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117 lines
4.6 KiB
117 lines
4.6 KiB
from manim import *
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class ClearProof(Scene):
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def construct(self):
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config.frame_width = 12.8
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config.frame_height = 10.24
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colors = {
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"a": "#4D9DE0",
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"b": "#E15554",
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"c": "#3BB273",
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"bg": "#1E1E1E",
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"text": "#FFFFFF"
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}
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self.camera.background_color = colors["bg"]
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a, b = 3, 4 # 直角边长度
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c = 5 # 斜边长度
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# ========== 第一步：初始构造 ==========
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step1 = Text("构造直角三角形", font_size=36, color=colors["text"]).to_edge(UP)
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tri = Polygon([-4, -2, 0], [2, -2, 0], [-4, 2, 0],
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color=colors["text"], stroke_width=4)
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labels = VGroup(
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MathTex("a", color=colors["a"]).next_to(tri.get_bottom(), DOWN, buff=0.3),
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MathTex("b", color=colors["b"]).next_to(tri.get_left(), LEFT, buff=0.3),
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MathTex("c", color=colors["c"]).move_to(tri.get_vertices()[2] + UR*0.5)
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)
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self.play(Write(step1), run_time=1.5)
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self.play(Create(tri), run_time=2)
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self.play(LaggedStart(*[Write(l) for l in labels], lag_ratio=0.4))
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self.wait(2)
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# ========== 第二步：构建正方形 ==========
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step2 = Text("构建边长的正方形", font_size=36, color=colors["text"]).to_edge(UP)
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square_a = Square(a, color=colors["a"], fill_opacity=0.3).next_to(tri, RIGHT, buff=2)
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square_b = Square(b, color=colors["b"], fill_opacity=0.3).next_to(tri, LEFT, buff=2)
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square_c = Square(c, color=colors["c"], fill_opacity=0.3).move_to(ORIGIN + DOWN*1.5)
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self.play(
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ReplacementTransform(step1, step2),
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DrawBorderThenFill(square_a),
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DrawBorderThenFill(square_b),
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run_time=2
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)
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self.wait(1.5)
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# ========== 第三步：分割图形 ==========
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step3 = Text("分割正方形为可重组部件", font_size=36, color=colors["text"]).to_edge(UP)
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# 分割a²正方形
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a_pieces = VGroup(
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tri.copy().set_fill(colors["a"], 0.3),
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tri.copy().rotate(PI/2).set_fill(colors["a"], 0.3).shift(RIGHT*a)
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)
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# 分割b²正方形
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b_pieces = VGroup(
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tri.copy().rotate(-PI/2).set_fill(colors["b"], 0.3),
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tri.copy().rotate(PI).set_fill(colors["b"], 0.3).shift(LEFT*b)
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)
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self.play(
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ReplacementTransform(step2, step3),
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square_a.animate.set_fill(opacity=0),
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square_b.animate.set_fill(opacity=0),
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LaggedStart(
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Transform(square_a, a_pieces),
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Transform(square_b, b_pieces),
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lag_ratio=0.5
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),
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run_time=3
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)
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self.wait(2)
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# ========== 第四步：重组图形 ==========
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step4 = Text("重组部件构成大正方形", font_size=36, color=colors["text"]).to_edge(UP)
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# 计算重组后的位置
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final_positions = [
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[-c/2, -c/2 -1.5, 0], [c/2, -c/2 -1.5, 0],
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[c/2, c/2 -1.5, 0], [-c/2, c/2 -1.5, 0]
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]
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# 创建重组动画
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animations = []
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for i, piece in enumerate(a_pieces):
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animations.append(piece.animate.move_to(final_positions[i]))
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for i, piece in enumerate(b_pieces):
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animations.append(piece.animate.move_to(final_positions[i+2]))
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self.play(
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ReplacementTransform(step3, step4),
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LaggedStart(*animations, lag_ratio=0.3),
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FadeIn(square_c, shift=UP),
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run_time=4
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)
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self.wait(2)
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# ========== 第五步：面积等式 ==========
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step5 = Text("面积守恒证明定理", font_size=36, color=colors["text"]).to_edge(UP)
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equation = MathTex(
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"a^2", "+", "b^2", "=", "c^2",
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substrings_to_isolate=["a^2", "b^2", "c^2"]
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).scale(1.5).set_color_by_tex("a^2", colors["a"]).set_color_by_tex("b^2", colors["b"]).set_color_by_tex("c^2", colors["c"])
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self.play(
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ReplacementTransform(step4, step5),
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FadeOut(VGroup(a_pieces, b_pieces, square_c)),
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Write(equation),
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run_time=2
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)
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self.wait(3)
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# ========== 最终总结 ==========
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conclusion = Text("勾股定理得证！", font_size=48, color=colors["c"])
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self.play(
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FadeOut(equation),
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FadeOut(step5),
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Write(conclusion, run_time=2)
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)
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self.wait(3) |