tag:blogger.com,1999:blog-2400513859305780710.post1704382963099110299..comments2023-01-28T07:31:02.673-08:00Comments on Mathematical Food For Thought: Barycentric Coordinates. Topic: Analytic Geometry. Level: Olympiad.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2400513859305780710.post-8791771393622694612006-03-19T12:53:07.000-08:002006-03-19T12:53:07.000-08:00It's strange trying to find an intuitive justi...It's strange trying to find an intuitive justification for barycentric coordinates, though... quite odd. How does the technique extend to area ratios? (Cross product?)QCnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-25870711162326959162006-03-19T13:53:52.000-08:002006-03-19T13:53:52.000-08:00I think if you make an affine transformation from ...I think if you make an affine transformation from ABC to R^3 that preserves the coordinates of A,B, and C it's just three arbitrary points in the plane x+y+z = 1, so you can use the same method as with space coordinates.<br><br>Not completely certain about this method yet, but it seems like it works.<br><br>Another Idea: (from MathWorld) If you write the equation of a line with two of the points, you can see that the third point has to make the determinant zero in order to be on the line as well.paladin8noreply@blogger.com