Miklos Schweitzer 1951_15
Source:
October 8, 2008
rotationgeometrygeometric transformationadvanced fieldsadvanced fields unsolved
Problem Statement
Let the line
z\equal{}x, \, y\equal{}0
rotate at a constant speed about the -axis; let at the same time the point of intersection of this line with the -axis be displaced along the -axis at constant speed.
(a) Determine that surface of rotation upon which the resulting helical surface can be developed (i.e. isometrically mapped).
(b) Find those lines of the surface of rotation into which the axis and the generators of the helical surface will be mapped by this development.