Quadric Surfaces¶
Some Examples¶
23 Aug 2018
Below you will find plots of some of the quadric surfaces that we studied in class. I used SageMath (http://sagemath.org) in a web-based Jupyter notebook (http://jupyter.org) to make these.
Hyperbolic Paraboloids¶
Also known as "saddle surfaces," equations are of the form $\left(\frac{x}{h}\right)^2 - \left(\frac{y}{k}\right)^2 = z$.
In [1]:
var('x y');
plot3d(x**2 - y**2,(x,-2,2),(y,-2,2),viewer='tachyon')
Out[1]:
Elliptic Paraboloids¶
Equations are of the form $\left(\frac{x}{h}\right)^2 + \left(\frac{y}{k}\right)^2 = z$.
In [2]:
plot3d(x**2 + y**2,(x,-2,2),(y,-2,2),viewer='tachyon')
Out[2]:
In [3]:
plot3d((x)**2 + (y/3)**2,(x,-2,2),(y,-2,2),viewer='tachyon')
Out[3]:
Ellipsoids¶
Equations are of the form $\left(\frac{x}{h}\right)^2 + \left(\frac{y}{k}\right)^2 + \left(\frac{z}{\ell}\right)^2 = 1$
In [4]:
show(plot3d(sqrt(1 - (x/2)**2 - (y/3)**2),(x,-2,2),(y,-3,3),viewer='tachyon') +
plot3d(-sqrt(1 - (x/2)**2 - (y/3)**2),(x,-2,2),(y,-3,3),viewer='tachyon',aspect_ratio=1))
