论文标题
建筑物画廊：可视化建筑物
The Buildings Gallery: visualising buildings
论文作者
论文摘要
建筑物是美丽的数学对象，在非常直接的意义上将各种主题与代数的各种主题绑在一起。它们形成了自然的桥梁，以可视化群体理论中更复杂的原理。因此，它们提供了一个机会，可以向更广泛的受众谈论数学的内部运作，但是这些可视化也可以作为教学小组和建立理论的教学工具，我们相信它们甚至可以激发未来的研究。 我们提出了一种可视化这些几何对象的算法方法。主要成就是使用现有理论生成与$ bn $ pair相关的建筑物的三个维度交互式模型。最终产品是一种称为“建筑物库”的交互式Web应用程序，可以在https://buildings.gallery \ citep {bekker2020}上找到。
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an opportunity to talk about the inner workings of mathematics to a broader audience, but the visualisations could also serve as a didactic tool in teaching group and building theory, and we believe they can even inspire future research. We present an algorithmic method to visualise these geometric objects. The main accomplishment is the use of existing theory to produce three dimensional, interactive models of buildings associated to groups with a $BN$-pair. The final product, an interactive web application called The Buildings Gallery, can be found at https://buildings.gallery \citep{Bekker2020}.
