Barycentric calculus in Euclidean and hyperbolic geometry: a comparative introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2010
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and index Euclidean barycentric coordinates and the classic triangle centers -- Gyrovector spaces and Cartesian models of hyperbolic geometry -- The interplay of Einstein addition and vector addition -- Hyperbolic barycentric coordinates and hyperbolic triangle centers -- Hyperbolic incircles and excircles -- Hyperbolic tetrahedra -- Comparative patterns The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers. This unique book on barycentric calculus in Euclidean and hyperbolic geometry provides an introduction to the fascinating and beautiful subject of novel triangle centers in hyperbolic geometry along with analogies they share with familiar triangle centers in Euclidean geometry. As such, the book uncovers magnificent unifying notions that Euclidean and hyperbolic triangle centers share. In his earlier books the author adopted Cartesian coordinates, trigonometry and vector algebra for use in hyperbolic geometry that is fully analogous to the common use of Cartesian coordinates, trigonometry and vector algebra in Euclidean geometry. As a result, powerful tools that are commonly available in Euclidean geometry became available in hyperbolic geometry as well, enabling one to explore hyperbolic geometry in novel ways. In particular, this new book establishes hyperbolic barycentric coordinates that are used to determine various hyperbolic triangle centers just as Euclidean barycentric coordinates are commonly used to determine various Euclidean triangle centers. The hunt for Euclidean triangle centers is an old tradition in Euclidean geometry, resulting in a repertoire of more than three thousand triangle centers that are known by their barycentric coordinate representations. The aim of this book is to initiate a fully analogous hunt for hyperbolic triangle centers that will broaden the repertoire of hyperbolic triangle centers provided here |
| Beschreibung: | 1 Online-Ressource (xiv, 344 p.) |
| ISBN: | 9789814304931 9789814304948 981430493X 9814304948 |
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| 500 | |a The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers. This unique book on barycentric calculus in Euclidean and hyperbolic geometry provides an introduction to the fascinating and beautiful subject of novel triangle centers in hyperbolic geometry along with analogies they share with familiar triangle centers in Euclidean geometry. As such, the book uncovers magnificent unifying notions that Euclidean and hyperbolic triangle centers share. In his earlier books the author adopted Cartesian coordinates, trigonometry and vector algebra for use in hyperbolic geometry that is fully analogous to the common use of Cartesian coordinates, trigonometry and vector algebra in Euclidean geometry. As a result, powerful tools that are commonly available in Euclidean geometry became available in hyperbolic geometry as well, enabling one to explore hyperbolic geometry in novel ways. In particular, this new book establishes hyperbolic barycentric coordinates that are used to determine various hyperbolic triangle centers just as Euclidean barycentric coordinates are commonly used to determine various Euclidean triangle centers. The hunt for Euclidean triangle centers is an old tradition in Euclidean geometry, resulting in a repertoire of more than three thousand triangle centers that are known by their barycentric coordinate representations. The aim of this book is to initiate a fully analogous hunt for hyperbolic triangle centers that will broaden the repertoire of hyperbolic triangle centers provided here | ||
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| 650 | 7 | |a Calculus |2 fast | |
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| 650 | 4 | |a Geometry, Hyperbolic | |
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Datensatz im Suchindex
| _version_ | 1804175618816868352 |
|---|---|
| any_adam_object | |
| author | Ungar, Abraham A. |
| author_facet | Ungar, Abraham A. |
| author_role | aut |
| author_sort | Ungar, Abraham A. |
| author_variant | a a u aa aau |
| building | Verbundindex |
| bvnumber | BV043154845 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)743806200 (DE-599)BVBBV043154845 |
| dewey-full | 516.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.22 |
| dewey-search | 516.22 |
| dewey-sort | 3516.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:09Z |
| institution | BVB |
| isbn | 9789814304931 9789814304948 981430493X 9814304948 |
| language | English |
