133.sagews

# Graph for 15.1 #2
# -----------------

# our function and its plot
# (now with more correct function!)

f(x,y) = y^2 - 2*x^2
theplot = plot3d(f,(x,-1,3),(y,0,2),aspect_ratio=[1,1.5,1/5])

# The volumes of the 6 boxes defined here are the summands of the
# Riemann sum approximating the volume under f(x,y) on [-1,3]x[0,2].

from sage.plot.plot3d.shapes import Box
for m in range(4):
    for n in range(2):
        fval = f(m-1,n+1)/2
        theplot += Box([0.5,0.5,abs(fval)],color='orange',opacity=0.5).translate((-0.5+m,0.5+n,fval))

theplot.show(figsize=6)