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from manimlib.imports import*
import numpy as np
class intro(GraphScene):
CONFIG = {
"x_min": -3,
"x_max": 3,
"x_axis_width": 6,
"y_min": -5,
"y_max": 5,
"graph_origin": 10.5*LEFT,
"axes_color": BLUE,
"exclude_zero_label": True,
"x_labeled_nums": range(-2, 3, 1),
}
def func(self,t,n1,n2):
s=0
for i in range(n1,n2+1):
s+=((-2/(i*np.pi))*((-1)**i)*np.sin(2*np.pi*i*t))
return s
def construct(self):
image=ImageMobject('image.png').shift(5.5*LEFT+2.5*UP).scale(1.5)
self.play(ShowCreation(image))
self.setup_axes(scalee=1)
mainGraphs=[
self.get_graph(lambda x:self.func(x,2,7),x_max=2,x_min=-2).shift(9.3*RIGHT+3*UP).set_color([ORANGE,GREEN_B,RED_E,YELLOW_E,RED_D,YELLOW_D]).scale(1.4),
self.get_graph(lambda x:self.func(x,3,7),x_max=2,x_min=-2).shift(10.8*RIGHT+3*UP).set_color([GREEN_B,ORANGE,RED_D,YELLOW_E,YELLOW_D]).scale(1.4),
self.get_graph(lambda x:self.func(x,4,7),x_max=2,x_min=-2).shift(10.8*RIGHT+3*UP).set_color([GREEN_B,YELLOW_E,ORANGE,YELLOW_D]).scale(1.4),
self.get_graph(lambda x:self.func(x,5,7),x_max=2,x_min=-2).shift(10.8*RIGHT+3*UP).set_color([YELLOW_E,GREEN_B,YELLOW_D]).scale(1.4),
self.get_graph(lambda x:self.func(x,6,7),x_max=2,x_min=-2).shift(10.8*RIGHT+3*UP).set_color([YELLOW_D,GREEN_B]).scale(1.4),
self.get_graph(lambda x:self.func(x,7,7),x_max=2,x_min=-2,color=GREEN_B).shift(10.8*RIGHT+3*UP).scale(1.4),
]
self.play(ApplyMethod(mainGraphs[0].shift,1.5*RIGHT))
graph1=self.get_graph(lambda x:self.func(x,2,2),x_max=2,x_min=-2,color=RED_E).shift(10.8*RIGHT+3*UP).scale(1.5)
graph2=self.get_graph(lambda x:self.func(x,3,3),x_max=2,x_min=-2,color=RED_D).shift(10.8*RIGHT+3*UP).scale(1.5)
graph3=self.get_graph(lambda x:self.func(x,4,4),x_max=2,x_min=-2,color=ORANGE).shift(10.8*RIGHT+3*UP).scale(1.5)
graph4=self.get_graph(lambda x:self.func(x,5,5),x_max=2,x_min=-2,color=YELLOW_E).shift(10.8*RIGHT+3*UP).scale(1.5)
graph5=self.get_graph(lambda x:self.func(x,6,6),x_max=2,x_min=-2,color=YELLOW_D).shift(10.8*RIGHT+3*UP).scale(1.5)
coeff=[
TextMobject("$\\frac { -1 }{ \pi } sin(4\pi t)$").scale(0.5).shift(DOWN+4.6*RIGHT+3*UP).set_color(RED_E),
TextMobject("$\\frac { 2 }{ 3\pi } sin(6\pi t)$").scale(0.5).shift(2*DOWN+4.6*RIGHT+3*UP).set_color(RED_D),
TextMobject("$\\frac { -1 }{ 2\pi } sin(8\pi t)$").scale(0.5).shift(3*DOWN+4.6*RIGHT+3*UP).set_color(ORANGE),
TextMobject("$\\frac { 2 }{ 5\pi } sin(10\pi t)$").scale(0.5).shift(4*DOWN+4.6*RIGHT+3*UP).set_color(YELLOW_E),
