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140 lines
4.5 KiB
140 lines
4.5 KiB
from manim import *
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import numpy as np
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class PythagoreanProof(Scene):
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def construct(self):
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self.show_title()
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self.show_triangle()
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self.create_squares()
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self.transform_shapes()
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self.show_final_equation()
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def show_title(self):
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"""显示标题"""
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title = Text("勾股定理证明", font_size=48)
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title.set_color_by_gradient(BLUE, GREEN)
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self.play(Write(title))
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self.wait(2)
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self.play(title.animate.to_edge(UP))
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self.title = title
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def show_triangle(self):
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"""创建初始三角形"""
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# 使用三维坐标定义三角形顶点
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self.A = [-2, -1, 0]
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self.B = [2, -1, 0]
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self.C = [2, 2, 0]
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self.triangle = Polygon(self.A, self.B, self.C,
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color=WHITE, fill_opacity=0.5)
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self.play(Create(self.triangle), run_time=2)
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# 添加边标签
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self.label_a = MathTex("a").next_to(self.triangle, LEFT)
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self.label_b = MathTex("b").next_to(self.triangle, DOWN)
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self.label_c = MathTex("c", color=YELLOW).next_to(self.triangle, UR)
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self.play(LaggedStart(
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Write(self.label_a),
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Write(self.label_b),
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Write(self.label_c),
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lag_ratio=0.3
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))
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self.wait()
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def create_squares(self):
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"""创建三个正方形"""
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# 计算正方形边长
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a_length = np.linalg.norm(np.array(self.B) - np.array(self.A))
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b_length = np.linalg.norm(np.array(self.C) - np.array(self.B))
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c_length = np.linalg.norm(np.array(self.C) - np.array(self.A))
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# 创建正方形并保存为实例属性
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self.square_a = Square(side_length=a_length, color=RED, fill_opacity=0.3)
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self.square_a.next_to(self.triangle, LEFT)
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self.square_b = Square(side_length=b_length, color=BLUE, fill_opacity=0.3)
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self.square_b.next_to(self.triangle, DOWN)
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self.square_c = Square(side_length=c_length, color=GREEN, fill_opacity=0.3)
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self.square_c.rotate(np.arctan2(3, 4)).next_to(self.triangle, UR)
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# 添加面积标签
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self.area_a = MathTex("a^2").next_to(self.square_a, LEFT)
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self.area_b = MathTex("b^2").next_to(self.square_b, DOWN)
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self.area_c = MathTex("c^2").next_to(self.square_c, UR)
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# 动画序列
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self.play(
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LaggedStart(
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Create(self.square_a),
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Create(self.square_b),
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Create(self.square_c),
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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.play(
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Write(self.area_a),
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Write(self.area_b),
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Write(self.area_c)
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)
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self.wait(2)
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def transform_shapes(self):
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"""形状变换动画"""
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# 分解正方形为三角形
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self.triangles = VGroup()
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for _ in range(4):
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tri = Polygon(self.A, self.B, self.C,
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color=RED, fill_opacity=0.3)
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self.triangles.add(tri)
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# 定义目标位置（三维坐标）
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target_positions = [
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[3, 2, 0], # 右上
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[-3, 2, 0], # 左上
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[3, -3, 0], # 右下
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[-3, -3, 0] # 左下
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]
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# 创建动画序列
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animations = []
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for i, pos in enumerate(target_positions):
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anim = self.triangles[i].animate.rotate(PI / 2).move_to(pos)
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animations.append(anim)
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# 执行动画
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self.play(
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Transform(self.square_a, self.triangles),
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*animations,
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run_time=3
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)
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self.wait()
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# 创建最终正方形
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final_square = Square(side_length=5, color=GOLD, fill_opacity=0.3)
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self.play(Create(final_square))
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self.wait(2)
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def show_final_equation(self):
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"""显示最终公式"""
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equation = MathTex("a^2 + b^2 = c^2", color=YELLOW).scale(2)
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equation.set_color_by_gradient(RED, BLUE, GREEN)
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self.play(
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Write(equation),
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Flash(equation, color=YELLOW, line_length=1),
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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.background_color = "#1a1a1a"
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config.frame_width = 16
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config.frame_height = 9
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config.pixel_width = 1920
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config.pixel_height = 1080
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scene = PythagoreanProof()
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scene.render() |