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from manim import *
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import numpy as np
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class PythagoreanProof(Scene):
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def update_step(self, current_text, new_content, duration=1.5):
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"""带淡入淡出效果的步骤更新"""
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new_text = Text(new_content, font="Microsoft YaHei", font_size=32).to_edge(UP, buff=0.8)
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new_text.set_color_by_gradient(GOLD, ORANGE)
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if current_text:
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self.play(
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FadeOut(current_text, shift=UP * 0.3),
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FadeIn(new_text, shift=DOWN * 0.3),
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run_time=0.8
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)
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else:
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self.play(FadeIn(new_text, shift=DOWN))
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self.wait(duration)
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return new_text
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def create_square(self, start, end, color):
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"""创建与边垂直的正方形"""
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# 计算边的向量
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edge_vector = end - start
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# 获取垂直向量（逆时针90度）
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perp_vector = np.array([-edge_vector[1], edge_vector[0], 0])
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# 标准化垂直向量
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perp_unit = perp_vector / np.linalg.norm(perp_vector)
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# 生成正方形四个顶点
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return Polygon(
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start,
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end,
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end + perp_unit * np.linalg.norm(edge_vector),
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start + perp_unit * np.linalg.norm(edge_vector),
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color=color,
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fill_opacity=0.8,
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stroke_width=4
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)
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def construct(self):
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current_step = None
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elements = VGroup()
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# === 步骤1：绘制直角三角形 ===
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current_step = self.update_step(None, "步骤1：绘制直角三角形")
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# 定义三角形顶点（使用NumPy数组）
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A = np.array([-2.0, -1.0, 0.0])
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B = np.array([2.0, -1.0, 0.0])
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C = np.array([0.0, 2.0, 0.0]) # 调整为更明显的直角三角形
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triangle = Polygon(A, B, C, color=BLUE, fill_opacity=0.8, stroke_width=4)
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elements.add(triangle)
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self.play(Create(triangle), run_time=2)
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self.wait()
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# === 步骤2：构建三个正方形 ===
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current_step = self.update_step(current_step, "步骤2：构建三个正方形")
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# 创建三个边的正方形（正确垂直方向）
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square_AB = self.create_square(A, B, ORANGE)
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square_BC = self.create_square(B, C, GREEN)
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square_AC = self.create_square(C, A, YELLOW)
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# 调整正方形位置使其向外扩展
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square_AB.shift((A + B) / 2 - square_AB.get_center() + DOWN * 0.5)
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square_BC.rotate(PI / 2, about_point=B)
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square_AC.rotate(-PI / 2, about_point=C)
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self.play(
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LaggedStart(
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Create(square_AB),
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Create(square_BC),
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Create(square_AC),
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lag_ratio=0.3
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),
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run_time=4
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)
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elements.add(square_AB, square_BC, square_AC)
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self.wait()
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# === 步骤3：面积变换演示 ===
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current_step = self.update_step(current_step, "步骤3：面积恒等变换")
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# 创建可移动三角形（从AC边开始）
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moving_tri = self.create_square(A, C, PINK)
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self.play(FadeIn(moving_tri), run_time=1)
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# 旋转动画
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self.play(
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Rotate(
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moving_tri,
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angle=PI / 2,
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about_point=A,
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rate_func=smooth
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),
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run_time=2
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)
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self.wait()
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# === 步骤4：最终结论 ===
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current_step = self.update_step(current_step, "步骤4：得出结论")
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# 数学公式
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formula = MathTex(r"a^2 + b^2 = c^2", color=GOLD).scale(2)
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formula_box = SurroundingRectangle(formula, color=WHITE, buff=0.5)
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self.play(
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FadeOut(elements),
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FadeOut(moving_tri),
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run_time=1
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)
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self.play(
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DrawBorderThenFill(formula_box),
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Write(formula),
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run_time=2
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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"
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}
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with tempconfig(config):
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scene = PythagoreanProof()
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scene.render() |
