标题： Manim在STEM教育中的应用：通过动画可视化复杂问题 显示英文标题

标题： Manim for STEM Education: Visualizing Complex Problems Through Animation

摘要： 许多STEM概念由于其固有的复杂性和抽象性，对学生来说学习起来具有重大挑战。 通过动画可视化复杂问题可以显著提高学习效果。 然而，创建动画可能耗时且不方便。 因此，许多教育者通过在黑板或数字设备上手绘来解释复杂概念。 虽然静态图形有助于理解，但它们的效果不如动画。 免费开源的Python包Manim使教育者能够轻松创建视觉吸引人的动画。 Python简洁的语法结合Manim的一整套内置类和方法，大大简化了实现过程。 本文展示了一系列示例，说明如何使用Manim为计算机科学和数学的各种主题创建动画视频课程。 此外，它还分析了从多个社交媒体平台收集的观众反馈，以评估这些可视化的有效性和可访问性。 本文进一步探讨了Manim Python库的更广泛潜力，通过展示将它的应用扩展到计算机科学和数学以外学科领域的演示。 显示英文摘要

摘要： Many STEM concepts pose significant learning challenges to students due to their inherent complexity and abstract nature. Visualizing complex problems through animations can significantly enhance learning outcomes. However, the creation of animations can be time-consuming and inconvenient. Hence, many educators illustrate complex concepts by hand on a board or a digital device. Although static graphics are helpful for understanding, they are less effective than animations. The free and open-source Python package Manim enables educators to create visually compelling animations easily. Python's straightforward syntax, combined with Manim's comprehensive set of built-in classes and methods, greatly simplifies implementation. This article presents a series of examples that demonstrate how Manim can be used to create animated video lessons for a variety of topics in computer science and mathematics. In addition, it analyzes viewer feedback collected across multiple social media platforms to evaluate the effectiveness and accessibility of these visualizations. The article further explores broader potentials of the Manim Python library by showcasing demonstrations that extend its applications to subject areas beyond computer science and mathematics.