Quartic Polynomials and the Golden Ratio
Totland investigates graphs of quartic polynomials with inflection points by means of certain naturally defined points and length ratios. He sees that the graph of every quartic polynomial with inflection points can be obtained as the image of the graph of the symmetric quartic subject to an appro...
Gespeichert in:
| Veröffentlicht in: | Mathematics magazine 2009-06, Vol.82 (3), p.197-201 |
|---|---|
| 1. Verfasser: | |
| Format: | Magazinearticle |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 201 |
|---|---|
| container_issue | 3 |
| container_start_page | 197 |
| container_title | Mathematics magazine |
| container_volume | 82 |
| creator | TOTLAND, HARALD |
| description | Totland investigates graphs of quartic polynomials with inflection points by means of certain naturally defined points and length ratios. He sees that the graph of every quartic polynomial with inflection points can be obtained as the image of the graph of the symmetric quartic subject to an appropriate affine transformation. An affine transformation consists of an invertible linear transformation followed by translation along a constant vector. An affine transformation of the plane has the following properties: straight lines are mapped to straight lines, parallel lines to parallel lines, and tangents to tangents, while length ratios between parallel line segments are preserved. |
| doi_str_mv | 10.1080/0025570X.2009.11953618 |
| format | Magazinearticle |
| fullrecord | <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_miscellaneous_229875602</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>27765901</jstor_id><sourcerecordid>27765901</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2072-e3c82484e75e9602f55d62549c2c8656c7c0e30a486280d0787a99dbfa7937673</originalsourceid><addsrcrecordid>eNo9kDtPwzAURi0EEqXwE0DZYEm4vo5fI6qgIFXiIZDYLOM4IlUSFzsd-u9JVMp0h3vONxxCrigUFBTcAiDnEj4LBNAFpZozQdURmVHNIAet4JjMJiifqFNyltIagKJAMSM3r1sbh8ZlL6Hd9aFrbJsy21fZ8O2zZWgr32dvdmjCOTmpx5-_-Ltz8vFw_754zFfPy6fF3Sp3CBJzz5zCUpVecq8FYM15JZCX2qFTggsnHXgGtlQCFVQglbRaV1-1lZpJIdmcXO93NzH8bH0aTNck59vW9j5sk0HUSvJxeSTFnnQxpBR9bTax6WzcGQpmKmMOZcxUxhzKjOLlXlynIcR_C6UUXANlv-AEXVA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>magazinearticle</recordtype><pqid>229875602</pqid></control><display><type>magazinearticle</type><title>Quartic Polynomials and the Golden Ratio</title><source>Jstor Complete Legacy</source><source>Alma/SFX Local Collection</source><source>JSTOR Mathematics & Statistics</source><creator>TOTLAND, HARALD</creator><creatorcontrib>TOTLAND, HARALD</creatorcontrib><description> Totland investigates graphs of quartic polynomials with inflection points by means of certain naturally defined points and length ratios. He sees that the graph of every quartic polynomial with inflection points can be obtained as the image of the graph of the symmetric quartic subject to an appropriate affine transformation. An affine transformation consists of an invertible linear transformation followed by translation along a constant vector. An affine transformation of the plane has the following properties: straight lines are mapped to straight lines, parallel lines to parallel lines, and tangents to tangents, while length ratios between parallel line segments are preserved.</description><identifier>ISSN: 0025-570X</identifier><identifier>EISSN: 1930-0980</identifier><identifier>DOI: 10.1080/0025570X.2009.11953618</identifier><language>eng</language><publisher>Washington: Mathematical Association of America</publisher><subject>Geometric lines ; Geometry ; Golden mean ; Graphs ; Inflection points ; Line graphs ; Mathematics education ; Parallel lines ; Pentagrams ; Polynomials ; Property lines ; Quartic polynomials ; Tangents ; Theorems ; Vertices</subject><ispartof>Mathematics magazine, 2009-06, Vol.82 (3), p.197-201</ispartof><rights>Copyright 2009 Mathematical Association of America (Incorporated)</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2072-e3c82484e75e9602f55d62549c2c8656c7c0e30a486280d0787a99dbfa7937673</citedby><cites>FETCH-LOGICAL-c2072-e3c82484e75e9602f55d62549c2c8656c7c0e30a486280d0787a99dbfa7937673</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/27765901$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/27765901$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>776,780,799,828,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>TOTLAND, HARALD</creatorcontrib><title>Quartic Polynomials and the Golden Ratio</title><title>Mathematics magazine</title><description> Totland investigates graphs of quartic polynomials with inflection points by means of certain naturally defined points and length ratios. He sees that the graph of every quartic polynomial with inflection points can be obtained as the image of the graph of the symmetric quartic subject to an appropriate affine transformation. An affine transformation consists of an invertible linear transformation followed by translation along a constant vector. An affine transformation of the plane has the following properties: straight lines are mapped to straight lines, parallel lines to parallel lines, and tangents to tangents, while length ratios between parallel line segments are preserved.