{"id":12305,"date":"2015-03-31T19:17:43","date_gmt":"2015-03-31T18:17:43","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12305"},"modified":"2022-02-06T00:22:25","modified_gmt":"2022-02-06T00:22:25","slug":"topics-in-the-history-of-mathematics","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12305","title":{"rendered":"Topics in the History of Mathematics"},"content":{"rendered":"<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2015\/03\/THM.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12306\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12306\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2015\/03\/THM.png\" data-orig-size=\"794,403\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"THM\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2015\/03\/THM.png\" class=\"alignright wp-image-12306\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2015\/03\/THM-300x152.png\" alt=\"THM\" width=\"400\" height=\"203\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2015\/03\/THM-300x152.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2015\/03\/THM.png 794w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>The Emergence of Greek Mathematics<\/li>\n<li>The Vernacular Tradition<\/li>\n<li style=\"text-align: left;\">Marin Mersenne: The Birth of Modern Geometry<\/li>\n<li>The Founding of the Royal Society<\/li>\n<li>The Birth of Calculus<\/li>\n<li>Non-Euclidean Geometry<\/li>\n<li>Paris and the New Mathematics<\/li>\n<li>The Liberation of \u00c1lgebra<\/li>\n<\/ol>\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_69795\"  width=\"480\" height=\"270\"  data-origwidth=\"480\" data-origheight=\"270\" src=\"https:\/\/www.youtube.com\/embed\/UPlqJaUi5jE?enablejsapi=1&#038;origin=https:\/\/www.acasinhadamatematica.pt&#038;list=PLLEMpXvr0s1RdMeDq6zdvwiOJUUfPMitr&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=1&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;hl=pt_PT&#038;theme=dark&#038;color=red&#038;controls=1&#038;disablekb=0&#038;\" class=\"__youtube_prefs__  epyt-is-override  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\n<p style=\"text-align: left;\">\n<h4 style=\"text-align: left;\">The Emergence of Greek Mathematics<\/h4>\n<p style=\"text-align: left;\"><a href=\"http:\/\/en.wikipedia.org\/wiki\/Euclid\" target=\"_blank\" rel=\"noopener noreferrer\">Euclid<\/a>\u2019s \u2018<a href=\"http:\/\/aleph0.clarku.edu\/~djoyce\/java\/elements\/elements.html\" target=\"_blank\" rel=\"noopener noreferrer\">Elements<\/a>\u2019 is one of the world\u2019s most reprinted books. How did it come about and why does it remain a classic textbook? Examines the 13 books in detail starting with the idea of proof.<\/p>\n<h4 style=\"text-align: left;\">The Vernacular Tradition<\/h4>\n<p style=\"text-align: left;\">Deals largely with the low-level mathematics of the Middle Ages and its application to problems of commerce and everyday life. Renaissance notational styles are compared by looking at the works of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Luca_Pacioli\" target=\"_blank\" rel=\"noopener noreferrer\">Luca Pacioli<\/a> and <a href=\"http:\/\/en.wikipedia.org\/wiki\/Nicolas_Chuquet\" target=\"_blank\" rel=\"noopener noreferrer\">Nicholas Chuquet<\/a>. Each of these works were compendiums of basic mathematical knowledge which themselves derive from the work of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Fibonacci\" target=\"_blank\" rel=\"noopener noreferrer\">Leonardo of Pisa<\/a>, also known as Fibonacci. Leonardo\u2019s \u2018<a href=\"http:\/\/en.wikipedia.org\/wiki\/Liber_Abaci\" target=\"_blank\" rel=\"noopener noreferrer\">Liber Abaci<\/a>\u2019 was the first in Europe to promote calculation methods using the Hindu-Arabic numerals. Illustrates a problem-solving method known as double false position, which could be used to solve algebraic-type problems without any knowledge of algebra. These methods owe their inspiration to a work by an Islamic mathematician, <a href=\"http:\/\/en.wikipedia.org\/wiki\/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB\" target=\"_blank\" rel=\"noopener noreferrer\">Al-Khwarizmi<\/a>. Shows his method of solving quadratic equations. Concludes by showing how the Hindu-Arabic numeral system developed and was adopted first in the Arabic countries, then later in Europe.