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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_polygon(self, points, color, fill_opacity=0.8):
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"""创建带样式的多边形"""
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return Polygon(*points,
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color=color,
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fill_opacity=fill_opacity,
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stroke_width=4)
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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：使用NumPy数组定义坐标 ===
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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([1.0, 1.5, 0.0])
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triangle = self.create_polygon([A, B, C], BLUE)
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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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# 计算向量
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vector_AC = C - A
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vector_BC = C - B
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# 构建正方形坐标点（使用向量运算）
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square_a = Square(side_length=4, color=ORANGE).shift(DOWN * 2)
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square_b_points = [
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A,
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C,
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C + vector_AC * 0.8,
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A + vector_AC * 0.8
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]
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square_b = self.create_polygon(square_b_points, ORANGE)
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square_c_points = [
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B,
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C,
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C + vector_BC * 0.8,
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B + vector_BC * 0.8
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]
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square_c = self.create_polygon(square_c_points, ORANGE)
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self.play(
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LaggedStart(
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Create(square_a),
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Create(square_b),
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Create(square_c),
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lag_ratio=0.4
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),
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run_time=3
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)
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elements.add(square_a, square_b, square_c)
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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
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moving_tri_points = [C, A, A + (A - C) * 0.8]
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moving_tri = self.create_polygon(moving_tri_points, YELLOW)
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self.play(Create(moving_tri), run_time=1)
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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", # 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() |
