Mathematical Experiment 10

No classes May 15, 2002

 Construct a knot like this:
 Construct a knot like this:
 Construct a chain of five rings each encloses the other four.
 Construct a chain of five rings of the same size each encloses exactly two others.
 Construct the image of the Cartesian grid lines under the stereographic projection > with(plots):with(plottools): > a:=coordplot(cartesian,[-10..10,-10..10],scaling=constrained): > f:=transform((x,y) -> [2*x/(x^2+y^2+1),2*y/(x^2+y^2+1),(x^2+y^2-1)/(x^2+y^2+1)]): > b:=display(f(a),scaling=constrained): > c:=sphere([0,0,0],0.99,style=patchnogrid,color=yellow): > h:=display(b,c): ¡@
 Construct the cyclide by inverting a torus.
 Construct any four mutually tangent spheres of different sizes. ¡@ ¡@
 Apply the command "tubeplot" to construct the seashell.
 Construct the astroidal ellipsoid given byx = (cos u cos v)3 y = (sin u cos v)3 z = sin3v Reference: A. Gray, Modern Differential Geometry of Curves and Surfaces, p. 304.
 Construct the cupola as thus: