Pythagorean Triples from Harmonic Sequences
Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)
Gespeichert in:
Veröffentlicht in: | The Mathematics teacher 2001-03, Vol.94 (3), p.218-222 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 222 |
---|---|
container_issue | 3 |
container_start_page | 218 |
container_title | The Mathematics teacher |
container_volume | 94 |
creator | DiDomenico, Angelo S. Tanner, Randy J. |
description | Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR) |
doi_str_mv | 10.5951/MT.94.3.0218 |
format | Article |
fullrecord | <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_journals_204701805</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ericid>EJ673730</ericid><jstor_id>20870637</jstor_id><sourcerecordid>20870637</sourcerecordid><originalsourceid>FETCH-LOGICAL-c1075-77c7d3332089f163b64f28851f5afef0e4d337407299eac112df1f83939634df3</originalsourceid><addsrcrecordid>eNo9kE1LAzEQhoMoWKs3jwqL17rr5GuTHKVUq7QouJ5DTBPd0m5q0h76701Z6Vzm8DzMy7wIXWOouOL4Yd5UilW0AoLlCRoQSqEELskpGgAQXnJRq3N0kdIS8jAJAzR6329_zHeIznRFE9vNyqXCx7AupiauQ9fa4sP97lxnXbpEZ96skrv630P0-TRpxtNy9vb8Mn6clRaD4KUQViwopQSk8rimXzXzREqOPTfeeXAsU8FAEKWcsRiThcdeUkVVTdnC0yG66-9uYsjRaauXYRe7HKkJMAFYAs_SfS_ZGFKKzutNbNcm7jUGfWhDzxutmKb60EbWb3rdxdYe1clrLaigkPFtj5dpG-KR5xcE1Nn4AxLgYnI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>204701805</pqid></control><display><type>article</type><title>Pythagorean Triples from Harmonic Sequences</title><source>JSTOR Mathematics & Statistics</source><source>JSTOR</source><creator>DiDomenico, Angelo S. ; Tanner, Randy J.</creator><creatorcontrib>DiDomenico, Angelo S. ; Tanner, Randy J.</creatorcontrib><description>Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)</description><identifier>ISSN: 0025-5769</identifier><identifier>EISSN: 2330-0582</identifier><identifier>DOI: 10.5951/MT.94.3.0218</identifier><identifier>CODEN: MATAAP</identifier><language>eng</language><publisher>Reston: National Council of Teachers of Mathematics</publisher><subject>Algebra ; Arithmetic ; Deduction ; Discovery Learning ; Fibonacci numbers ; Geometric Concepts ; High School Students ; Induction ; Integers ; Interdisciplinary Approach ; Mathematical sequences ; Mathematical sets ; Mathematics education ; Mathematics Instruction ; Mathematics Teachers ; Numbers ; Patterns in Mathematics ; Pythagoreanism ; Secondary Education ; Secondary school students ; Teaching Methods ; Triangles</subject><ispartof>The Mathematics teacher, 2001-03, Vol.94 (3), p.218-222</ispartof><rights>Copyright © 2001 The National Council of Teachers of Mathematics, Inc.</rights><rights>Copyright National Council of Teachers of Mathematics Mar 2001</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/20870637$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/20870637$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27924,27925,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttp://eric.ed.gov/ERICWebPortal/detail?accno=EJ673730$$DView record in ERIC$$Hfree_for_read</backlink></links><search><creatorcontrib>DiDomenico, Angelo S.</creatorcontrib><creatorcontrib>Tanner, Randy J.</creatorcontrib><title>Pythagorean Triples from Harmonic Sequences</title><title>The Mathematics teacher</title><description>Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)</description><subject>Algebra</subject><subject>Arithmetic</subject><subject>Deduction</subject><subject>Discovery Learning</subject><subject>Fibonacci numbers</subject><subject>Geometric Concepts</subject><subject>High School Students</subject><subject>Induction</subject><subject>Integers</subject><subject>Interdisciplinary Approach</subject><subject>Mathematical sequences</subject><subject>Mathematical sets</subject><subject>Mathematics education</subject><subject>Mathematics Instruction</subject><subject>Mathematics Teachers</subject><subject>Numbers</subject><subject>Patterns in Mathematics</subject><subject>Pythagoreanism</subject><subject>Secondary Education</subject><subject>Secondary school students</subject><subject>Teaching Methods</subject><subject>Triangles</subject><issn>0025-5769</issn><issn>2330-0582</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNo9kE1LAzEQhoMoWKs3jwqL17rr5GuTHKVUq7QouJ5DTBPd0m5q0h76701Z6Vzm8DzMy7wIXWOouOL4Yd5UilW0AoLlCRoQSqEELskpGgAQXnJRq3N0kdIS8jAJAzR6329_zHeIznRFE9vNyqXCx7AupiauQ9fa4sP97lxnXbpEZ96skrv630P0-TRpxtNy9vb8Mn6clRaD4KUQViwopQSk8rimXzXzREqOPTfeeXAsU8FAEKWcsRiThcdeUkVVTdnC0yG66-9uYsjRaauXYRe7HKkJMAFYAs_SfS_ZGFKKzutNbNcm7jUGfWhDzxutmKb60EbWb3rdxdYe1clrLaigkPFtj5dpG-KR5xcE1Nn4AxLgYnI</recordid><startdate>20010301</startdate><enddate>20010301</enddate><creator>DiDomenico, Angelo S.</creator><creator>Tanner, Randy J.