tag:blogger.com,1999:blog-2433841880619171855.post987124546354097450..comments2024-03-27T21:09:44.320+00:00Comments on Pat'sBlog: Just an Average PointUnknownnoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2433841880619171855.post-77872809144203355372009-04-13T05:52:00.000+01:002009-04-13T05:52:00.000+01:00The centroid divides the medians in the ratio of 2...The centroid divides the medians in the ratio of 2:1. My book has it, with coordinates, as an advanced exercise. (They suggest using the origin, (6a,0) and (6b,6c))<BR/><BR/>The nice piece about this... the kids are reminded through the work that:<BR/>x avg (y avg z) is not (x avg y) avg z...<BR/><BR/>It is, on the other hand, a fairly old fashioned book. (Jurgensen Brown Jurgensen)<BR/><BR/>JonathanAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-57597805351376345982009-03-20T19:19:00.000+00:002009-03-20T19:19:00.000+00:00Joshua, I think the Barycentric approach is a wond...Joshua,<BR/> I think the Barycentric approach is a wonderful way to show stuff like this, but would much prefer to see your comments on some introductory approaches. If you write a couple of short "guest blogs" about it I would love to post them here...or for that matter, almost anything else you would like to share.<BR/>PatPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-80589736210325697412009-03-20T05:43:00.000+00:002009-03-20T05:43:00.000+00:00I like the n:1 fact.My proof of it is that the cen...I like the n:1 fact.<BR/><BR/>My proof of it is that the centroid of all the points is the weighted average of the 1 point (vertex) and the n points (centroid of the opposite edge/face). So naturally the segment is split in an n:1 ratio.Joshua Zuckerhttps://www.blogger.com/profile/04689961247338617418noreply@blogger.com