tag:blogger.com,1999:blog-30611202.post1697725957634586469..comments2017-09-25T08:05:19.219-07:00Comments on Thalesâ€™ triangles: Snell and EscherJoshua Bowmanhttps://plus.google.com/103262883740888913105noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-30611202.post-21541642850479889352016-05-22T16:24:42.092-07:002016-05-22T16:24:42.092-07:00Ramsay: Neat! I hadn't made the connection bet...Ramsay: Neat! I hadn't made the connection between Snell's Law and Clairaut's relation before, but you're absolutely right.Joshua Bowmanhttps://www.blogger.com/profile/05825513382152813711noreply@blogger.comtag:blogger.com,1999:blog-30611202.post-55506761185609248962016-05-22T10:28:01.408-07:002016-05-22T10:28:01.408-07:00This is nice. In elementary differential geometry,...This is nice. In elementary differential geometry, this Snell's law is usually introduced as Clairaut's relation. It applies to surfaces of revolution, for example, but more generally it applies whenever there exists local parameterizations that render the metric diagonal with entries depending on only one of the two parameters (i.e., both entries independent of the same parameter). See, for example O'Neill (Elem. Diff. Geom), Sec 7.5, or Do Carmo (Diff. Geom. of Curves and Surfaces), Sec 4.4, p. 257. Neither of these popular books mention Snell's law; it is nice to see that here.Ramsayhttps://www.blogger.com/profile/13772059334641143246noreply@blogger.com