Meissner’s Mysterious Bodies
Meissner’s Mysterious Bodies
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DOI：
10.1007/s00283-011-9239-y
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发表时间：
2011-07
期刊：
影响因子：
--
通讯作者：
B. Kawohl;Christof Weber
中科院分区：
文献类型：
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作者：
B. Kawohl;Christof Weber
某些三维凸体有一个违反直觉的性质：它们的宽度是恒定的。在这一点上，它们看起来像一个球体，但又不是一个球体。迈斯纳天体发现于一个世纪以前，人们经常对它进行修正，以使给定宽度的天体的体积最小化。然而，这一猜想仍然是开放的。我们提请注意这一具有挑战性的和美丽的开放的问题，通过介绍它的一些历史和最近的发展。
Certain three-dimensional convex bodies have a counterintuitive property; they are of constant width. In this particular respect they resemble a sphere without being one. Discovered a century ago, Meissner’s bodies have often been conjectured to minimize volume among bodies of given constant width. However, this conjecture is still open. We draw attention to this challenging and beautiful open problem by presenting some of its history and its recent development.