1 files changed, 108 insertions, 0 deletions
diff --git a/FSF-2020/series-and-transformations/Power Series/script4.py b/FSF-2020/series-and-transformations/Power Series/script4.py
new file mode 100644
index 0000000..412d20c
--- /dev/null
+++ b/FSF-2020/series-and-transformations/Power Series/script4.py
@@ -0,0 +1,108 @@
+from manimlib.imports import *
+import math
+
+class intro(Scene):
+    def construct(self):
+        introText1=TextMobject("Consider the","above","example..")
+        introText1.scale(0.8)
+        introText1.set_color_by_tex_to_color_map({"above":YELLOW})
+        self.play(Write(introText1))
+        self.wait(1)
+
+class graphScene(GraphScene,MovingCameraScene):
+    CONFIG = {
+        "x_min": -5,
+        "x_max": 5,
+        "y_min": -5,
+        "y_max": 5,
+        "graph_origin": ORIGIN,
+        "function_color": RED,
+        "axes_color": GREEN,
+        "x_axis_label": "$x$",
+        "y_axis_label": "$y$",
+        "exclude_zero_label": True,
+        "x_labeled_nums": range(-1, 2, 1),
+        "y_labeled_nums": range(0,2,1),
+        "y_axis_height":7,
+        "x_axis_width":7
+    }
+
+    def setup(self):
+        GraphScene.setup(self)
+        MovingCameraScene.setup(self)
+
+    def construct(self):
+        x_each_unit = self.x_axis_width / (self.x_max - self.x_min)
+        y_each_unit = self.y_axis_height / (self.y_max - self.y_min)
+
+        function_expan=TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }+{ x }^{ 8 }+..$")
+        function_expan.scale(0.6)
+        function_expan.set_color(RED)
+        function_expan.to_edge(UP+RIGHT)
+        self.add(function_expan)
+
+        self.setup_axes()
+
+        equation = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14)+math.pow(x,16)-math.pow(x,18),color = RED,x_min = -1.1,x_max=1.1)
+        self.play(ShowCreation(equation))
+        self.wait(1)
+
+        dashLineLeft=DashedLine(start=ORIGIN+y_each_unit*5*UP,end=ORIGIN+y_each_unit*5*DOWN)
+        dashLineRight=DashedLine(start=ORIGIN+y_each_unit*5*UP,end=ORIGIN+y_each_unit*5*DOWN)
+        dashLineLeft.shift(ORIGIN+LEFT*x_each_unit)
+        dashLineRight.shift(ORIGIN+RIGHT*x_each_unit)
+        radiusLine=Line(start=ORIGIN,end=ORIGIN+RIGHT*x_each_unit)
+        rangeLine=Line(start=ORIGIN+LEFT*x_each_unit,end=ORIGIN+RIGHT*x_each_unit)
+        circle=Circle(radius=x_each_unit)
+        movingPoint=Circle(radius=0.025)
+        movingPoint.shift(ORIGIN+RIGHT*x_each_unit)
+        circleEq1=self.get_graph(lambda x:math.sqrt(1-x**2),color=BLUE,x_max=-1,x_min=1)
+        circleEq2=self.get_graph(lambda x:-math.sqrt(1-x**2),color=BLUE,x_max=1,x_min=-1)
+
+        self.play(Write(dashLineLeft),Write(dashLineRight))
+        self.wait(1)
+
+        equation_updated=self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14)+math.pow(x,16)-math.pow(x,18),color = GREEN,x_min = -1,x_max=1)
+        self.play(FadeOut(self.axes),ReplacementTransform(equation,equation_updated))
+        self.wait(0.5)
+        self.play(Write(radiusLine))
+        self.play(MoveAlongPath(movingPoint,circleEq1))
+        self.play(MoveAlongPath(movingPoint,circleEq2))
+        self.play(FadeIn(circle))
+        self.wait(1)
+
+        radiusText=TextMobject("Radius of convergence")
+        radiusText.scale(0.14)
+        radiusText.shift(ORIGIN+RIGHT*x_each_unit*0.45+DOWN*y_each_unit*0.2)
+
+        self.play(Write(radiusText))
+        self.wait(0.6)
+
+        self.camera_frame.save_state()
+        self.camera_frame.set_width(5.5)
+        self.play(self.camera_frame.move_to, ORIGIN)
+        self.wait(1)
+        self.camera_frame.set_width(14)
+        self.wait(1.3)
+
+        self.play(FadeOut(radiusText),FadeOut(circle),FadeOut(movingPoint))
+        extendLine=Line(start=ORIGIN,end=ORIGIN+x_each_unit*LEFT)
+        self.play(Write(extendLine))
+        doubleArrow=TextMobject("$\longleftrightarrow$")
+        doubleArrow.scale(1.6)
+        doubleArrow.set_color(BLUE)
+        doubleArrow.shift(ORIGIN+DOWN*y_each_unit*0.5)
+        self.play(FadeIn(doubleArrow))
+        self.wait(1)
+        rangeText=TextMobject("Interval of convergence")
+        rangeText.scale(0.15)
+        rangeText.shift(ORIGIN+y_each_unit*DOWN)
+        self.play(Write(rangeText))
+        self.wait(0.6)
+
+        self.camera_frame.save_state()
+        self.camera_frame.set_width(5.5)
+        self.play(self.camera_frame.move_to, ORIGIN)
+        self.wait(1)
+        self.camera_frame.set_width(14)
+        self.wait(1.5)