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Reshaping Convex Polyhedra by Orourke Joseph (14 results)
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Reshaping Convex Polyhedra
Seller: GreatBookPricesUK, Woodford Green, United Kingdom
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£ 109.92
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Reshaping Convex Polyhedra
Seller: Ria Christie Collections, Uxbridge, United Kingdom
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Reshaping Convex Polyhedra
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Reshaping Convex Polyhedra (Hardcover)
Published by Springer International Publishing AG, Cham, 2024
ISBN 10: 3031475100 ISBN 13: 9783031475108
Language: English
£ 124.99
Convert currency£ 37 shipping from United Kingdom to U.S.A.Quantity: 1 available
Add to basketHardcover. Condition: new. Hardcover. ^ the="" study="" of="" convex="" polyhedra="" in="" ordinary="" space="" is="" a="" central="" piece="" classical="" and="" modern="" geometry="" that="" has="" had="" significant="" impact="" on="" many="" areas="" mathematics="" also="" computer="" science.="" present="" book="" project="" by="" joseph="" orourke="" costin="" vilcu="" brings="" together="" two="" important="" strands="" subject="" ="" combinatorics="" polyhedra,="" intrinsic="" underlying="" surface.="" this="" leads="" to="" remarkable="" interplay="" concepts="" come="" life="" wide="" range="" very="" attractive="" topics="" concerning="" polyhedra.="" gets="" message="" across="" thetheory="" although="" with="" roots,="" still="" much="" alive="" today="" continues="" be="" inspiration="" basis="" lot="" current="" research="" activity.="" work="" presented="" manuscript="" interesting="" applications="" discrete="" computational="" geometry,="" as="" well="" other="" mathematics.="" treated="" detail="" include="" unfolding="" onto="" surfaces,="" continuous="" flattening="" convexity="" theory="" minimal="" length="" enclosing="" polygons.="" along="" way,="" open="" problems="" suitable="" for="" graduate="" students="" are="" raised,="" both="" aThe focus of this monograph is convertingreshapingone 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 Keplers 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 vertex-merging reshapes P to be closer to planarity. One endpoint of such a process leads to P being cut up and pasted inside a cylinder. Then rolling the cylinder on a plane achieves an unfolding of P. The underlying subtext is a question posed by Geoffrey Shephard in 1975 and already implied by drawings by Albrecht Duerer in the 15th century: whether every convex polyhedron can be unfolded to a planar net. Toward this end, the authors initiate an exploration of convexity on convex polyhedra, a topic rarely studiedin the literature but with considerable promise for future development.This monograph uncovers new research directions and reveals connections among several, apparently distant, topics in geometry: Alexandrovs Gluing Theorem, shortest paths and cut loci, Cauchys Arm Lemma, domes, quasigeodesics, convexity, and algorithms throughout. The interplay between these topics and the way the main ideas develop throughout the book could make the journey worthwhile for students and researchers in geometry, even if not directly interested in specific topics. Parts of the material will be of interest and accessible even to undergraduates. Although the proof difficulty varies from simple to quite intricate, with some proofs spanning several chapters, many examples and 125 figures help ease the exposition and illustrate th Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.
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Add to basketHardcover. Condition: Brand New. 257 pages. 9.26x6.10x0.75 inches. In Stock.
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£ 109.99
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Add to basketHardcover. Condition: Brand New. 257 pages. 9.26x6.10x0.75 inches. In Stock. This item is printed on demand.
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Reshaping Convex Polyhedra
Published by Springer Verlag Gmbh Apr 2025, 2025
ISBN 10: 3031475135 ISBN 13: 9783031475139
Language: English
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Add to basketTaschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware Englisch.
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Reshaping Convex Polyhedra
Published by Springer, Berlin|Springer Nature Switzerland|Springer, 2024
ISBN 10: 3031475100 ISBN 13: 9783031475108
Language: English
£ 95.25
Convert currency£ 41.25 shipping from Germany to U.S.A.Quantity: Over 20 available
Add to basketCondition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 Eucli.
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£ 171.76
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