D "urer's Unfolding Problem for Convex Polyhedra
D "urer's Unfolding Problem for Convex Polyhedra
复制标题
丢勒的凸多面体展开问题
DOI：
10.1090/noti1609
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发表时间：
2018
影响因子：
--
通讯作者：
Ghomi, Mohammad
中科院分区：
文献类型：
--
作者：
Ghomi, Mohammad
凸多面体是最古老的数学对象之一。事实上，构成欧几里得著作高潮的五个柏拉图立体，早在4,000年前就为苏格兰古人所知;见图1。在文艺复兴时期，多面体是艺术和数学的显着汇合再次着迷的对象，而画家发现的规则的角度和奠定基础的射影几何。艺术和数学的这种非凡融合体现在许多极具创造力的人身上，其中包括德国画家阿尔布雷希特·丢勒（Albrecht Dürer），他于16世纪初定居纽伦堡，被认为是北方文艺复兴的先驱。在阿尔卑斯山的长途旅行中，丢勒从他的意大利同时代人那里学到了透视法的规则，他随后在他有影响力的书《画家手册》中描述了这些规则。除了是第一个几何文本出版的德语，这项工作是显着的包含第一个记录的例子展开的多面体;见图2.一个（边）展开的多面体是切割它的过程沿着收集其边缘，没有断开它，使所得的表面可能会发展等距到平面。𝑃许多学校的孩子都熟悉剪出的过程
Convex polyhedra are among the oldest mathematical objects. Indeed the five platonic solids, which constitute the climax of Euclid’s books, were already known to the ancient people of Scotland some 4,000 years ago; see Figure 1. During the Renaissance, polyhedra were remarkable confluence of art and mathematics once again objects of fascination while painters were discovering the rules of perspective and laying the foundations of projective geometry. This remarkable confluence of art and mathematics was personified in a number of highly creative individuals including the German painter Albrecht Dürer, who was based in Nüremberg at the dawn of the sixteenth century and is credited with ushering in the Renaissance in Northern Europe. During extended trips over the Alps, Dürer learned the rules of perspective from his Italian contemporaries, and he subsequently described them in his influential book, The Painter’s Manual. Aside from being the first geometry text published in German, this work is remarkable for containing the first recorded examples of unfoldings of polyhedra; see Figure 2.An (edge) unfolding of a polyhedron 𝑃 is the process of cutting it along a collection of its edges, without disconnecting it, so that the resulting surface may be developed isometrically into the plane. Many school children are familiar with the process of cutting out
影响因子：
0.8
作者：
Barvinok, Nicholas;Ghomi, Mohammad
通讯作者：
Ghomi, Mohammad
凸多面体的仿射展开
DOI：
--
发表时间：
2013
期刊：
影响因子：
--
作者：
M. Ghomi
通讯作者：
M. Ghomi