{"id":2535,"date":"2022-03-17T01:00:49","date_gmt":"2022-03-17T05:00:49","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2022\/?p=2535"},"modified":"2022-01-17T17:46:46","modified_gmt":"2022-01-17T22:46:46","slug":"lecture-15-curvature-of-surfaces","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2022\/2022\/03\/17\/lecture-15-curvature-of-surfaces\/","title":{"rendered":"Lecture 15: Curvature of Surfaces"},"content":{"rendered":"<p><a href=\"https:\/\/youtu.be\/e-erMrqBd1w\"><img loading=\"lazy\" src=\"https:\/\/brickisland.net\/DDGSpring2021\/wp-content\/uploads\/2020\/03\/DDG_458_SP20_Lecture15_SmoothCurvature.jpg\" alt=\"\" width=\"512\" height=\"288\"\/><\/a><\/p>\n<p>Much of the geometry we encounter in everyday life (such as curves and surfaces sitting in space) is well-described by it curvatures. For instance, the fundamental theorem for plane curves says that an arc-length parameterized plane curve is determined by its curvature function, up to rigid motions. Similar statements can be made about surfaces and their curvatures, which we explore in this lecture.<\/p>\n<ul>\n<li><a href=\"https:\/\/youtu.be\/e-erMrqBd1w\">Video<\/a><\/li>\n<li><a href=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2020\/03\/DDG_458_SP20_Lecture15_SmoothCurvature.pdf\">Slides<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Much of the geometry we encounter in everyday life (such as curves and surfaces sitting in space) is well-described by it curvatures. For instance, the fundamental theorem for plane curves says that an arc-length parameterized plane curve is determined by its curvature function, up to rigid motions. Similar statements can be made about surfaces and &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/2022\/03\/17\/lecture-15-curvature-of-surfaces\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 15: Curvature of 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":{"_links_to":"","_links_to_target":""},"categories":[7,3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/2535"}],"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=2535"}],"version-history":[{"count":4,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/2535\/revisions"}],"predecessor-version":[{"id":3450,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/2535\/revisions\/3450"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/media?parent=2535"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/categories?post=2535"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/tags?post=2535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}