Mathematical Experiment 7

  1. Make a ``movie'' of the horizontal and the vertical grids {(x,y,-1):x, y Î Z} along the curve (t,t2,0), t Î [-2,2] when viewing along the tangent.
  2. Make a ``movie'' of the complete binary tree when zoomed in and zoomed out continuously and indefinitely.
  3. There are three basic rotations of a cube each having a period of two, three and four. Write a program that a player can perform each of the three operations of rotation, at the same time the appearance of the cube as well as the corresponding permutation of the faces should also be displayed.
  4. Draw various sectons of a right cone.
  5. Make a ``movie'' of the solution of the string equation
  6. y(x,t) = sin x cos t+ 1
    sin 3x cos 3t
with x Î [0,2p].