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| physical | 1 Online-Ressource (xiv, 344 p.) |
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| publisher | World Scientific |
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| spelling | Ungar, Abraham A. Verfasser aut Barycentric calculus in Euclidean and hyperbolic geometry a comparative introduction Abraham Albert Ungar Singapore World Scientific c2010 1 Online-Ressource (xiv, 344 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and index Euclidean barycentric coordinates and the classic triangle centers -- Gyrovector spaces and Cartesian models of hyperbolic geometry -- The interplay of Einstein addition and vector addition -- Hyperbolic barycentric coordinates and hyperbolic triangle centers -- Hyperbolic incircles and excircles -- Hyperbolic tetrahedra -- Comparative patterns The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers. This unique book on barycentric calculus in Euclidean and hyperbolic geometry provides an introduction to the fascinating and beautiful subject of novel triangle centers in hyperbolic geometry along with analogies they share with familiar triangle centers in Euclidean geometry. As such, the book uncovers magnificent unifying notions that Euclidean and hyperbolic triangle centers share. In his earlier books the author adopted Cartesian coordinates, trigonometry and vector algebra for use in hyperbolic geometry that is fully analogous to the common use of Cartesian coordinates, trigonometry and vector algebra in Euclidean geometry. As a result, powerful tools that are commonly available in Euclidean geometry became available in hyperbolic geometry as well, enabling one to explore hyperbolic geometry in novel ways. In particular, this new book establishes hyperbolic barycentric coordinates that are used to determine various hyperbolic triangle centers just as Euclidean barycentric coordinates are commonly used to determine various Euclidean triangle centers. The hunt for Euclidean triangle centers is an old tradition in Euclidean geometry, resulting in a repertoire of more than three thousand triangle centers that are known by their barycentric coordinate representations. The aim of this book is to initiate a fully analogous hunt for hyperbolic triangle centers that will broaden the repertoire of hyperbolic triangle centers provided here MATHEMATICS / Geometry / General bisacsh Calculus fast Geometry, Hyperbolic fast Geometry, Plane fast Triangle fast Geometry, Plane Geometry, Hyperbolic Triangle Calculus Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Spezielle Relativitätstheorie (DE-588)4182215-8 gnd rswk-swf Spezielle Relativitätstheorie (DE-588)4182215-8 s Hyperbolische Geometrie (DE-588)4161041-6 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=374868 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ungar, Abraham A. Barycentric calculus in Euclidean and hyperbolic geometry a comparative introduction MATHEMATICS / Geometry / General bisacsh Calculus fast Geometry, Hyperbolic fast Geometry, Plane fast Triangle fast Geometry, Plane Geometry, Hyperbolic Triangle Calculus Hyperbolische Geometrie (DE-588)4161041-6 gnd Spezielle Relativitätstheorie (DE-588)4182215-8 gnd |
| subject_GND | (DE-588)4161041-6 (DE-588)4182215-8 |
| title | Barycentric calculus in Euclidean and hyperbolic geometry a comparative introduction |
| title_auth | Barycentric calculus in Euclidean and hyperbolic geometry a comparative introduction |
| title_exact_search | Barycentric calculus in Euclidean and hyperbolic geometry a comparative introduction |
| title_full | Barycentric calculus in Euclidean and hyperbolic geometry a comparative introduction Abraham Albert Ungar |
| title_fullStr | Barycentric calculus in Euclidean and hyperbolic geometry a comparative introduction Abraham Albert Ungar |
| title_full_unstemmed | Barycentric calculus in Euclidean and hyperbolic geometry a comparative introduction Abraham Albert Ungar |
| title_short | Barycentric calculus in Euclidean and hyperbolic geometry |
| title_sort | barycentric calculus in euclidean and hyperbolic geometry a comparative introduction |
| title_sub | a comparative introduction |
| topic | MATHEMATICS / Geometry / General bisacsh Calculus fast Geometry, Hyperbolic fast Geometry, Plane fast Triangle fast Geometry, Plane Geometry, Hyperbolic Triangle Calculus Hyperbolische Geometrie (DE-588)4161041-6 gnd Spezielle Relativitätstheorie (DE-588)4182215-8 gnd |
| topic_facet | MATHEMATICS / Geometry / General Calculus Geometry, Hyperbolic Geometry, Plane Triangle Hyperbolische Geometrie Spezielle Relativitätstheorie |
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