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20231025_1_over_3_series.py
110 lines (86 loc) · 5.15 KB
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20231025_1_over_3_series.py
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import numpy as np
from manim import *
import math
# configs
config.background_color = BLACK
config.pixel_width = 180 * 12
config.pixel_height = 320 * 12
class SeriesSumFromOneOver3(Scene):
def construct(self):
formula = MathTex(r"{{\frac{1}{3}}}+{{(\frac{1}{3})^{2}}}+ {{(\frac{1}{3})^{3}}}+ {{(\frac{1}{3})^{4}}} + {{("
r"\frac{1}{3})^{5}}}"
r"+{{...}}"
).scale(1.5).shift(UP * 8)
self.play(Write(formula), run_time=1)
question_mark = Text("？", font_size=100, color=RED).next_to(formula, DOWN * 10)
self.play(ShowCreationThenFadeOut(question_mark))
run_t = 0.5
square_1 = Square(side_length=8)
self.play(Create(square_1), run_time=run_t)
brace_left = BraceBetweenPoints([-4, 4, 0], [-4, -4, 0])
txt1 = MathTex("1").next_to(brace_left, LEFT)
brace_down = BraceBetweenPoints([-4, -4, 0], [4, -4, 0])
txt2 = txt1.copy().next_to(brace_down, DOWN)
self.play(Create(brace_left), Create(txt1), Create(brace_down), Create(txt2), run_time=1)
line1_1 = DashedLine(start=[-4, 4/3, 0], end=[4, 4/3, 0])
line1_2 = line1_1.copy().shift(DOWN*8/3)
self.play(Create(line1_1), Create(line1_2))
rect1 = Rectangle(width=8, height=8/3, fill_color=BLUE, fill_opacity=0.4, color=BLUE).shift(8/3*UP)
self.play(GrowFromEdge(rect1, UP))
formula1 = formula.submobjects[0].copy()
self.play(formula1.animate.move_to(rect1.get_center_of_mass()))
line2_1 = DashedLine(start=[-4+8/3, -4+8/3, 0], end=[-4+8/3, 4-8/3, 0])
line2_2 = line2_1.copy().shift(RIGHT*8/3)
self.play(Create(line2_1), Create(line2_2))
rect2 = Polygon([-4, -4/3, 0], [-4, 4/3, 0], [-4+8/3, 4/3, 0], [-4+8/3, -4/3, 0], fill_color=BLUE, fill_opacity=0.4)
self.play(GrowFromEdge(rect2, LEFT))
formula2 = formula.submobjects[2].copy()
self.play(formula2.animate.move_to(rect2.get_center_of_mass()))
line3_1 = DashedLine(start=[-4+8/3, -4+8/3+8/3/3, 0], end=[4-8/3, -4+8/3+8/3/3, 0])
line3_2 = line3_1.copy().shift(UP*8/3/3)
self.play(Create(line3_2), Create(line3_1))
rect3 = Polygon([-4+8/3, -4+8/3+8/3/3, 0], [4-8/3, -4+8/3+8/3/3, 0], [4-8/3, -4+8/3, 0], [-4+8/3, -4+8/3, 0],
fill_opacity=0.4, fill_color=BLUE)
self.play(GrowFromEdge(rect3, LEFT))
formula3 = formula.submobjects[4].copy()
self.play(formula3.animate.scale(1/2).move_to(rect3.get_center_of_mass()))
line4_1 = DashedLine(start=[-4+8/3+8/3/3, -4+8/3+8/3/3, 0], end=[-4+8/3+8/3/3, -4+8/3+8/3/3+8/3/3, 0])
line4_2 = line4_1.copy().shift(RIGHT*8/3/3)
self.play(Create(line4_2), Create(line4_1))
rect4 = Polygon([-4+8/3+8/3/3, -4+8/3+8/3/3, 0], [-4+8/3+8/3/3, -4+8/3+8/3/3+8/3/3, 0],
[-4+8/3, -4+8/3+8/3/3+8/3/3, 0], [-4+8/3, -4+8/3+8/3/3, 0], fill_color=BLUE, fill_opacity=0.4).shift(RIGHT*8/3/3*2)
self.play(GrowFromEdge(rect4, DOWN))
formula4 = formula.submobjects[6].copy()
self.play(formula4.animate.scale(1 / 2).move_to(rect4.get_center_of_mass()))
line_5_1 = DashedLine(start=[-4+8/3+8/3/3, -4+8/3+8/3/3+8/3/3/3*2, 0],
end=[-4+8/3+8/3/3*2, -4+8/3+8/3/3+8/3/3/3*2, 0])
line_5_2 = line_5_1.copy().shift(DOWN*8/3/3/3)
self.play(Create(line_5_2), Create(line_5_1))
rect5 = Polygon([-4+8/3+8/3/3, -4+8/3+8/3/3+8/3/3/3*2, 0], [-4+8/3+8/3/3*2, -4+8/3+8/3/3+8/3/3/3*2, 0],
[-4+8/3+8/3/3*2, -4+8/3+8/3/3+8/3/3, 0], [-4+8/3+8/3/3, -4+8/3+8/3/3+8/3/3, 0],
fill_opacity=0.4, fill_color=BLUE)
self.play(GrowFromEdge(rect5, UP))
formula5 = formula.submobjects[8].copy()
self.play(formula5.animate.scale(1 / 4).move_to(rect5.get_center_of_mass()))
formula6 = formula.submobjects[10].copy()
self.play(formula6.animate.scale(1 / 4).move_to(ORIGIN))
group1 = VGroup(rect5, rect4, rect3, rect2, rect1)
group1_1 = VGroup(rect5, rect4, rect3, rect2, rect1,
formula6, formula5, formula4, formula3, formula2, formula1)
group2 = group1.copy().set_fill(PURE_RED)
self.play(Rotate(group2, PI, about_point=ORIGIN))
#self.play(group2.animate.rotate(PI, about_point=ORIGIN))
self.remove(line1_1, line1_2, line2_2, line2_1, line3_1, line3_2, line4_2, line4_1, line_5_2, line_5_1,
square_1)
self.remove(brace_down, brace_left, txt2, txt1)
self.play(group1_1.animate.shift(UL*3),
group2.animate.shift(DR*3))
txt1_1 = MathTex(r"\frac{1}{2}").scale(3).move_to(group1_1.get_center())
txt2_2 = txt1_1.copy().move_to(group2.get_center())
self.play(GrowFromCenter(txt1_1), GrowFromCenter(txt2_2))
self.play(FadeOut(group2), FadeOut(txt2_2), FadeOut(group1_1))
#self.play(formula.submobjects[0].animate.move_to(formula.submobjects[0], LEFT))
equal = MathTex("=").scale(3).next_to(txt1_1, LEFT*2)
self.play(Write(equal))
self.play(txt1_1.animate.next_to(equal, RIGHT))
self.wait(3)