{"id":2247,"date":"2024-06-29T10:16:48","date_gmt":"2024-06-29T10:16:48","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2247"},"modified":"2024-06-30T00:11:00","modified_gmt":"2024-06-30T00:11:00","slug":"reflecting-on-parabolas","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/reflecting-on-parabolas\/","title":{"rendered":"Reflecting on parabolas"},"content":{"rendered":"\n
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Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

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Reflecting on parabolas<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

David E. Dobbs <\/strong><\/i>
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320, USA.<\/p>\n\n\n\n

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Pages 45-77 | Received 15 July 2023, Accepted 08 October 2023, Published 30 June 2024 <\/span><\/p>\n\n\n\n

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Abstract<\/span><\/strong><\/p>\n\n\n\n

Two known results are proven in this teaching note. First, a proof of the reflection property of parabolas is given; that proof would be accessible early in a calculus class or in a course that combines precalculus with an introduction to differential calculus. Second, that reflection property plays a key role in a characterization of parabolas; that proof solves an initial value problem concerning a first order ordinary differential equation, and so it would be accessible early in a course on differential equations or in some courses on integral calculus. A closing remark discusses characterization results and classification results.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  Euclidean analytic geometry, parabola, focus, directrix, tangential half-line, vector, dot product, inverse cosine function, derivative, initial value problem.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 51-02; Secondary 51N20, 33B10, 97G70, 26A06, 34-01.<\/p>\n\n\n\n

Downloads:<\/strong> Full-text PDF<\/a><\/p>\n<\/div>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles Reflecting on parabolas David E. Dobbs  Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320, USA. Pages 45-77 | Received 15 July 2023, Accepted 08 October 2023, Published 30 June 2024 Abstract Two known results are proven in this teaching note. First, a proof of Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-2247","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2247","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=2247"}],"version-history":[{"count":3,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2247\/revisions"}],"predecessor-version":[{"id":2316,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2247\/revisions\/2316"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}