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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)
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