{"id":5803,"date":"2020-07-23T14:54:49","date_gmt":"2020-07-23T18:54:49","guid":{"rendered":"https:\/\/notes.math.ca\/article\/richard-guy-and-geometry\/"},"modified":"2020-09-16T14:13:36","modified_gmt":"2020-09-16T18:13:36","slug":"richard-guy-and-geometry","status":"publish","type":"article","link":"https:\/\/notes.math.ca\/fr\/article\/richard-guy-and-geometry\/","title":{"rendered":"Richard Guy et la g\u00e9om\u00e9trie"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"5803\" class=\"elementor elementor-5803 elementor-5153\" data-elementor-post-type=\"article\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-59f020f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"59f020f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0095046\" data-id=\"0095046\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a751fe1 elementor-widget elementor-widget-text-editor\" data-id=\"a751fe1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>La recherche de Richard Guy en G\u00e9om\u00e9trie \u00e9tait motiv\u00e9e par (1) les liens entre la th\u00e9orie \u00e9l\u00e9mentaire des nombres et la g\u00e9om\u00e9trie, et (2) les nombreux probl\u00e8mes g\u00e9om\u00e9triques qui sont intuitifs (dans le sens de faciles \u00e0 \u00e9noncer) ou interpellant les \u00e9tudiants et les enseignants (dans les camps de math\u00e9matiques et les comp\u00e9titions). Ses contributions au domaine sont du style des g\u00e9om\u00e8tres britaniques tels D.M. Sommerville et H.F. Baker. Ce dernier est bien connu de nous avec ses six volumes <em>Principles of Geometry<\/em> [<a href=\"#EndnotesRG2\">Baker 10<\/a>] et <em>An Introduction to Plane Geometry<\/em> [<a href=\"#EndnotesRG2\">Baker 71<\/a>].<\/p><p>Comme exemples de (1), nous avons The <em>Lighthouse Theorem, Morley &amp; Malfatti \u2013 a budget of paradoxes<\/em> [<a href=\"#EndnotesRG2\">Guy 07<\/a>] et <em>Triangle-rectangle pairs with a common area and a common perimeter<\/em> [<a href=\"#EndnotesRG2\">Bremner et Guy 06<\/a>]. Dans le premier cas, Richard a fait la remarque: \u00a0\u201c<em>La combinaison de la g\u00e9om\u00e9trie et de la th\u00e9orie des nombres m\u2019est ch\u00e8re au coeur <\/em>\u201d, ladite combinaison ici \u00e9tant entre les triangles avec c\u00f4t\u00e9s entiers et les premiers <em>p<\/em> &gt; 7 ayant la propri\u00e9t\u00e9 que <em>p<\/em> = 3<em>n<\/em> + 1 et <em>p<\/em><sup>6<\/sup> = <em>a<\/em><sup>2<\/sup> + 4762800<em>b<\/em><sup>2<\/sup> avec des entiers uniques |<em>a<\/em>| et |<em>b<\/em>|. Dans le second cas, lui et Andrew Bremner ont prouv\u00e9 que de telles paires de triangles rectangles sont param\u00e9tr\u00e9es par une famille de courbes elliptiques.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9bb4355 elementor-widget elementor-widget-image\" data-id=\"9bb4355\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"768\" height=\"519\" src=\"https:\/\/notes.math.ca\/wp-content\/uploads\/2020\/07\/F3-768x519.jpg\" class=\"attachment-medium_large size-medium_large wp-image-5875\" alt=\"\" srcset=\"https:\/\/notes.math.ca\/wp-content\/uploads\/2020\/07\/F3-768x519.jpg 768w, https:\/\/notes.math.ca\/wp-content\/uploads\/2020\/07\/F3-300x203.jpg 300w, https:\/\/notes.math.ca\/wp-content\/uploads\/2020\/07\/F3-1024x693.jpg 1024w, https:\/\/notes.math.ca\/wp-content\/uploads\/2020\/07\/F3-1536x1039.jpg 