</creator><general>National Council of Teachers of Mathematics</general><scope>7SW</scope><scope>BJH</scope><scope>BNH</scope><scope>BNI</scope><scope>BNJ</scope><scope>BNO</scope><scope>ERI</scope><scope>PET</scope><scope>REK</scope><scope>WWN</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>0-V</scope><scope>3V.</scope><scope>7XB</scope><scope>88B</scope><scope>8A4</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ALSLI</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CJNVE</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M0P</scope><scope>M2O</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQEDU</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20010301</creationdate><title>Pythagorean Triples from Harmonic Sequences</title><author>DiDomenico, Angelo S. ; Tanner, Randy J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1075-77c7d3332089f163b64f28851f5afef0e4d337407299eac112df1f83939634df3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Algebra</topic><topic>Arithmetic</topic><topic>Deduction</topic><topic>Discovery Learning</topic><topic>Fibonacci numbers</topic><topic>Geometric Concepts</topic><topic>High School Students</topic><topic>Induction</topic><topic>Integers</topic><topic>Interdisciplinary Approach</topic><topic>Mathematical sequences</topic><topic>Mathematical sets</topic><topic>Mathematics education</topic><topic>Mathematics Instruction</topic><topic>Mathematics Teachers</topic><topic>Numbers</topic><topic>Patterns in Mathematics</topic><topic>Pythagoreanism</topic><topic>Secondary Education</topic><topic>Secondary school students</topic><topic>Teaching Methods</topic><topic>Triangles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>DiDomenico, Angelo S.</creatorcontrib><creatorcontrib>Tanner, Randy J.</creatorcontrib><collection>ERIC</collection><collection>ERIC (Ovid)</collection><collection>ERIC</collection><collection>ERIC</collection><collection>ERIC (Legacy Platform)</collection><collection>ERIC( SilverPlatter )</collection><collection>ERIC</collection><collection>ERIC PlusText (Legacy Platform)</collection><collection>Education Resources Information Center (ERIC)</collection><collection>ERIC</collection><collection>CrossRef</collection><collection>ProQuest Social Sciences Premium Collection</collection><collection>ProQuest Central (Corporate)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Education Database (Alumni Edition)</collection><collection>Education Periodicals</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Social Science Premium Collection</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Education Collection</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Education Journals</collection><collection>ProQuest Research Library</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Research Library China</collection><collection>ProQuest One Education</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><collection>ProQuest Central Basic</collection><jtitle>The Mathematics teacher</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>DiDomenico, Angelo S.</au><au>Tanner, Randy J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><ericid>EJ673730</ericid><atitle>Pythagorean Triples from Harmonic Sequences</atitle><jtitle>The Mathematics teacher</jtitle><date>2001-03-01</date><risdate>2001</risdate><volume>94</volume><issue>3</issue><spage>218</spage><epage>222</epage><pages>218-222</pages><issn>0025-5769</issn><eissn>2330-0582</eissn><coden>MATAAP</coden><abstract>Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)</abstract><cop>Reston</cop><pub>National Council of Teachers of Mathematics</pub><doi>10.5951/MT.94.3.0218</doi><tpages>5</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0025-5769 |
ispartof | The Mathematics teacher, 2001-03, Vol.94 (3), p.218-222 |
issn | 0025-5769 2330-0582 |
language | eng |
recordid | cdi_proquest_journals_204701805 |
source | JSTOR Mathematics & Statistics; JSTOR |
subjects | Algebra Arithmetic Deduction Discovery Learning Fibonacci numbers Geometric Concepts High School Students Induction Integers Interdisciplinary Approach Mathematical sequences Mathematical sets Mathematics education Mathematics Instruction Mathematics Teachers Numbers Patterns in Mathematics Pythagoreanism Secondary Education Secondary school students Teaching Methods Triangles |
title | Pythagorean Triples from Harmonic Sequences |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T22%3A29%3A41IST&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=Pythagorean%20Triples%20from%20Harmonic%20Sequences&rft.jtitle=The%20Mathematics%20teacher&rft.au=DiDomenico,%20Angelo%20S.&rft.date=2001-03-01&rft.volume=94&rft.issue=3&rft.spage=218&rft.epage=222&rft.pages=218-222&rft.issn=0025-5769&rft.eissn=2330-0582&rft.coden=MATAAP&rft_id=info:doi/10.5951/MT.94.3.0218&rft_dat=%3Cjstor_proqu%3E20870637%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=204701805&rft_id=info:pmid/&rft_ericid=EJ673730&rft_jstor_id=20870637&rfr_iscdi=true |