1 files changed, 52 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py
new file mode 100644
index 0000000..a1396fc
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py
@@ -0,0 +1,52 @@
+from manimlib.imports import*
+import math as m
+
+    class Constraints(ThreeDScene):
+    def construct(self):
+       axes = ThreeDAxes().rotate(m.radians(75))
+        label_x = TextMobject("$x$").shift([-5.5,1,0]).fade(0.4)  #---- x axis
+        label_y = TextMobject("$y$").shift([1,5.5,0]).rotate(-4.5).fade(0.4)  #---- y axis
+
+        cylinder = ParametricSurface(
+            lambda u, v: np.array([
+                np.cos(TAU * u),
+                np.sin(TAU * u),
+                2 * (1-1.5*v)
+            ]),checkerboard_colors=[YELLOW_C,YELLOW_D,YELLOW_E]).shift([0.5,0.5,-0.13]).scale(1) 
+
+        plane =  ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                u+v
+            ]),checkerboard_colors=[TEAL_C,TEAL_D,TEAL_E]).shift([0,0,0]).rotate(m.radians(-40),RIGHT).scale(4).fade(0.3)
+
+        c = Circle(color='#FF00FF',fill_opacity=0.3).shift([0.7,-1.3,0.4]).rotate(2.5,UP).scale(1.32)
+
+        f_text = TextMobject("$f(x,y)=x^2+y^2+z^2$",color = '#FFA074').scale(0.6).to_corner(UL)
+        g_text = TextMobject("$g(x,y)=x^2+y^2+1$",color = '#FFA074').scale(0.6).to_corner(UL)
+        h_text = TextMobject("$h(x,y)=x+y-z=1$",color = '#FFA074').scale(0.6).to_corner(UL)
+
+
+
+        self.set_camera_orientation(phi=65*DEGREES,theta=95*DEGREES)
+
+        self.add(axes)        
+        self.add(label_x) 
+        self.add(label_y)
+        self.wait(1) 
+        self.add_fixed_in_frame_mobjects(f_text)    
+        self.play(Write(c))
+        self.wait(1)
+        self.play(FadeOut(f_text))
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(g_text)
+        self.play(Write(cylinder)) 
+        self.wait(1)
+        self.play(FadeOut(g_text))
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(h_text)
+        self.play(Write(plane))            
+        self.wait(1)
+        self.play(FadeOut(h_text))
+        self.wait(1)