphere1.set_color(RED)
+                self.add(sphere1)
+                sphere2 = Sphere(center=(-0.5, -1, 0.5), radius=1.2, resolution=(20, 20))
+                sphere2.set_color(GREEN)
+                self.add(sphere2)
+                sphere3 = Sphere(center=(1, -1, 0), radius=1.1, resolution=(20, 20))
+                sphere3.set_color(BLUE)
+                self.add(sphere3)
+
+    In this example, by modifying ``u_range`` (the range of the azimuthal angle) and
+    ``v_range`` (the range of the polar angle), it is possible to obtain a portion of a
+    sphere:
+
+    .. manim:: ExamplePartialSpheres
+        :save_last_frame:
+
+        class ExamplePartialSpheres(ThreeDScene):
+            def construct(self):
+                self.set_camera_orientation(phi=PI / 4)
+                sphere1 = Sphere(
+                    center=(-3, 0, 0),
+                    resolution=(10, 20),
+                    u_range=[TAU / 4, 3 * TAU / 4],
+                )
+                sphere1.set_color(RED)
+                self.add(sphere1)
+                sphere2 = Sphere(
+                    center=(0, 0, 0),
+                    resolution=(20, 10),
+                    v_range=[0, TAU / 4],
+                )
+                sphere2.set_color(GREEN)
+                self.add(sphere2)
+                sphere3 = Sphere(
+                    center=(3, 0, 0),
+                    resolution=(5, 10),
+                    u_range=[3 * TAU / 4, TAU],
+                    v_range=[TAU / 4, TAU / 2],
+                )
+                sphere3.set_color(BLUE)
+                self.add(sphere3)
     """
 
     def __init__(