Talk:Envelope (mathematics)
From Wikipedia, the free encyclopedia
Interesting, but I can find only one mention of it because "cyclic" (even cyclid/cyclide) is such a common word. take a circle and a curve that does not come into the circle. Take the circles that are centered on the curve and orthogonal to the given circle. The envelope of those circles is the cyclic. 142.177.169.115 19:27, 13 Aug 2004 (UTC)
[edit] Problem with Example 2 or definition
It seems to me there is a problem with example 2, the point (u, v) is a solution to the simultaneous equations F = Ft = 0 whether the curvature is 0 or not. The only thing that curvature = 0 implies is that the system of equations has a unique solution for the given t. When the curvature is 0, the equations are dependent and there is a line of solutions corresponding to the tangent line. So the solution to the simultaneous equations is really the union of the curve with all tangent lines at points of inflection. Is there another condition needed to eliminate these extra lines as solutions? Also, if the family is defined by F(x,y,t) = x − t2 then the solution to F = Ft = 0 is x = 0, but this does not satisfy the definition given. In this case the family of curves consists of parallel lines and has no envelope. --RDBury (talk) 06:13, 2 April 2008 (UTC)
