A mathematical tapestry demonstrating the beautiful unity of mathematics
This easy-to-read 2010 book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any...
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| Sprache: | English |
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2010
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| 245 | 1 | 0 | |a A mathematical tapestry |b demonstrating the beautiful unity of mathematics |c Peter Hilton, Jean Pedersen ; with illustrations by Sylvie Donmoyer |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Flexagons : a beginning thread -- Another thread : 1-period paper folding -- More paper folding threads : 2-period paper-folding -- A number-theory thread : folding numbers, a number trick, and some titbits -- The polyhedron thread : building some polyhedra and defining a regular polyhedron -- Constructing dipyramids and rotating rings from straight strips of triangles -- Continuing the paper-folding and number-theory threads -- A geometry and algebra thread : constructing, and using, Jennifer's puzzle -- A polyhedral geometry thread : constructing braided Platonic solids and other woven polyhedra -- Combinatorial and symmetry threads -- Some golden threads : constructing more dodecahedra -- More combinatorial threads : collapsoids -- Group theory : the faces of the trihexaflexagon -- Combinatorial and group-theoretical threads : extended face planes of the Platonic solids -- A historical thread : involving the Euler characteristic, Descartes' total angular defect, and Pólya's dream -- Tying some loose ends together : symmetry, group theory, homologues, and the Pólya enumeration theorem -- Returning to the number-theory thread : generalized quasi-order and coach theorems | |
| 520 | |a This easy-to-read 2010 book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Paper work | |
| 650 | 4 | |a Geometrical models | |
| 650 | 4 | |a Polyhedra / Models | |
| 650 | 4 | |a Mathematics / Study and teaching | |
| 650 | 4 | |a Geometry / Study and teaching | |
| 650 | 4 | |a Combinatorial geometry / Study and teaching | |
| 650 | 4 | |a Mathematical recreations | |
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Datensatz im Suchindex
| _version_ | 1819298752982155264 |
|---|---|
| any_adam_object | |
| author | Hilton, Peter John 1923-2010 |
| author2 | Donmoyer, Sylvie |
| author2_role | ill |
| author2_variant | s d sd |
| author_GND | (DE-588)115702822 (DE-588)115702997 (DE-588)142985783 |
| author_facet | Hilton, Peter John 1923-2010 Donmoyer, Sylvie |
| author_role | aut |
| author_sort | Hilton, Peter John 1923-2010 |
| author_variant | p j h pj pjh |
| building | Verbundindex |
| bvnumber | BV043945195 |
| classification_rvk | SK 180 SK 380 |
| collection | ZDB-20-CBO |
| contents | Flexagons : a beginning thread -- Another thread : 1-period paper folding -- More paper folding threads : 2-period paper-folding -- A number-theory thread : folding numbers, a number trick, and some titbits -- The polyhedron thread : building some polyhedra and defining a regular polyhedron -- Constructing dipyramids and rotating rings from straight strips of triangles -- Continuing the paper-folding and number-theory threads -- A geometry and algebra thread : constructing, and using, Jennifer's puzzle -- A polyhedral geometry thread : constructing braided Platonic solids and other woven polyhedra -- Combinatorial and symmetry threads -- Some golden threads : constructing more dodecahedra -- More combinatorial threads : collapsoids -- Group theory : the faces of the trihexaflexagon -- Combinatorial and group-theoretical threads : extended face planes of the Platonic solids -- A historical thread : involving the Euler characteristic, Descartes' total angular defect, and Pólya's dream -- Tying some loose ends together : symmetry, group theory, homologues, and the Pólya enumeration theorem -- Returning to the number-theory thread : generalized quasi-order and coach theorems |
| ctrlnum | (ZDB-20-CBO)CR9780511777004 (OCoLC)967688090 (DE-599)BVBBV043945195 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511777004 |
| format | Electronic eBook |
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| id | DE-604.BV043945195 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T05:34:27Z |
| institution | BVB |
| isbn | 9780511777004 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029354165 |
