from manim import*



class circulate_prove(Scene):
    def construct(self):
        #self.add(NumberPlane())
        t=Tex(r"$0.\dot{9}$   ?  1",color=BLUE).scale(3)
        t1 = Tex(r"$0.\dot{9}$   $<$  1", color=BLUE).scale(3)
        t2=Tex(r"$0.\dot{9}$   =  1", color=BLUE).scale(3)
        t3=Tex(r"$0.\dot{9}$   $>$  1",color=BLUE).scale(3)
        #  &=可以用作等号对齐

        self.play(ReplacementTransform(t,t1))
        self.play(ReplacementTransform(t1,t2))
        self.play(ReplacementTransform(t2,t3))
        self.play(FadeOut(t3))
       
        tex_1=MathTex(r'0.\dot{9} &= x\\ 9.\dot{9} &=10x\\ 9 &=9x\\ x&=1',font_size=80).move_to(LEFT*3)
        tex_2 = MathTex(r'{1\over3} &= 0.\dot{3} \\ {1\over3}\times3 &= 0.\dot{3}\times3 \\ 1&=0.\dot{9}', font_size=80).move_to(RIGHT * 3)
        #\times表示这样的'×'符号
        self.play(Write(tex_1),run_time=4)
        self.play(Write(tex_2),run_time=4)
        # self.play(FadeTransformPieces(tex_1,tex_2,stretch=False,dim_to_match=2))
        tex_3 = MathTex(r'0&=0+0+0+0+0 \dots \\ 0&=1-1+1-1+1-1+1-1 \dots \\ 0&=1+(-1)+1+(-1)+(1)+(-1)\dots\\ 0&=1', font_size=60, color="#66D9EF")
        box_1=SurroundingRectangle(tex_3[0][16])
        box_2=SurroundingRectangle(tex_3[0][36])
        box_3 = SurroundingRectangle(tex_3[0][63])
        grp_box=VGroup(box_1,box_2,box_3)

        tex_4=MathTex(r'\dot{9}.0&=x\\ \dot{9}0.0&=10x\\ 9&=-9x\\ x&=-1=\dot{9}999\dots',font_size=80,color=YELLOW)
        grp=VGroup(tex_1,tex_2)
        self.play(ReplacementTransform(grp,tex_3),run_time=3)
        self.play(Create(grp_box))
        self.wait(1.5)

        grp1=VGroup(tex_3,grp_box)
        self.play(ReplacementTransform(grp1,tex_4),run_time=3)
        self.wait()
        text=Text("用等比数列求和试试",font="KaiTi",font_size=60,color=BLUE).to_edge(UP)
        self.play(Write(text))
        self.wait()
        tex_6=Tex(r'$0.\dot{9}=1$',font_size=60,color=BLUE).to_edge(UP)
        self.play(ReplacementTransform(text,tex_6))
        self.wait()
        tex_5 = MathTex(r'a_{0}= 0.9,a_{1}= 0.09,a_{2}= 0.009,\dots,a_{n}= 0.\dot{0}9',color=YELLOW,font_size=60)
        self.play(ReplacementTransform(tex_4,tex_5),run_time=2)

        self.wait(2)
        self.play(tex_5.animate.move_to(UP*2),run_time=2,rate_functions=smooth)
        tex_7=MathTex(r'S_{n} =\frac{a_{0}\times \left ( 1-q^{n}  \right )  }{1-q} =\frac{0.9\times \left ( 1-({\frac{1}{10}})^n   \right ) }{1-\frac{1}{10} } ',font_size=60,color=YELLOW).next_to(tex_5,DOWN)
        self.play(Write(tex_7))
        self.wait(1)

        tex_8 = MathTex(r'\lim_{n \to \infty} (\frac{1}{10}) ^n=0',color=YELLOW,font_size=60).next_to(tex_7,DOWN)
        self.play(Write(tex_8))
        self.wait()

        grp2=VGroup(tex_5,tex_7,tex_8)
        self.play(FadeOut(grp2))
        self.wait()

        tex_9=tex_6.copy().scale(3)
        tex_9.set_color(YELLOW)
        tex_9.move_to(ORIGIN)
        self.play(ReplacementTransform(tex_6,tex_9),run_time=5)
        self.wait(5)