| 书目名称 | Reshaping Convex Polyhedra | | 编辑 | Joseph O‘Rourke,Costin Vîlcu | | 视频video | | | 概述 | Beautifully illustrated, the more elementary concepts of geometry are accessible to non-experts.Remarkable interplay of concepts come to life on a wide range of topics on polyhedra.Theory of convex po | | 图书封面 |  | | 描述 | .The focus of this monograph is converting—reshaping—one 3D convex polyhedron to another via an operation the authors call “tailoring.” A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a “vertex”) of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler’s “vertex truncation,” but differs in that the hole left by a truncated vertex is filled with new surface, whereas tailoring zips the hole closed. A powerful “gluing” theorem of A.D. Alexandrov from 1950 guarantees that, after closing the hole, the result is a new convex polyhedron. Given two convex polyhedra P, and Q inside P, repeated tailoringallows P to be reshaped to Q. Rescaling any Q to fit inside P, the result is universal: any P can be reshaped to any Q. This is one of the main theorems in Part I, with unexpected theoretical consequences..Part II carries out a systematic study of “vertex-merging,” a technique that can be viewed as a type of inverse operation to tailoring. Here the start is P which is gradually enlarged as much as possible, by inserting new surface along slits. In a sense, repeated verte | | 出版日期 | Book 2024 | | 关键词 | Alexandrov Gluing Theorem; tailoring operation; convex polyhedra; vertex-merging; digon-tailoring | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-47511-5 | | isbn_softcover | 978-3-031-47513-9 | | isbn_ebook | 978-3-031-47511-5 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 18:33:04
