genius-common 1.0.21-1 / usr / share / genius / examples / peano.gel

# Category: Calculus
# Name: Peano surface (using polar coordinates)
#
# The Peano surface drawn using polar coordinates.
#
# z = (y-x^2)(2x^2-y)
#
# The function giving the surface has a maximum on every line through the origin,
# but the origin is not an extremum of the function.  Note that second derivative
# test fails on the line y=0, even though along that line the function still has
# a maximum.  While the function has a maximum along every line, it has a minimum
# along a curve y=ax^2 for any 1 < a < 2.
#
# The properties of the function can be easily seen from the factorization and seeing
# the regions where each factor is positive or negative.

data = null;
for r=0 to 0.25 by 0.02 do (
  for theta=0 to 2*pi by pi/15 do (
    x = r*cos(theta);
    y = r*sin(theta);
    data = [data;[x,y,3*x^2*y-y^2-2*x^4]]
  )
);

SurfacePlotDrawLegends = false; # don't draw the legend
PlotWindowPresent(); # Make sure the window is raised

# Plot the data
SurfacePlotData(data);