<\/p>\n<h4 style=\"text-align: left;\">Marin Mersenne: The Birth of Modern Geometry<\/h4>\n<p style=\"text-align: left;\"><a href=\"http:\/\/en.wikipedia.org\/wiki\/Marin_Mersenne\" target=\"_blank\" rel=\"noopener noreferrer\">Marin Mersenne<\/a> was a 17th-century French monk who was also an able scientist who wrote widely on the study of sound. His contribution to mathematics comes from his ambition to see the formation of scientific societies. Amongst the great discoveries of the time, which Mersenne had a part in publicising, are <a href=\"http:\/\/en.wikipedia.org\/wiki\/Gilles_de_Roberval\" target=\"_blank\" rel=\"noopener noreferrer\">Roberval<\/a>\u2019s method for the calculation of the area under a cycloid, <a href=\"http:\/\/en.wikipedia.org\/wiki\/Ren%C3%A9_Descartes\" target=\"_blank\" rel=\"noopener noreferrer\">Descartes<\/a>\u2019 method of co-ordinate geometry, <a href=\"http:\/\/en.wikipedia.org\/wiki\/Girard_Desargues\" target=\"_blank\" rel=\"noopener noreferrer\">Desargues<\/a>\u2019 projective geometry, and <a href=\"http:\/\/en.wikipedia.org\/wiki\/Blaise_Pascal\" target=\"_blank\" rel=\"noopener noreferrer\">Pascal<\/a>\u2019s theorem on the hexagon. The concepts of Mersenne led to the foundation of the French Academy of Science shortly after his death. Re-creates the character of Mersenne, interspersed with animation and studio demonstrations constructed to match readings from the works of some of the mathematicians of the time. Uses contemporary etchings, books and music to reconstruct the mood of the period.<\/p>\n<h4 style=\"text-align: left;\">The Founding of the Royal Society<\/h4>\n<p style=\"text-align: left;\">Describes the various scientific groups that began to form in 17th-century England: at Gresham College, London, in 1645 and in Oxford in 1657, culminating with the founding of the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Royal_Society\" target=\"_blank\" rel=\"noopener noreferrer\">Royal Society <\/a>in 1660. Looks at the problems addressed by the society, particularly the calculation of longitude at sea, which lead to the foundation of the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Royal_Observatory,_Greenwich\" target=\"_blank\" rel=\"noopener noreferrer\">Royal Greenwich Observatory<\/a>. Discusses <a href=\"http:\/\/en.wikipedia.org\/wiki\/Isaac_Newton\" target=\"_blank\" rel=\"noopener noreferrer\">Newton<\/a>\u2019s \u2018<a href=\"http:\/\/en.wikipedia.org\/wiki\/Principia_Mathematica\" target=\"_blank\" rel=\"noopener noreferrer\">Principia Mathematica<\/a>\u2019 of 1687.<\/p>\n<h4 style=\"text-align: left;\">The Birth of Calculus<\/h4>\n<p style=\"text-align: left;\">With the discovery of calculus, mathematics received its greatest boost since the time of the Greeks. Discusses the early work of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Isaac_Newton\" target=\"_blank\" rel=\"noopener noreferrer\">Newton<\/a> and <a href=\"http:\/\/en.wikipedia.org\/wiki\/Gottfried_Wilhelm_Leibniz\" target=\"_blank\" rel=\"noopener noreferrer\">Leibniz<\/a> that led to their independent formulations of the methods of calculus. Filmed in Cambridge, tracing Newton\u2019s lines of thought through his notebooks, and in Hanover, where Leibniz\u2019s original notes are stored, noting his very different approach to the same problem.<\/p>\n<h4 style=\"text-align: left;\">Non-Euclidean Geometry<\/h4>\n<p style=\"text-align: left;\">During the 18th and 19th centuries mathematicians were increasingly questioning the foundations of geometry. Shows how investigations led to the development of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Non-Euclidean_geometry\" target=\"_blank\" rel=\"noopener noreferrer\">non-Euclidean geometry<\/a>, discussing the work of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Giovanni_Girolamo_Saccheri\" target=\"_blank\" rel=\"noopener noreferrer\">Saccheri<\/a>, <a href=\"http:\/\/en.wikipedia.org\/wiki\/Johann_Heinrich_Lambert\" target=\"_blank\" rel=\"noopener noreferrer\">Lambert<\/a>, <a href=\"http:\/\/en.wikipedia.org\/wiki\/J%C3%A1nos_Bolyai\" target=\"_blank\" rel=\"noopener noreferrer\">Bolyai<\/a>, <a href=\"http:\/\/en.wikipedia.org\/wiki\/Nikolai_Lobachevsky\" target=\"_blank\" rel=\"noopener noreferrer\">Lobachevskii<\/a> and <a href=\"http:\/\/en.wikipedia.org\/wiki\/Eugenio_Beltrami\" target=\"_blank\" rel=\"noopener noreferrer\">Beltrami<\/a>.