Algebra and geometry of Hamilton's quaternions
Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he consi...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2016-06 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Krishnaswami, Govind S Sachdev, Sonakshi |
| description | Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations. |
| format | Article |
| fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2079150293</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2079150293</sourcerecordid><originalsourceid>FETCH-proquest_journals_20791502933</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQc8xJT00qSlRIzEtRSE_Nz00tKapUyE9T8EjMzcwpyc9TL1YoLE0sSS3Ky8zPK-ZhYE1LzClO5YXS3AzKbq4hzh66BUX5haWpxSXxWfmlRXlAqXgjA3NLQ1MDI0tjY-JUAQDrNDJQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2079150293</pqid></control><display><type>article</type><title>Algebra and geometry of Hamilton's quaternions</title><source>Free E- Journals</source><creator>Krishnaswami, Govind S ; Sachdev, Sonakshi</creator><creatorcontrib>Krishnaswami, Govind S ; Sachdev, Sonakshi</creatorcontrib><description>Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algebra ; Complex numbers ; Division ; Geometry ; Number systems ; Quaternions</subject><ispartof>arXiv.org, 2016-06</ispartof><rights>2016. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Krishnaswami, Govind S</creatorcontrib><creatorcontrib>Sachdev, Sonakshi</creatorcontrib><title>Algebra and geometry of Hamilton's quaternions</title><title>arXiv.org</title><description>Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations.</description><subject>Algebra</subject><subject>Complex numbers</subject><subject>Division</subject><subject>Geometry</subject><subject>Number systems</subject><subject>Quaternions</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQc8xJT00qSlRIzEtRSE_Nz00tKapUyE9T8EjMzcwpyc9TL1YoLE0sSS3Ky8zPK-ZhYE1LzClO5YXS3AzKbq4hzh66BUX5haWpxSXxWfmlRXlAqXgjA3NLQ1MDI0tjY-JUAQDrNDJQ</recordid><startdate>20160610</startdate><enddate>20160610</enddate><creator>Krishnaswami, Govind S</creator><creator>Sachdev, Sonakshi</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20160610</creationdate><title>Algebra and geometry of Hamilton's quaternions</title><author>Krishnaswami, Govind S ; Sachdev, Sonakshi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20791502933</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algebra</topic><topic>Complex numbers</topic><topic>Division</topic><topic>Geometry</topic><topic>Number systems</topic><topic>Quaternions</topic><toplevel>online_resources</toplevel><creatorcontrib>Krishnaswami, Govind S</creatorcontrib><creatorcontrib>Sachdev, Sonakshi</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Krishnaswami, Govind S</au><au>Sachdev, Sonakshi</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Algebra and geometry of Hamilton's quaternions</atitle><jtitle>arXiv.org</jtitle><date>2016-06-10</date><risdate>2016</risdate><eissn>2331-8422</eissn><abstract>Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2016-06 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_proquest_journals_2079150293 |
| source | Free E- Journals |
| subjects | Algebra Complex numbers Division Geometry Number systems Quaternions |
| title | Algebra and geometry of Hamilton's quaternions |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T17%3A52%3A25IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Algebra%20and%20geometry%20of%20Hamilton's%20quaternions&rft.jtitle=arXiv.org&rft.au=Krishnaswami,%20Govind%20S&rft.date=2016-06-10&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2079150293%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2079150293&rft_id=info:pmid/&rfr_iscdi=true |