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from manim import *
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class PythagoreanProof(Scene):
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def construct(self):
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# 场景1：问题引入
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# 创建直角三角形
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tri = Polygon([-2, -1, 0], [1, -1, 0], [-2, 2, 0], color=WHITE)
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labels = VGroup(
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Tex("a", color=RED).next_to(tri.get_vertices()[1], DOWN),
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Tex("b", color=BLUE).next_to(tri.get_vertices()[2], LEFT),
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Tex("c", color=GREEN).next_to(tri.get_midpoint(), UR, buff=0.3)
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)
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self.play(Create(tri), run_time=2)
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self.play(Write(labels), run_time=1.5)
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# 显示平方表达式
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equation = VGroup(
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Tex("a^2 + b^2 = ?", color=RED_B).shift(UP * 2),
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Tex("c^2 = ?", color=GREEN_B).shift(DOWN * 2)
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)
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arrows = VGroup(
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Arrow(equation[0].get_bottom(), labels[0].get_center() + DOWN * 0.5, color=RED),
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Arrow(equation[0].get_bottom(), labels[1].get_center() + LEFT * 0.5, color=BLUE),
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Arrow(equation[1].get_top(), labels[2].get_center() + UR * 0.3, color=GREEN)
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)
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self.play(Write(equation), run_time=1.5)
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self.play(LaggedStart(*[GrowArrow(a) for a in arrows]), run_time=2)
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self.wait(1)
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# 场景2：构造辅助图形
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# 创建三个正方形
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square_a = Square(side_length=2, color=RED).next_to(tri, LEFT, buff=0)
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square_b = Square(side_length=3, color=BLUE).next_to(tri, DOWN, buff=0)
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square_c = Square(side_length=np.sqrt(13), color=GREEN).rotate(np.arctan(3 / 2)).next_to(tri, UR, buff=0)
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for s, t in zip([square_a, square_b, square_c], ["a^2", "b^2", "c^2"]):
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s.set_fill(opacity=0.2)
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self.play(Create(s), Write(Tex(t).move_to(s.get_center())), run_time=1.5)
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# 镜头聚焦
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self.play(
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self.camera.frame.animate.set_width(square_a.width * 3).move_to(VGroup(square_a, square_b)),
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run_time=2
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)
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# 场景3：图形重组动画
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# 切割正方形为三角形
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triangles = VGroup()
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for square in [square_a, square_b]:
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points = square.get_vertices()
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tri1 = Polygon(points[0], points[1], points[3], color=RED if square == square_a else BLUE)
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tri2 = Polygon(points[1], points[2], points[3], color=RED if square == square_a else BLUE)
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triangles.add(tri1, tri2)
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# 动画重组
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self.play(LaggedStart(*[tri.animate.rotate(PI / 2).shift(UR * 2) for tri in triangles]),
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run_time=3, rate_func=smooth)
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# 拼合新正方形
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new_square = Square(color=GREEN).surround(triangles)
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self.play(Transform(VGroup(triangles), new_square), run_time=2)
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# 场景4：面积等价证明
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# 并排对比
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original = VGroup(tri.copy(), square_a.copy(), square_b.copy()).scale(0.5).to_edge(LEFT)
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transformed = VGroup(new_square.copy(), square_c.copy()).scale(0.5).to_edge(RIGHT)
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self.play(
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FadeOut(arrows),
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Transform(VGroup(tri, square_a, square_b), original),
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Transform(VGroup(triangles, square_c), transformed),
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run_time=2
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)
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# 显示等式
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final_eq = Tex(r"a^2 + b^2 = c^2", color=YELLOW).scale(2)
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self.play(
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Write(final_eq),
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final_eq.animate.shift(UP * 1.5),
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self.camera.frame.animate.move_to(final_eq),
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run_time=2
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)
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# 粒子特效
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self.add(final_eq)
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self.play(
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final_eq.animate.scale(1.5).set_color_by_gradient(RED, BLUE, GREEN),
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rate_func=there_and_back,
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run_time=3
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)
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# 三维旋转（需启用ThreeDScene）
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self.play(
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final_eq.animate.rotate(30 * DEGREES, axis=UP),
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run_time=2,
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rate_func=smooth
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)
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self.wait(3)
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if __name__ == "__main__":
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config = {
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"quality": "high_quality",
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"preview": True,
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"media_dir": "./output",
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"pixel_height": 1080,
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"pixel_width": 1920,
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"background_color": "#333333", # 深色背景
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"format": "png" # 解决部分系统渲染问题
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}
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with tempconfig(config):
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scene = PythagoreanProof()
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scene.render() |