| oclc_num | 967688090 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xv, 290 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Hilton, Peter John 1923-2010 Verfasser (DE-588)115702822 aut A mathematical tapestry demonstrating the beautiful unity of mathematics Peter Hilton, Jean Pedersen ; with illustrations by Sylvie Donmoyer Cambridge Cambridge University Press 2010 1 online resource (xv, 290 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Flexagons : a beginning thread -- Another thread : 1-period paper folding -- More paper folding threads : 2-period paper-folding -- A number-theory thread : folding numbers, a number trick, and some titbits -- The polyhedron thread : building some polyhedra and defining a regular polyhedron -- Constructing dipyramids and rotating rings from straight strips of triangles -- Continuing the paper-folding and number-theory threads -- A geometry and algebra thread : constructing, and using, Jennifer's puzzle -- A polyhedral geometry thread : constructing braided Platonic solids and other woven polyhedra -- Combinatorial and symmetry threads -- Some golden threads : constructing more dodecahedra -- More combinatorial threads : collapsoids -- Group theory : the faces of the trihexaflexagon -- Combinatorial and group-theoretical threads : extended face planes of the Platonic solids -- A historical thread : involving the Euler characteristic, Descartes' total angular defect, and Pólya's dream -- Tying some loose ends together : symmetry, group theory, homologues, and the Pólya enumeration theorem -- Returning to the number-theory thread : generalized quasi-order and coach theorems This easy-to-read 2010 book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth Mathematik Mathematics Paper work Geometrical models Polyhedra / Models Mathematics / Study and teaching Geometry / Study and teaching Combinatorial geometry / Study and teaching Mathematical recreations Regelmäßiges Polygon (DE-588)4312085-4 gnd rswk-swf Unterhaltungsmathematik (DE-588)4124357-2 gnd rswk-swf Regelmäßiges Polygon (DE-588)4312085-4 s 1\p DE-604 Unterhaltungsmathematik (DE-588)4124357-2 s DE-604 Pedersen, Jean Sonstige (DE-588)115702997 oth Donmoyer, Sylvie (DE-588)142985783 ill Erscheint auch als Druckausgabe 978-0-521-12821-6 Erscheint auch als Druckausgabe 978-0-521-76410-0 https://doi.org/10.1017/CBO9780511777004 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hilton, Peter John 1923-2010 A mathematical tapestry demonstrating the beautiful unity of mathematics Flexagons : a beginning thread -- Another thread : 1-period paper folding -- More paper folding threads : 2-period paper-folding -- A number-theory thread : folding numbers, a number trick, and some titbits -- The polyhedron thread : building some polyhedra and defining a regular polyhedron -- Constructing dipyramids and rotating rings from straight strips of triangles -- Continuing the paper-folding and number-theory threads -- A geometry and algebra thread : constructing, and using, Jennifer's puzzle -- A polyhedral geometry thread : constructing braided Platonic solids and other woven polyhedra -- Combinatorial and symmetry threads -- Some golden threads : constructing more dodecahedra -- More combinatorial threads : collapsoids -- Group theory : the faces of the trihexaflexagon -- Combinatorial and group-theoretical threads : extended face planes of the Platonic solids -- A historical thread : involving the Euler characteristic, Descartes' total angular defect, and Pólya's dream -- Tying some loose ends together : symmetry, group theory, homologues, and the Pólya enumeration theorem -- Returning to the number-theory thread : generalized quasi-order and coach theorems Mathematik Mathematics Paper work Geometrical models Polyhedra / Models Mathematics / Study and teaching Geometry / Study and teaching Combinatorial geometry / Study and teaching Mathematical recreations Regelmäßiges Polygon (DE-588)4312085-4 gnd Unterhaltungsmathematik (DE-588)4124357-2 gnd |
| subject_GND | (DE-588)4312085-4 (DE-588)4124357-2 |
| title | A mathematical tapestry demonstrating the beautiful unity of mathematics |
| title_auth | A mathematical tapestry demonstrating the beautiful unity of mathematics |
| title_exact_search | A mathematical tapestry demonstrating the beautiful unity of mathematics |
| title_full | A mathematical tapestry demonstrating the beautiful unity of mathematics Peter Hilton, Jean Pedersen ; with illustrations by Sylvie Donmoyer |
| title_fullStr | A mathematical tapestry demonstrating the beautiful unity of mathematics Peter Hilton, Jean Pedersen ; with illustrations by Sylvie Donmoyer |
| title_full_unstemmed | A mathematical tapestry demonstrating the beautiful unity of mathematics Peter Hilton, Jean Pedersen ; with illustrations by Sylvie Donmoyer |
| title_short | A mathematical tapestry |
| title_sort | a mathematical tapestry demonstrating the beautiful unity of mathematics |
| title_sub | demonstrating the beautiful unity of mathematics |
| topic | Mathematik Mathematics Paper work Geometrical models Polyhedra / Models Mathematics / Study and teaching Geometry / Study and teaching Combinatorial geometry / Study and teaching Mathematical recreations Regelmäßiges Polygon (DE-588)4312085-4 gnd Unterhaltungsmathematik (DE-588)4124357-2 gnd |
| topic_facet | Mathematik Mathematics Paper work Geometrical models Polyhedra / Models Mathematics / Study and teaching Geometry / Study and teaching Combinatorial geometry / Study and teaching Mathematical recreations Regelmäßiges Polygon Unterhaltungsmathematik |
| url | https://doi.org/10.1017/CBO9780511777004 |
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