1536w, https:\/\/notes.math.ca\/wp-content\/uploads\/2020\/07\/F3-2048x1385.jpg 2048w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Robert Woodrow, Richard et la doyenne de la Facult\u00e9 des sciences Lesley Rigg, mai 2017<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1cf4cca elementor-widget elementor-widget-text-editor\" data-id=\"1cf4cca\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Concernant (2), nous relions les nombreuses contributions de Richard aux sections de probl\u00e8mes du Am. Math. Monthly et de Math. Magazine, et \u00e0 son volume conjoint avec H. Croft et K. Falconer, <em>Unsolved Problems in Geometry<\/em> [<a href=\"#EndnotesRG2\">Croft et al. 94<\/a>]. Tel que W. Moser l\u2019a pr\u00e9dit pour l\u2019AMS dans sa critique de ce dernier volume [<a href=\"#EndnotesRG2\">Moser 94<\/a>], ledit volume est devenu la source d\u2019informations pour ceux et celles qui veulent faire de la recherche en g\u00e9om\u00e9trie intuitive (convexe, discr\u00e8te et combinatoire).<\/p>\n<p>Richard K. Guy \u00e9tait le coll\u00e8gue id\u00e9al: un grand connaisseur, toujours dispos\u00e9 \u00e0 aider et d\u2019une gentillesse sans borne. Avec la porte de son bureau ouverte en permanence, toujours dispos\u00e9 \u00e0 donner des conseils et \u00e0 \u00e9changer des id\u00e9es, il \u00e9tait l\u2019exemple parfait du v\u00e9n\u00e9rable professeur que l\u2019on puisse virtuellement imaginer. Nous sommes remplis de gratitude pour toutes les dizaines d\u2019ann\u00e9es qu\u2019il a pass\u00e9es avec nous.<\/p>\n<p><span style=\"color: #777777;\"><strong>Esquisses &nbsp;biographiques<\/strong><\/span><\/p>\n<p><span style=\"color: #777777;\">Tibor (Ted) Bisztriczky <em>est professeur de facult\u00e9 et professeur \u00e9m\u00e9rite au d\u00e9partement de math\u00e9matiques et de statistique \u00e0 l\u2019Universit\u00e9 de Calgary. Ses int\u00e9r\u00eats de recherche incluent la g\u00e9om\u00e9trie discr\u00e8te et convexe, particuli\u00e8rement l\u2019\u00e9tude des polytopes. Lui et Richard ont \u00e9t\u00e9 coll\u00e8gues plus de 40 ans et ont partag\u00e9 le m\u00eame corridor pendant les 30 derni\u00e8res ann\u00e9es.<\/em><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-68cb205 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"68cb205\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bc9be95\" data-id=\"bc9be95\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-44f9ddb elementor-widget elementor-widget-menu-anchor\" data-id=\"44f9ddb\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-menu-anchor\" id=\"EndnotesRG2\"><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c379cf3 elementor-widget elementor-widget-text-editor\" data-id=\"c379cf3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong>References<\/strong><\/p><p>[Baker 71] H. F. Baker, <em>An Introduction to Plane Geometry, With Many Examples<\/em>. Reprint of 1943 first edition. Chelsea Publishing Co., Bronx, NY, 1971.<\/p><p>[Baker 10] H. F. Baker, <em>Principles of Geometry<\/em>. Reprint of the original 6 volumes. Cambridge Library Collection. Cambridge University Press, 2010.<\/p><p>[Bremner and Guy 06] A. Bremner and R. K. Guy, Triangle-rectangle pairs with a common area and a common perimeter,<em> Int. J. Number Theory<\/em> <strong>2<\/strong> (2006), no. 2, 217-223.