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diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py
new file mode 100644
index 0000000..fcbc410
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py
@@ -0,0 +1,145 @@
+from manimlib.imports import *

+

+class Sphere(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() # creates a 3D Axis

+

+        text3d1 = TextMobject(r"$z = f(x,y) =  \sqrt{r^2 - x^2 - y^2}$")

+

+        text3d1.scale(0.7)

+

+        text3d1.to_corner(UL)

+

+        text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) 

+        self.play(Write(text3d1))

+        self.wait(1)

+        

+        self.add_fixed_in_frame_mobjects(text3d1)

+

+        sphere = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                2*np.cos(u)

+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],

+            resolution=(15, 32)).scale(1)

+

+

+        #Experiment with circles by changing difference value of u and v

+        '''

+        sphere_points = [np.array([2*np.sin(u*DEGREES)*np.cos(v*DEGREES), 2*np.sin(u*DEGREES)*np.sin(v*DEGREES), 2*np.cos(u*DEGREES)]) for u in range(0, 185, 5) for v in range(0, 365, 5)]

+

+        sphere_spheres = [Dot().move_to(pts) for pts in sphere_points]

+

+        sphere = VGroup(*sphere_spheres)

+        '''

+        

+        self.set_camera_orientation(phi=75 * DEGREES, theta = 45*DEGREES)

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1]) 

+

+        dot_x_y1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,0]))

+        dot_x_y_z1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,1.414]))

+

+        line1 = DashedLine(np.array([-1,1,0]), np.array([-1,1,1.414]), color = YELLOW_C)

+

+        point_x_y1 = TexMobject("(-1,1,0)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,0])).scale(0.5)

+        point_x_y_z1 = TexMobject("(-1,1,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+        point_x_y_z1_2 = TexMobject("(-1,1,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+        point_x_y_z1_3 = TexMobject("(-1,1,\\sqrt{4 - 1 - 1})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+        point_x_y_z1_4 = TexMobject("(-1,1,\\sqrt{2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+        point_x_y_z1_5 = TexMobject("(-1,1,1.414)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+    

+        

+        self.play(ShowCreation(dot_x_y1))

+        self.add_fixed_orientation_mobjects(point_x_y1)

+        self.play(ShowCreation(dot_x_y_z1), ShowCreation(line1))

+        self.add_fixed_orientation_mobjects(point_x_y_z1)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z1,point_x_y_z1_2))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_2)

+

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z1_2,point_x_y_z1_3))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_3)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z1_3,point_x_y_z1_4))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_4)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z1_4,point_x_y_z1_5))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_5)

+        

+

+

+        dot_x_y2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,0]))

+        dot_x_y_z2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,1.87]))

+    

+        line2 = DashedLine(np.array([0.5,-0.5,0]), np.array([0.5,-0.5,1.87]), color = YELLOW_C)

+

+        point_x_y2 = TexMobject("(0.5,-0.5,0)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,0])).scale(0.5)

+        point_x_y_z2 = TexMobject("(0.5,-0.5,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+        point_x_y_z2_2 = TexMobject("(0.5,-0.5,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+        point_x_y_z2_3 = TexMobject("(0.5,-0.5,\\sqrt{4 - 0.25 - 0.25})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+        point_x_y_z2_4 = TexMobject("(0.5,-0.5,\\sqrt{3.5})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+        point_x_y_z2_5 = TexMobject("(0.5,-0.5,1.87)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+       

+        

+        self.play(ShowCreation(dot_x_y2))

+        self.add_fixed_orientation_mobjects(point_x_y2)

+        self.play(ShowCreation(dot_x_y_z2), ShowCreation(line2))

+        self.add_fixed_orientation_mobjects(point_x_y_z2)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z2,point_x_y_z2_2))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_2)

+

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z2_2,point_x_y_z2_3))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_3)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z2_3,point_x_y_z2_4))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_4)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z2_4,point_x_y_z2_5))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_5)

+

+        self.play(FadeOut(point_x_y1), FadeOut(point_x_y_z1_5))

+        self.play(FadeOut(point_x_y2), FadeOut(point_x_y_z2_5))

+        

+

+

+

+        sphere_final = []

+    

+        for u in range(0, 90, 15): 

+            sphere_points1 = [np.array([2*np.sin(u*DEGREES)*np.cos(v*DEGREES), 2*np.sin(u*DEGREES)*np.sin(v*DEGREES), 2*np.cos(u*DEGREES)]) for v in range(0, 370, 10)]

+            sphere_dots1 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points1]

+

+            sphere_points2 = [np.array([2*np.sin((u+5)*DEGREES)*np.cos(v*DEGREES), 2*np.sin((u+5)*DEGREES)*np.sin(v*DEGREES), 2*np.cos((u+5)*DEGREES)]) for v in range(0, 370, 10)]

+            sphere_dots2 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points2]

+

+            sphere_points3 = [np.array([2*np.sin((u+10)*DEGREES)*np.cos(v*DEGREES), 2*np.sin((u+10)*DEGREES)*np.sin(v*DEGREES), 2*np.cos((u+10)*DEGREES)]) for v in range(0, 370, 10)]

+            sphere_dots3 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points3]

+

+            sphere_final = sphere_final + sphere_dots1 + sphere_dots2 + sphere_dots3

+

+            sphere_dots = sphere_dots1 + sphere_dots2 + sphere_dots3

+   

+            sphere_with_dots = VGroup(*sphere_dots)

+            self.play(ShowCreation(sphere_with_dots))

+

+        sphere_final_with_dots = VGroup(*sphere_final)

+        

+        

+        self.begin_ambient_camera_rotation(rate=0.5)

+        self.wait(3)

+        self.play(ReplacementTransform(sphere_final_with_dots, sphere))

+        self.wait(5)
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