Envelope (mathematics)
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, an envelope of a family of manifolds (especially a family of curves) is a manifold that is tangent to each member of the family at some point.A one-parameter family Ct of smooth curves in the plane, parameterised by t in an open interval I, can be described as the zero loci of a family of smooth functions F : I × R2 R. Holding t fixed, F determines a function in x and y alone via ft(x,y) := F(t,(x,y)). The curve Ct is then identified with the zero loc...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, an envelope of a family of manifolds (especially a family of curves) is a manifold that is tangent to each member of the family at some point.A one-parameter family Ct of smooth curves in the plane, parameterised by t in an open interval I, can be described as the zero loci of a family of smooth functions F : I × R2 R. Holding t fixed, F determines a function in x and y alone via ft(x,y) := F(t,(x,y)). The curve Ct is then identified with the zero locus of ft. Assume that, for all t, 0 R is a regular value or ft.
