{"id":420,"date":"2022-03-20T12:33:00","date_gmt":"2022-03-20T09:33:00","guid":{"rendered":"http:\/\/www.math.bas.bg\/omi\/didmod\/?page_id=420"},"modified":"2023-07-14T12:49:33","modified_gmt":"2023-07-14T09:49:33","slug":"vol-7-pp-21-29","status":"publish","type":"page","link":"http:\/\/www.math.bas.bg\/omi\/didmod\/?page_id=420","title":{"rendered":"Vol. 7, pp. 21-29"},"content":{"rendered":"\n<p style=\"font-size:14px;text-align:left\"> <em><a href=\"http:\/\/www.math.bas.bg\/omi\/didmod\/?page_id=58\">Didactical Modeling<\/a>, <a href=\"http:\/\/www.math.bas.bg\/omi\/didmod\/?page_id=243\">Vol. 7<\/a>, pp. 21-29<\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"text-align:center\"><strong>HILBERT\u2019S THIRD PROBLEM AND THE TEACHING OF GEOMETRY<\/strong><\/h3>\n\n\n\n<p style=\"text-align:center\"><em>Kiril Bankov <\/em><br><em>Faculty of Mathematics and Informatics, <\/em> <em>Sofia University \u201cSt, Kliment Ohridski\u201d <\/em><br><em>Institute of Mathematics and Informatics, Bulgarian Academy of Sciences <\/em><br><em>kbankov@fmi.uni-sofia.bg<\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Abstract &nbsp;<\/h3>\n\n\n\n<p>During the Second International Congress of Mathematicians\nheld in Paris in 1900, David Hilbert presented 23 unsolved mathematics\nproblems. Only one of them, the third, is related to teaching of mathematics.\nThe article examines the prerequisites that led to Hilbert&#8217;s third problem, its\nsolution, and its implication to the teaching of geometry \u2013 in particular, the\nsimilarity and difference between theoretical study of area and volume. <\/p>\n\n\n\n<p>Keywords: Hilbert\u2019s third problem, polygons of\nequal area, polyherdas of equal volume, equidecomposable figures.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"text-align:center\"><strong>REFERENCES <\/strong><\/h3>\n\n\n\n<p class=\"reference\">[1]&nbsp;&nbsp;&nbsp;&nbsp; Aigner,\nM., G. Ziegler. <em>Proofs from\nTHE BOOK<\/em> (Fourth Edition). Springer, 2010.&nbsp; <\/p>\n\n\n\n[2]&nbsp;&nbsp;&nbsp;&nbsp; \u0411\u0430\u043d\u043a\u043e\u0432,\n\u041a., \u0422. \u0412\u0438\u0442\u0430\u043d\u043e\u0432. <em>Geometry<\/em>, Anubis, Sofia, 2003.<\/p>\n\n\n\n[3]&nbsp;&nbsp;&nbsp;&nbsp; \u0411\u043e\u043b\u0442\u044f\u043d\u0441\u043a\u0438\u0439, \u0412. \u0413. \u0422\u0440\u0435\u0442\u044c\u044f \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0413\u0438\u043b\u0431\u0435\u0440\u0442\u0430. \u041d\u0430\u0443\u043a\u0430, \u041c\u043e\u0441\u043a\u0432\u0430, 1977<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>  <\/p>\n\n\n\n<div class=\"wp-block-button aligncenter is-style-squared\"><a class=\"wp-block-button__link has-text-color has-very-light-gray-color has-background\" href=\"http:\/\/www.math.bas.bg\/omi\/didmod\/articles\/volume07\/DidMod_Hilbert.pdf\" style=\"background-color:#009933\">FULL TEXT (In Bulgarian)<br><\/a><\/div>\n\n\n\n<p><br><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Didactical Modeling, Vol. 7, pp. 21-29 HILBERT\u2019S THIRD PROBLEM AND THE TEACHING OF GEOMETRY Kiril Bankov Faculty of Mathematics and Informatics, Sofia University \u201cSt, Kliment Ohridski\u201d Institute of Mathematics and Informatics, Bulgarian Academy of Sciences kbankov@fmi.uni-sofia.bg Abstract &nbsp; During the Second International Congress of Mathematicians held in Paris in 1900, David Hilbert presented 23 unsolved &hellip; <a href=\"http:\/\/www.math.bas.bg\/omi\/didmod\/?page_id=420\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Vol. 7, pp. 21-29<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":243,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-420","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.math.bas.bg\/omi\/didmod\/index.php?rest_route=\/wp\/v2\/pages\/420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.math.bas.bg\/omi\/didmod\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.math.bas.bg\/omi\/didmod\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.math.bas.bg\/omi\/didmod\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.math.bas.bg\/omi\/didmod\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=420"}],"version-history":[{"count":9,"href":"http:\/\/www.math.bas.bg\/omi\/didmod\/index.php?rest_route=\/wp\/v2\/pages\/420\/revisions"}],"predecessor-version":[{"id":707,"href":"http:\/\/www.math.bas.bg\/omi\/didmod\/index.php?rest_route=\/wp\/v2\/pages\/420\/revisions\/707"}],"up":[{"embeddable":true,"href":"http:\/\/www.math.bas.bg\/omi\/didmod\/index.php?rest_route=\/wp\/v2\/pages\/243"}],"wp:attachment":[{"href":"http:\/\/www.math.bas.bg\/omi\/didmod\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}