{"id":1779,"date":"2024-03-07T11:19:25","date_gmt":"2024-03-07T16:19:25","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2024\/?p=1779"},"modified":"2024-03-15T23:26:55","modified_gmt":"2024-03-16T03:26:55","slug":"lecture-12-smooth-surfaces","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2024\/2024\/03\/07\/lecture-12-smooth-surfaces\/","title":{"rendered":"Lecture 12\u2014Smooth Surfaces"},"content":{"rendered":"<p>This lecture gives a crash course in the differential geometry of surfaces. There&#8217;s of course way more to know about surfaces than we can pack into a single lecture (and we&#8217;ll see plenty more later on), but this lecture will cover basic concepts like how to describe a surface and its normals. It also starts to connect surface theory to the other tools we&#8217;ve been building up, via <em>vector-valued<\/em> differential forms.<\/p>\n<p><a href=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/03\/DDG_458_SP19_Lecture12_SmoothSurfaces.pdf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/03\/DDG_458_SP19_Lecture12_SmoothSurfaces.jpg\" alt=\"\" width=\"419\" height=\"243\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This lecture gives a crash course in the differential geometry of surfaces. There&#8217;s of course way more to know about surfaces than we can pack into a single lecture (and we&#8217;ll see plenty more later on), but this lecture will cover basic concepts like how to describe a surface and its normals. It also starts &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2024\/2024\/03\/07\/lecture-12-smooth-surfaces\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 12\u2014Smooth Surfaces&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1779"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/comments?post=1779"}],"version-history":[{"count":1,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1779\/revisions"}],"predecessor-version":[{"id":1782,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1779\/revisions\/1782"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/media?parent=1779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/categories?post=1779"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/tags?post=1779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}