{"id":1788,"date":"2024-03-07T11:26:32","date_gmt":"2024-03-07T16:26:32","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2024\/?p=1788"},"modified":"2024-04-04T14:42:04","modified_gmt":"2024-04-04T18:42:04","slug":"lecture-14-smooth-curvature","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2024\/2024\/03\/07\/lecture-14-smooth-curvature\/","title":{"rendered":"Lecture 14\u2014Smooth Curvature"},"content":{"rendered":"<p>Much of the geometry we encounter in everyday life (such as curves and surfaces sitting in space) is well-described by it <em>curvatures<\/em>. 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<p><a href=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/03\/DDG_458_SP19_Lecture14_SmoothCurvature.pdf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/03\/DDG_458_SP19_Lecture14_SmoothCurvature.jpg\" alt=\"\" width=\"419\" height=\"243\" \/><\/a><a href=\"https:\/\/brickisland.net\/DDGSpring2021\/wp-content\/uploads\/2020\/03\/DDG_458_SP20_Lecture15_SmoothCurvature.pdf\">Here<\/a> are the slides from 2021.<\/p>\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\/DDGSpring2024\/2024\/03\/07\/lecture-14-smooth-curvature\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 14\u2014Smooth Curvature&#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\/1788"}],"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=1788"}],"version-history":[{"count":2,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1788\/revisions"}],"predecessor-version":[{"id":2389,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1788\/revisions\/2389"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/media?parent=1788"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/categories?post=1788"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/tags?post=1788"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}