Illustrating Mathematics
Illustrating Mathematics
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说明数学
DOI：
10.1080/10724117.2021.1940509
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Eischen, Ellen
中科院分区：
文献类型：
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作者：
Eischen, Ellen
当你听到“说明数学”这个短语时，你会想到什么？也许你会想到你在餐巾纸背面画的草图，试图理解一个数学问题，作为推广项目的一部分的3D打印对象，允许研究人员进行实验的计算机图形，博物馆里的优雅雕塑，或者完全不同的东西。数学插图扮演着各种各样的强大角色，这些角色往往模糊在一起，相互影响。在《图解数学》（AMS 2020）一书中，编辑戴安娜·戴维斯收集了一系列令人印象深刻的图片和数学艺术家的描述，展示了插图在数学中的多方面作用。这本书是按媒介组织的，从古老的方法，如绘画，到较新的方法，如3D打印。在这本书中，我们遇到了木材，激光反射系统的镜子，乐高积木，激光切割拼图，流形编织纱线，等等，在一系列广泛的主题表示。虽然图片本身很漂亮，但伴随的故事增加了深度和灵感。每一章交替之间的一个完整的页面图像的一块和一个页面与创作者的讨论的一块。一些贡献者透露了他们在制作可视化时的意外发现。例如，数学家史蒂夫·特雷特尔（Steve Trettel）写道，他只是在打印一个瓷砖家族的木材切割图时才发现的特征，但在相应的计算机图像中没有注意到。在新旧技术的结合中，数学家凯瑟琳·斯坦格描述了如何打印她的计算机生成的图形，并用尺子和指南针测量它们，从而得出了一些定理，这些定理后来成为她在《国际数学研究通告》上发表的一篇论文中证明的定理。斯坦格还写道，她在编码时犯的错误经常会导致洞察力。许多贡献者分享了他们遇到的挑战，这对于考虑使用类似媒介的读者来说是一个有价值的功能。有时，创作者只是警告困难，而其他时候，他们也提供解决方案。在数学家和设计师之间合作的一个特别令人满意的例子中，Heidi Robb和Peter Benson解释了数学家Dylan Thurston如何帮助他们克服了最初制作激光切割木材瓷砖的问题。另一方面，有时一个人必须在内部工作，
Reviewed by Ellen Eischen hat comes to mind when you hear the phrase “illustrating mathematics”? Perhaps you think of a sketch you drew on the back of a napkin to try to understand a math problem, an object 3D printed as part of an outreach project, computer graphics that allow a researcher to experiment, an elegant sculpture in a museum, or something entirely different. Mathematical illustration plays a wide variety of powerful roles, which often blur together and influence each other. In the book Illustrating Mathematics (AMS 2020), editor Diana Davis has assembled an impressive collection of pictures and mathematical artists’ descriptions that show off the multifaceted roles of illustration in mathematics. The book is organized by medium, ranging from ancient approaches, like drawing, to newer ones, like 3D printing. In the book, we encounter wood, lasers bouncing off systems of mirrors, LEGO bricks, laser-cut puzzles, manifolds knit from yarn, and more, in representations of a wide array of topics. While the pictures are beautiful on their own, the accompanying stories add depth and inspiration. Each chapter alternates between a full-page image of a piece and a page with the creator’s discussion of the piece. Several contributors reveal unexpected discoveries that they made while producing their visualizations. For example, mathematician Steve Trettel writes of features he discovered only as he printed wood cutouts of a family of tilings but had not noticed in the corresponding computer images. In a mix of old and new technologies, mathematician Katherine Stange describes how printing her computer-generated graphics and measuring them with a ruler and compass led to conjectures, which later became theorems that she proved in a paper published in International Mathematics ResearchNotices. Stange also writes that errors she made while coding often led to insights. Many contributors share challenges that they encountered, a valuable feature for readers considering working with similar mediums. Sometimes, the creators merely warn of difficulties, while other times they also provide solutions. In a particularly satisfying example of collaboration between mathematicians and designers, Heidi Robb and Peter Benson explain how mathematician Dylan Thurston helped them overcome an issue in their initial approach to making a laser-cut wood tiling. On the other hand, sometimes one must work within