标题： 仿射和凸空间：融合分析与几何观点 显示英文标题

标题： Affine and convex spaces: blending the analytic and geometric viewpoints

摘要： 这是一篇关于仿射空间和凸空间的简短介绍，特别为物理学生而写。 它总结了数学文献中不同的基本陈述，并融合了分析和几何风格的表述。 还提供了参考文献，以及对格拉斯曼空间的简要讨论，并给出一个示例，说明仿射空间在牛顿力学中的相关性和实用性。 显示英文摘要

摘要： This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured presentations. References are also provided, as well as a brief discussion of Grassmann spaces and an example showing the relevance and usefulness of affine spaces in Newtonian physics.