The envelope of a family of plane curves is a curve which touches in each of its points one of the curves of the family.
For example, the envelope of the family , with the parameter, may be justified geometrically. It is the open (http://planetmath.org/OpenSet) lower semicircle of the unit circle. Indeed, the distance of any line
of the family from the center of the unit circle is
whence the line is the tangent to the circle.
Below, the red curve is the lower semicircle of the unit circle, the black lines belong to the family , and the equation of each line is given.
|Date of creation||2013-03-22 17:10:19|
|Last modified on||2013-03-22 17:10:19|
|Last modified by||pahio (2872)|