Mathematical models as artefacts for research: Felix Klein and the case of Kummer surfaces
Mathematical models as artefacts for research: Felix Klein and the case of Kummer surfaces
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作为研究人工制品的数学模型：Felix Klein 和 Kummer 曲面的案例
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发表时间：
2013
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通讯作者：
D. Rowe
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作者：
D. Rowe
已经作为一个学生在波恩，菲利克斯克莱因接触到模型制作通过他的老师，朱利叶斯Plücker，谁使用模型可视化的性质，特殊的表面出现在线几何。之后，克莱因参加了库默的研讨会在柏林，在那里他开始探索之间的联系一般库默表面和所谓的复杂表面，首先研究了普吕克。在19世纪70年代末，克莱因和亚历山大布里尔监督工作的几个学生在慕尼黑技术学院谁设计了大量收集的模型有。随后，模型生产进入了一个新的时代，总部设在慕尼黑，但通过布里尔兄弟拥有的达姆施塔特公司进行销售。到1900年，L. Brill的石膏模型可以在世界各地的顶尖大学找到。我们的故事在这里集中在库默的著名模型，开始作为研究文物在柏林，然后传递到慕尼黑，然后扩散到点以外。
Already as a student in Bonn, Felix Klein was exposed to model-making through his teacher, Julius Plücker, who used models to visualize the properties of special surfaces that arise in line geometry. Afterward, Klein attended Kummer’s seminar in Berlin, where he began to explore the connections between general Kummer surfaces and so-called complex surfaces, first studied by Plücker. In the late 1870s, Klein and Alexander Brill supervised the work of several students at the Munich Technische Hochschule who designed a large collection of models there. There followed a new era in model production, based in Munich but marketed through the Darmstadt firm owned by Brill’s brother. By 1900 the plaster models of L. Brill could be found at leading universities around the world. Our story here centres on Kummer’s famous models, which began as research artefacts in Berlin, before passing to Munich and then proliferating to points beyond.