<\/p>\n<h4 style=\"text-align: left;\">Paris and the New Mathematics<\/h4>\n<p style=\"text-align: left;\">During the <a href=\"http:\/\/en.wikipedia.org\/wiki\/French_Revolution\" target=\"_blank\" rel=\"noopener noreferrer\">French Revolution<\/a> the new republic saw mathematics as a tool to be used in its service. Describes some of the revolutionary mathematics and the developments that were to arise from it. Centres around the the life of one of France\u2019s greatest revolutionary mathematicians, <a href=\"http:\/\/en.wikipedia.org\/wiki\/Gaspard_Monge\" target=\"_blank\" rel=\"noopener noreferrer\">Gaspard Monge<\/a>, who was to found the <a href=\"http:\/\/en.wikipedia.org\/wiki\/%C3%89cole_Polytechnique\" target=\"_blank\" rel=\"noopener noreferrer\">\u00c9cole Polytechnique<\/a>, originally to train military engineers. It was there that post-revolutionary mathematicians trained and did their research. Looks at the library of the present-day \u00c9cole Polytechnique and the early 19th-century books and papers which chronicle this period of French educational reform.<\/p>\n<h4 style=\"text-align: left;\">The Liberation of \u00c1lgebra<\/h4>\n<p style=\"text-align: left;\">Looks at the work of <a href=\"http:\/\/en.wikipedia.org\/wiki\/William_Rowan_Hamilton\" target=\"_blank\" rel=\"noopener noreferrer\">William Rowan Hamilton<\/a> in Dublin and <a href=\"http:\/\/en.wikipedia.org\/wiki\/George_Boole\" target=\"_blank\" rel=\"noopener noreferrer\">George Boole<\/a> in Cork. Uses Hamilton\u2019s discovery of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Quaternion\" target=\"_blank\" rel=\"noopener noreferrer\">quaternions<\/a> to Boole\u2019s \u2019<a href=\"http:\/\/en.wikipedia.org\/wiki\/The_Laws_of_Thought\" target=\"_blank\" rel=\"noopener noreferrer\">The Laws of Thought<\/a>\u2019, as the foundations for work in the fields of astrophysics and computer design.<\/p>\n<ul style=\"list-style-type: square;\">\n<li style=\"text-align: left;\">Fonte: <a href=\"http:\/\/bufvc.ac.uk\/allbufvc\/search.php?q=%22Topics+in+the+History+of+Mathematics%2C+Course+Ma290%22&amp;sort=relevance\" target=\"_blank\" rel=\"noopener noreferrer\">British Universities Film &amp; Video Council<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The Emergence of Greek Mathematics The Vernacular Tradition Marin Mersenne: The Birth of Modern Geometry The Founding of the Royal Society The Birth of Calculus Non-Euclidean Geometry Paris and the New Mathematics The Liberation&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21173,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3,7],"tags":[399,207,394,400,398,9,170,396,401,395,397,169,402,200],"series":[],"class_list":["post-12305","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematica","category-video","tag-bolyai","tag-descartes","tag-euclides","tag-george-boole","tag-hamilton","tag-historia-da-matematica","tag-leibniz","tag-leonardo-de-pisa","tag-lobachevskii","tag-luca-pacioli","tag-mersenne","tag-newton","tag-pascal","tag-video-2"],"views":2398,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2015\/03\/Topics_in_the_History_of_Mathematics_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12305","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12305"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12305\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21173"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12305"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12305"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12305"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}