{"id":1779,"date":"2022-03-01T01:00:25","date_gmt":"2022-03-01T06:00:25","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2022\/?p=1779"},"modified":"2022-01-17T17:45:22","modified_gmt":"2022-01-17T22:45:22","slug":"lecture-12-smooth-surfaces","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2022\/2022\/03\/01\/lecture-12-smooth-surfaces\/","title":{"rendered":"Lecture 12: Smooth Surfaces I"},"content":{"rendered":"<p><img loading=\"lazy\" src=\"http:\/\/brickisland.net\/DDGSpring2021\/wp-content\/uploads\/2020\/03\/DDG_12_SmoothSurfaces_I.png\" alt=\"\" width=\"480\" height=\"270\" \/><\/p>\n<p>This lecture takes a first look at smooth 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 two very important perspectives: the <em>extrinsic<\/em> description of a surface via a local parameterization, which tells us where points sit in space, and the <em>intrinsic<\/em> description of a surface via coordinate charts, which lets us work with a surface without worrying how it&#8217;s embedded in space.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=sV58Fy2s6ac\">Video<\/a><\/li>\n<li><a href=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2020\/03\/DDG_12_SmoothSurfacesI.pdf\">Slides<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>This lecture takes a first look at smooth 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 two very important perspectives: the extrinsic description of a surface via a local parameterization, which tells us &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/2022\/03\/01\/lecture-12-smooth-surfaces\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 12: Smooth Surfaces I&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[7,3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1779"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/comments?post=1779"}],"version-history":[{"count":5,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1779\/revisions"}],"predecessor-version":[{"id":3446,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1779\/revisions\/3446"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/media?parent=1779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/categories?post=1779"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/tags?post=1779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}