added codes

1 files changed, 225 insertions, 0 deletions

diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video5_CoinsAnalogy.py b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video5_CoinsAnalogy.py
new file mode 100644
index 0000000..10ee889
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video5_CoinsAnalogy.py
@@ -0,0 +1,225 @@
+from manimlib.imports import*
+import math
+import numpy as np
+
+class coinsAnalogy(Scene):
+    def construct(self):
+        text1=TextMobject("Consider we have","Rs 39").shift(2*UP).scale(0.75).set_color_by_tex_to_color_map({"Rs 39":[YELLOW,PURPLE]})
+        text2=TextMobject("and we want to represent them only in terms of","Rs 2","and","Rs 5").shift(UP).scale(0.6).set_color_by_tex_to_color_map({"Rs 2":YELLOW,"Rs 5":PURPLE})
+        text3=TextMobject("How many","Rs 2 coins","and","Rs 5 coins","do","we need?").scale(0.8).set_color_by_tex_to_color_map({"Rs 2 coins":YELLOW,"Rs 5 coins":PURPLE,"we need?":RED})
+        text4=TextMobject("We","perform","the following!").scale(0.75).shift(DOWN).set_color_by_tex_to_color_map({"perform":GREEN})
+
+        self.play(FadeIn(text1))
+        self.wait(0.6)
+        self.play(Write(text2))
+        self.wait(0.5)
+        self.play(Write(text3))
+        self.wait(0.7)
+        self.play(FadeIn(text4))
+        self.wait(1)
+        self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3),FadeOut(text4))
+
+        g1=self.group("Rs 39")
+        g1.shift(3*LEFT+0.75*UP)
+        l1=self.line()
+        l1.shift(4*LEFT)
+        f1=self.fiveGroup()
+        t1=self.twoGroup()
+        f1.shift(3.5*LEFT+0.7*DOWN)
+        andT=TextMobject("and").next_to(f1,buff=-0.1).scale(0.3)
+        t1.next_to(andT,buff=0.2)
+        equal1=TextMobject("$=$")
+        equal1.next_to(l1,buff=0.2)
+
+        self.play(ShowCreation(g1))
+        self.play(ShowCreation(l1))
+        self.play(ShowCreation(f1),Write(andT),ShowCreation(t1))
+        self.play(ShowCreation(equal1))
+        self.wait(0.6)
+
+        f2=self.fiveGroup().next_to(equal1,buff=0.4)
+        multiple1=TextMobject("$X7$","$\quad +$").next_to(f2,buff=0.2).set_color_by_tex_to_color_map({"$X7$":PURPLE})
+        l2=self.line().next_to(multiple1,buff=0.4)
+        g2=self.group("Rs 4").shift(2.75*RIGHT+0.75*UP)
+        t2=self.twoGroup().shift(2.75*RIGHT+0.7*DOWN)
+
+        self.play(ShowCreation(f2))
+        self.play(ShowCreation(multiple1))
+        self.play(ShowCreation(g2))
+        self.play(ShowCreation(l2))
+        self.play(ShowCreation(t2))
+        self.wait(1)
+
+        tempGrup=VGroup(g2,l2,t2)
+
+        t3=self.twoGroup().next_to(multiple1,buff=0.4)
+        multiple2=TextMobject("$X2$").next_to(t3,buff=0.2).set_color_by_tex_to_color_map({"$X2$":YELLOW})
+
+        self.play(ReplacementTransform(tempGrup,t3))
+        self.play(Write(multiple2))
+        self.wait(2)
+
+    def line(self):
+        l=Line(start=[0,0,0],end=[2,0,0])
+        return l
+
+    def twoGroup(self):
+        two=Circle(radius=0.25,color=BLACK,fill_color=YELLOW,fill_opacity=0.7)
+        twoText=TextMobject("Rs 2").scale(0.25).set_color(BLACK)
+        twoGrup=VGroup(two,twoText)
+        return twoGrup
+
+    def fiveGroup(self):
+        five=Circle(radius=0.35,color=BLACK,fill_color=PURPLE,fill_opacity=0.7)
+        fiveText=TextMobject("Rs 5").scale(0.3).set_color(BLACK)
+        fiveGrup=VGroup(five,fiveText)
+        return fiveGrup
+
+    def group(self,money):
+        coins=[