TextMobject("$\\frac { -1 }{ 3\pi } sin(12\pi t)$").scale(0.5).shift(5*DOWN+4.6*RIGHT+3*UP).set_color(YELLOW_D),
TextMobject("$\\frac { 2 }{ 7\pi } sin(14\pi t)$").scale(0.5).shift(6*DOWN+4.6*RIGHT+3*UP).set_color(GREEN_B)
]
self.wait(0.6)
self.play(ApplyMethod(graph1.shift,1*DOWN),ReplacementTransform(mainGraphs[0],mainGraphs[1]))
self.play(Write(coeff[0]))
self.play(ApplyMethod(graph2.shift,2*DOWN),ReplacementTransform(mainGraphs[1],mainGraphs[2]))
self.play(Write(coeff[1]))
self.play(ApplyMethod(graph3.shift,3*DOWN),ReplacementTransform(mainGraphs[2],mainGraphs[3]))
self.play(Write(coeff[2]))
self.play(ApplyMethod(graph4.shift,4*DOWN),ReplacementTransform(mainGraphs[3],mainGraphs[4]))
self.play(Write(coeff[3]))
self.play(ApplyMethod(graph5.shift,5*DOWN),ReplacementTransform(mainGraphs[4],mainGraphs[5]))
self.play(Write(coeff[4]))
self.play(ApplyMethod(mainGraphs[5].shift,6*DOWN))
self.play(Write(coeff[5]))
pluses=[TextMobject("+"),TextMobject("+"),TextMobject("+"),TextMobject("+"),TextMobject("+")]
for t in pluses:
t.scale(0.5).shift((2.2-1.5*pluses.index(t))*LEFT)
finalGraph=self.get_graph(lambda x:self.func(x,2,7),x_max=2,x_min=-2).shift(10.8*RIGHT+3*UP)
finalGraph.set_color([GREEN_B,YELLOW_D,YELLOW_E,ORANGE,RED_D,RED_E])
finalGroup=VGroup(graph1,graph2,graph3,graph4,graph5,mainGraphs[5])
self.play(ReplacementTransform(finalGroup,finalGraph))
self.play(ApplyMethod(coeff[0].scale,0.7),ApplyMethod(coeff[1].scale,0.7),ApplyMethod(coeff[2].scale,0.7),ApplyMethod(coeff[3].scale,0.7),ApplyMethod(coeff[4].scale,0.7),ApplyMethod(coeff[5].scale,0.7))
#self.play(ApplyMethod(coeff[0].shift,7*LEFT+1.6*DOWN),ApplyMethod(coeff[1].shift,5.5*LEFT+0.8*DOWN),ApplyMethod(coeff[2].shift,4*LEFT),ApplyMethod(coeff[3].shift,2.5*LEFT+0.8*UP),ApplyMethod(coeff[4].shift,LEFT+1.6*UP),ApplyMethod(coeff[5].shift,0.5*RIGHT+2.4*DOWN))
self.play(ApplyMethod(coeff[0].shift,7.6*LEFT+2*DOWN),ApplyMethod(coeff[1].shift,6.1*LEFT+DOWN),ApplyMethod(coeff[2].shift,4.6*LEFT),ApplyMethod(coeff[3].shift,3.1*LEFT+UP),ApplyMethod(coeff[4].shift,1.6*LEFT+2*UP),ApplyMethod(coeff[5].shift,0.1*LEFT+3*UP))
equal=TextMobject("=").scale(1.5).shift(1.5*UP)
self.play(Write(equal))
self.play(Write(pluses[0]),Write(pluses[1]),Write(pluses[2]),Write(pluses[3]),Write(pluses[4]))
group=VGroup(pluses[0],pluses[1],pluses[2],pluses[3],pluses[4],coeff[0],coeff[1],coeff[2],coeff[3],coeff[4],coeff[5])
self.play(ApplyMethod(group.scale,1.5))
self.wait(2)
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