<\/p><p>[Croft et al 94] H. T. Croft, K. J. Falconer and R. K. Guy, <em>Unsolved Problems in Geometry<\/em>. Problem Books in Mathematics. Unsolved Problems in Intuitive Mathematics, II. Springer, New York, 1994<\/p><p>[Guy 07] R. K. Guy, The lighthouse theorem, Morley &amp; Malfatti \u2012 a budget of paradoxes. <em>Amer. Math. Monthly<\/em> <strong>114<\/strong> (2007), no. 2, 97-141.<\/p><p>[Moser 94] W. Moser, Review of <em>Unsolved Problems in Geometry<\/em> by H. T. Croft, K. J. Falconer and R. K. Guy, MR1316393 (95k:52001).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"author":6,"template":"","section":[227],"keyword":[],"class_list":["post-5803","article","type-article","status-publish","hentry","section-richard-kenneth-guy-1916-2020"],"toolset-meta":{"author-4-info":{"author-4-surname":{"type":"textfield","raw":""},"author-4-given-names":{"type":"textfield","raw":""},"author-4-honorific":{"type":"textfield","raw":""},"author-4-institution":{"type":"textfield","raw":""},"author-4-email":{"type":"email","raw":""},"author-4-cms-role":{"type":"textfield","raw":""}},"author-3-info":{"author-3-surname":{"type":"textfield","raw":""},"author-3-given-names":{"type":"textfield","raw":""},"author-3-honorific":{"type":"textfield","raw":""},"author-3-institution":{"type":"textfield","raw":""},"author-3-email":{"type":"email","raw":""},"author-3-cms-role":{"type":"textfield","raw":""}},"author-2-info":{"author-2-surname":{"type":"textfield","raw":""},"author-2-given-names":{"type":"textfield","raw":""},"author-2-honorific":{"type":"textfield","raw":""},"author-2-institution":{"type":"textfield","raw":""},"author-2-email":{"type":"email","raw":""},"author-2-cms-role":{"type":"textfield","raw":""}},"author-info":{"author-surname":{"type":"textfield","raw":"Bisztriczky"},"author-given-names":{"type":"textfield","raw":"T."},"author-honorific":{"type":"textfield","raw":""},"author-email":{"type":"email","raw":""},"author-institution":{"type":"textfield","raw":""},"author-cms-role":{"type":"textfield","raw":""}},"unknown":{"downloadable-pdf":{"type":"file","raw":"https:\/\/notes.math.ca\/wp-content\/uploads\/2020\/07\/Richard-Guy-et-la-g\u00e9om\u00e9trie-Notes-de-la-SMC-2.pdf","attachment_id":6225},"article-toc-weight":{"type":"numeric","raw":"64"},"author-surname":{"type":"textfield","raw":"Bisztriczky"},"author-given-names":{"type":"textfield","raw":"T."}}},"_links":{"self":[{"href":"https:\/\/notes.math.ca\/fr\/wp-json\/wp\/v2\/article\/5803","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/notes.math.ca\/fr\/wp-json\/wp\/v2\/article"}],"about":[{"href":"https:\/\/notes.math.ca\/fr\/wp-json\/wp\/v2\/types\/article"}],"author":[{"embeddable":true,"href":"https:\/\/notes.math.ca\/fr\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":17,"href":"https:\/\/notes.math.ca\/fr\/wp-json\/wp\/v2\/article\/5803\/revisions"}],"predecessor-version":[{"id":6568,"href":"https:\/\/notes.math.ca\/fr\/wp-json\/wp\/v2\/article\/5803\/revisions\/6568"}],"wp:attachment":[{"href":"https:\/\/notes.math.ca\/fr\/wp-json\/wp\/v2\/media?parent=5803"}],"wp:term":[{"taxonomy":"section","embeddable":true,"href":"https:\/\/notes.math.ca\/fr\/wp-json\/wp\/v2\/section?post=5803"},{"taxonomy":"keyword","embeddable":true,"href":"https:\/\/notes.math.ca\/fr\/wp-json\/wp\/v2\/keyword?post=5803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}