Quadric Surfaces¶
Examples from Class¶
Below you will find the quadric surfaces that we tried to sketch in class. I made these using SageMath (http://sagemath.org) in a web-based Jupyter notebook (http://jupyter.org).
Ellipsoid¶
The ellipsoid that we plotted in class had the formula $$\left(\frac{x}{3}\right)^2 + \left(\frac{y}{2}\right)^2 + z^2 = 1.$$ The jagged edges near the equator of the graph are a numerical artifact. The surface should close smoothly.
In [1]:
var('x,y,z');
In [2]:
fu = sqrt(1 - (x/3)**2 - (y/2)**2);
fl = -fu;
In [3]:
show(plot3d(fu,(x,-3,3),(y,-2,2),aspect_ratio=1,viewer='tachyon') +
plot3d(fl,(x,-3,3),(y,-2,2),aspect_ratio=1,viewer='tachyon'))
Hyperbolic Paraboloid¶
The hyperbolic paraboloid from class had equation $$ z = x^2 - 2y^2.$$
In [4]:
saddle = x**2 - 2*y**2;
In [5]:
plot3d(saddle,(x,-2,2),(y,-1,1),aspect_ratio=1,viewer='tachyon')
Out[5]:
Elliptic Paraboloid¶
The elliptic paraboloid from class had equation $$z = x^2 + 2y^2.$$
In [6]:
ep = x**2 + 2*y**2;
In [7]:
plot3d(ep,(x,-2,2),(y,-1,1),aspect_ratio=1,viewer='tachyon')
Out[7]:
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