+            Circle(radius=0.35,color=GREY,fill_color=GREY,fill_opacity=0.75),
+            Circle(radius=0.35,color=GREY,fill_color=GREY,fill_opacity=0.8),
+            Circle(radius=0.35,color=GREY,fill_color=GREY,fill_opacity=0.7),
+            Circle(radius=0.35,color=GREY,fill_color=GREY,fill_opacity=0.75),
+            Circle(radius=0.35,color=GREY,fill_color=GREY,fill_opacity=0.8),
+            Circle(radius=0.35,color=GREY,fill_color=GREY,fill_opacity=0.7)
+        ]
+        coinsText=TextMobject(money).set_color(BLACK)
+        coinsText.scale(0.35)
+
+        coins[1].shift(0.2*RIGHT+0.2*UP)
+        coins[2].shift(0.2*RIGHT+0.1*DOWN)
+        coins[3].shift(0.2*DOWN)
+        coins[4].shift(0.2*UP+0.2*LEFT)
+        coins[5].shift(0.2*LEFT+0.1*LEFT)
+
+        coinsGrup=VGroup(coins[0],coins[1],coins[2],coins[3],coins[4],coins[5],coinsText)
+        return coinsGrup
+
+class divideFunction(GraphScene):
+    CONFIG = {
+        "x_min": -6,
+        "x_max": 6,
+        "y_min": -300,
+        "y_max": 300,
+        "x_tick_frequency": 2,
+        "y_tick_frequency": 300,
+        "graph_origin": 3*LEFT+1.5*UP+6*LEFT,
+        "function_color": RED,
+        "axes_color": BLUE,
+        "x_axis_label": "$t$",
+        "y_axis_label": "$y$",
+        "x_labeled_nums": [-6,0,6],
+        "y_labeled_nums": [-300,0,300],
+        "x_axis_width": 1.5,
+        "y_axis_height": 1
+    }
+    def line(self):
+        l=Line(start=[0,0,0],end=[2,0,0])
+        return l
+    def construct(self):
+        text1=TextMobject("Similarly,").scale(0.8).shift(UP).set_color(RED)
+        text2=TextMobject("To find the amount of","each frequency","present in","$f(x)$").scale(0.6).set_color_by_tex_to_color_map({"each frequency":[YELLOW,RED],"$f(x)$":RED})
+        text3=TextMobject("We","perform","the following!").scale(0.7).shift(DOWN).set_color_by_tex_to_color_map({"perform":GREEN})
+        
+        self.play(FadeIn(text1))
+        self.wait(0.6)
+        self.play(Write(text2))
+        self.wait(0.7)
+        self.play(FadeIn(text3))
+
+        self.wait(1)
+        self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3))
+
+        boxUP=Square(side_length=1.7,fill_color=BLUE_C,fill_opacity=0.5,color=BLACK).shift(3*LEFT+UP)
+        boxDOWN=Square(side_length=1.7,fill_color=BLUE_C,fill_opacity=0.5,color=BLACK).shift(3*LEFT+DOWN)    
+
+        axes=[]
+        self.graph_origin=10*LEFT+1.5*UP
+        self.setup_axes(scalee=1)
+        axes.append(self.axes)
+        fx=self.get_graph(lambda x:math.pow(x,3)-math.pow(x,2)+x-2,x_min=-2*math.pi,x_max=2*math.pi,color=RED).shift(7*RIGHT+0.5*DOWN)
+        
+        l=self.line().shift(4*LEFT)
+
+        self.graph_origin=10*LEFT+1.5*DOWN
+        self.y_min=-2
+        self.y_max=1
+        self.y_tick_frequency=1
+        self.y_labeled_nums=[-1,0,1]
+        self.setup_axes(scalee=1)
+        axes.append(self.axes)
+        sinx=self.get_graph(lambda x:np.sin(x),x_min=-2*math.pi,x_max=2*math.pi,color=PURPLE_C).shift(7*RIGHT+0.5*UP)
+        
+        equal=TextMobject("$=$").next_to(l,buff=0.3)
+        result1=TextMobject("Amount of").scale(0.6).next_to(equal,buff=0.3)
+        boxRIGHT=Square(side_length=1.7,fill_color=GOLD_B,fill_opacity=0.5,color=BLACK).next_to(result1,buff=0.2)
+        self.graph_origin=10*LEFT
+        sinxResult=self.get_graph(lambda x:np.sin(x),color=PURPLE_C).next_to(result1,buff=0.3)
+        axes.append(self.axes)
