The Non-Euclidean, Hyperbolic Plane: Its Structure and Consistency
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1981
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid's, had a profound in fluence on man's understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli dean geometry with some mastery |
| Beschreibung: | 1 Online-Ressource (333p) |
| ISBN: | 9781461381259 9780387905525 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4613-8125-9 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042420668 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1981 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461381259 |c Online |9 978-1-4613-8125-9 | ||
| 020 | |a 9780387905525 |c Print |9 978-0-387-90552-5 | ||
| 024 | 7 | |a 10.1007/978-1-4613-8125-9 |2 doi | |
| 035 | |a (OCoLC)863786985 | ||
| 035 | |a (DE-599)BVBBV042420668 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 516 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Kelly, Paul |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Non-Euclidean, Hyperbolic Plane |b Its Structure and Consistency |c by Paul Kelly, Gordon Matthews |
| 264 | 1 | |a New York, NY |b Springer New York |c 1981 | |
| 300 | |a 1 Online-Ressource (333p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Universitext |x 0172-5939 | |
| 500 | |a The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid's, had a profound in fluence on man's understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli dean geometry with some mastery | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Hyperbolische Geometrie |0 (DE-588)4161041-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichteuklidische Geometrie |0 (DE-588)4042073-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hyperbolische Geometrie |0 (DE-588)4161041-6 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Nichteuklidische Geometrie |0 (DE-588)4042073-5 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 700 | 1 | |a Matthews, Gordon |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4613-8125-9 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027856085 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153092858445824 |
|---|---|
| any_adam_object | |
| author | Kelly, Paul |
| author_facet | Kelly, Paul |
| author_role | aut |
| author_sort | Kelly, Paul |
| author_variant | p k pk |
| building | Verbundindex |
| bvnumber | BV042420668 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863786985 (DE-599)BVBBV042420668 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-8125-9 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03003nmm a2200505zc 4500</leader><controlfield tag="001">BV042420668</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1981 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461381259</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4613-8125-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387905525</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-387-90552-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4613-8125-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863786985</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042420668</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kelly, Paul</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Non-Euclidean, Hyperbolic Plane</subfield><subfield code="b">Its Structure and Consistency</subfield><subfield code="c">by Paul Kelly, Gordon Matthews</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1981</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (333p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Universitext</subfield><subfield code="x">0172-5939</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid's, had a profound in fluence on man's understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli dean geometry with some mastery</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hyperbolische Geometrie</subfield><subfield code="0">(DE-588)4161041-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichteuklidische Geometrie</subfield><subfield code="0">(DE-588)4042073-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hyperbolische Geometrie</subfield><subfield code="0">(DE-588)4161041-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Nichteuklidische Geometrie</subfield><subfield code="0">(DE-588)4042073-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Matthews, Gordon</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4613-8125-9</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856085</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042420668 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461381259 9780387905525 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856085 |
| oclc_num | 863786985 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (333p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Universitext |
| spelling | Kelly, Paul Verfasser aut The Non-Euclidean, Hyperbolic Plane Its Structure and Consistency by Paul Kelly, Gordon Matthews New York, NY Springer New York 1981 1 Online-Ressource (333p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid's, had a profound in fluence on man's understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli dean geometry with some mastery Mathematics Geometry Mathematik Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Nichteuklidische Geometrie (DE-588)4042073-5 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 s 1\p DE-604 Nichteuklidische Geometrie (DE-588)4042073-5 s 2\p DE-604 Matthews, Gordon Sonstige oth https://doi.org/10.1007/978-1-4613-8125-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kelly, Paul The Non-Euclidean, Hyperbolic Plane Its Structure and Consistency Mathematics Geometry Mathematik Hyperbolische Geometrie (DE-588)4161041-6 gnd Nichteuklidische Geometrie (DE-588)4042073-5 gnd |
| subject_GND | (DE-588)4161041-6 (DE-588)4042073-5 |
| title | The Non-Euclidean, Hyperbolic Plane Its Structure and Consistency |
| title_auth | The Non-Euclidean, Hyperbolic Plane Its Structure and Consistency |
| title_exact_search | The Non-Euclidean, Hyperbolic Plane Its Structure and Consistency |
| title_full | The Non-Euclidean, Hyperbolic Plane Its Structure and Consistency by Paul Kelly, Gordon Matthews |
| title_fullStr | The Non-Euclidean, Hyperbolic Plane Its Structure and Consistency by Paul Kelly, Gordon Matthews |
| title_full_unstemmed | The Non-Euclidean, Hyperbolic Plane Its Structure and Consistency by Paul Kelly, Gordon Matthews |
| title_short | The Non-Euclidean, Hyperbolic Plane |
| title_sort | the non euclidean hyperbolic plane its structure and consistency |
| title_sub | Its Structure and Consistency |
| topic | Mathematics Geometry Mathematik Hyperbolische Geometrie (DE-588)4161041-6 gnd Nichteuklidische Geometrie (DE-588)4042073-5 gnd |
| topic_facet | Mathematics Geometry Mathematik Hyperbolische Geometrie Nichteuklidische Geometrie |
| url | https://doi.org/10.1007/978-1-4613-8125-9 |
| work_keys_str_mv | AT kellypaul thenoneuclideanhyperbolicplaneitsstructureandconsistency AT matthewsgordon thenoneuclideanhyperbolicplaneitsstructureandconsistency |