</description><subject>Geometric lines</subject><subject>Geometry</subject><subject>Golden mean</subject><subject>Graphs</subject><subject>Inflection points</subject><subject>Line graphs</subject><subject>Mathematics education</subject><subject>Parallel lines</subject><subject>Pentagrams</subject><subject>Polynomials</subject><subject>Property lines</subject><subject>Quartic polynomials</subject><subject>Tangents</subject><subject>Theorems</subject><subject>Vertices</subject><issn>0025-570X</issn><issn>1930-0980</issn><fulltext>true</fulltext><rsrctype>magazinearticle</rsrctype><creationdate>2009</creationdate><recordtype>magazinearticle</recordtype><recordid>eNo9kDtPwzAURi0EEqXwE0DZYEm4vo5fI6qgIFXiIZDYLOM4IlUSFzsd-u9JVMp0h3vONxxCrigUFBTcAiDnEj4LBNAFpZozQdURmVHNIAet4JjMJiifqFNyltIagKJAMSM3r1sbh8ZlL6Hd9aFrbJsy21fZ8O2zZWgr32dvdmjCOTmpx5-_-Ltz8vFw_754zFfPy6fF3Sp3CBJzz5zCUpVecq8FYM15JZCX2qFTggsnHXgGtlQCFVQglbRaV1-1lZpJIdmcXO93NzH8bH0aTNck59vW9j5sk0HUSvJxeSTFnnQxpBR9bTax6WzcGQpmKmMOZcxUxhzKjOLlXlynIcR_C6UUXANlv-AEXVA</recordid><startdate>20090601</startdate><enddate>20090601</enddate><creator>TOTLAND, HARALD</creator><general>Mathematical Association of America</general><general>Taylor & Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20090601</creationdate><title>Quartic Polynomials and the Golden Ratio</title><author>TOTLAND, HARALD</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2072-e3c82484e75e9602f55d62549c2c8656c7c0e30a486280d0787a99dbfa7937673</frbrgroupid><rsrctype>magazinearticle</rsrctype><prefilter>magazinearticle</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Geometric lines</topic><topic>Geometry</topic><topic>Golden mean</topic><topic>Graphs</topic><topic>Inflection points</topic><topic>Line graphs</topic><topic>Mathematics education</topic><topic>Parallel lines</topic><topic>Pentagrams</topic><topic>Polynomials</topic><topic>Property lines</topic><topic>Quartic polynomials</topic><topic>Tangents</topic><topic>Theorems</topic><topic>Vertices</topic><toplevel>online_resources</toplevel><creatorcontrib>TOTLAND, HARALD</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Mathematics magazine</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>TOTLAND, HARALD</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quartic Polynomials and the Golden Ratio</atitle><jtitle>Mathematics magazine</jtitle><date>2009-06-01</date><risdate>2009</risdate><volume>82</volume><issue>3</issue><spage>197</spage><epage>201</epage><pages>197-201</pages><issn>0025-570X</issn><eissn>1930-0980</eissn><abstract> Totland investigates graphs of quartic polynomials with inflection points by means of certain naturally defined points and length ratios. He sees that the graph of every quartic polynomial with inflection points can be obtained as the image of the graph of the symmetric quartic subject to an appropriate affine transformation. An affine transformation consists of an invertible linear transformation followed by translation along a constant vector. An affine transformation of the plane has the following properties: straight lines are mapped to straight lines, parallel lines to parallel lines, and tangents to tangents, while length ratios between parallel line segments are preserved.</abstract><cop>Washington</cop><pub>Mathematical Association of America</pub><doi>10.1080/0025570X.2009.11953618</doi><tpages>5</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-570X |
| ispartof | Mathematics magazine, 2009-06, Vol.82 (3), p.197-201 |
| issn | 0025-570X 1930-0980 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_229875602 |
| source | Jstor Complete Legacy; Alma/SFX Local Collection; JSTOR Mathematics & Statistics |
| subjects | Geometric lines Geometry Golden mean Graphs Inflection points Line graphs Mathematics education Parallel lines Pentagrams Polynomials Property lines Quartic polynomials Tangents Theorems Vertices |
| title | Quartic Polynomials and the Golden Ratio |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-08T16%3A23%3A59IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Quartic%20Polynomials%20and%20the%20Golden%20Ratio&rft.jtitle=Mathematics%20magazine&rft.au=TOTLAND,%20HARALD&rft.date=2009-06-01&rft.volume=82&rft.issue=3&rft.spage=197&rft.epage=201&rft.pages=197-201&rft.issn=0025-570X&rft.eissn=1930-0980&rft_id=info:doi/10.1080/0025570X.2009.11953618&rft_dat=%3Cjstor_proqu%3E27765901%3C/jstor_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=229875602&rft_id=info:pmid/&rft_jstor_id=27765901&rfr_iscdi=true |