+        result2=TextMobject("in","$f(x)$").scale(0.6).next_to(sinxResult,buff=0.2).set_color_by_tex_to_color_map({"$f(x)$":RED})
+
+        self.play(FadeIn(boxUP))
+        self.play(ShowCreation(fx))
+        self.play(ShowCreation(l))
+        self.play(FadeIn(boxDOWN))
+        self.play(ShowCreation(sinx))
+        self.wait(0.4)
+        self.play(Write(equal))
+        self.play(Write(result1))
+        self.play(FadeIn(boxRIGHT))
+        self.play(ShowCreation(sinxResult))
+        self.play(Write(result2))
+        aText1=TextMobject("and").scale(0.65).shift(4*RIGHT+2*DOWN).set_color(GREEN)
+        self.play(Write(aText1))
+        self.wait(0.7)
+
+        self.graph_origin=10*LEFT
+        cos4x=self.get_graph(lambda x:np.cos(4*x),color=PURPLE_A).shift(7*RIGHT+0.5*UP)
+        axes.append(self.axes)
+        self.graph_origin=10*LEFT
+        cos4xResult=self.get_graph(lambda x:np.cos(4*x),color=PURPLE_A).next_to(result1,buff=0.3)
+        axes.append(self.axes)
+        self.play(ReplacementTransform(sinx,cos4x),ReplacementTransform(sinxResult,cos4xResult))
+        self.wait(0.7)
+
+        soText=TextMobject("And so on..!").scale(0.65).shift(4*RIGHT+2*DOWN).set_color(GREEN)
+        self.play(ReplacementTransform(aText1,soText))
+
+        self.graph_origin=10*LEFT
+        cosx=self.get_graph(lambda x:np.cos(x),color=GREEN_E).shift(7*RIGHT+0.5*UP)
+        axes.append(self.axes)
+        self.graph_origin=10*LEFT
+        cosxResult=self.get_graph(lambda x:np.cos(x),color=GREEN_E).next_to(result1,buff=0.3)
+        axes.append(self.axes)
+        self.play(ReplacementTransform(cos4x,cosx),ReplacementTransform(cos4xResult,cosxResult))      
+
+        self.graph_origin=10*LEFT
+        cos3x=self.get_graph(lambda x:np.cos(3*x),color=GREEN_C).shift(7*RIGHT+0.5*UP)
+        axes.append(self.axes)
+        self.graph_origin=10*LEFT
+        cos3xResult=self.get_graph(lambda x:np.cos(3*x),color=GREEN_C).next_to(result1,buff=0.3)
+        axes.append(self.axes)
+        self.play(ReplacementTransform(cosx,cos3x),ReplacementTransform(cosxResult,cos3xResult))
+
+        self.graph_origin=10*LEFT
+        const=self.get_graph(lambda x:1,color=YELLOW_B).shift(7*RIGHT+0.5*UP)
+        axes.append(self.axes)
+        self.graph_origin=10*LEFT
+        constResult=self.get_graph(lambda x:1,color=YELLOW_B).next_to(result1,buff=0.3)
+        axes.append(self.axes)
+        self.play(ReplacementTransform(cos3x,const),ReplacementTransform(cos3xResult,constResult))
+
+        self.wait(1)
+
+        self.play(FadeOut(soText),FadeOut(const),FadeOut(constResult),FadeOut(l),FadeOut(equal),FadeOut(result1),FadeOut(result2),FadeOut(fx),FadeOut(boxRIGHT),FadeOut(boxUP),FadeOut(boxDOWN))
+
+        finalFormula1=TexMobject(r"Therefore,",r"F(s)",r"=",r"\int _{ -\infty  }^{ \infty  }",r"{f(t)",r"\over",r"sines",r"\enspace and \enspace",r"cosines}",r"dt }").scale(0.7).set_color_by_tex_to_color_map({"F(s)":RED,"sines":BLUE,"cosines}":YELLOW,"{f(t)":GREEN})
+        finalFormula2=TexMobject(r"F(s)",r"=",r"\int _{ -\infty  }^{ \infty  }",r"{f(t)",r"\over",r"{ e }^",r"{ i\theta  }}",r"dt }").set_color_by_tex_to_color_map({"F(s)":RED,"{f(t)":GREEN})
+        subFinalFormula=TextMobject("where","$\\theta =2\pi st$").scale(0.5).shift(DOWN+2*RIGHT).set_color_by_tex_to_color_map({"$\\theta =2\pi st$":RED})
+
+        self.play(Write(finalFormula1))
+        self.wait(1)
+        self.play(ReplacementTransform(finalFormula1,finalFormula2))
+        self.play(Write(subFinalFormula))
+        self.wait(2)